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159 Pages

circles

Course: MA 114, Fall 2008
School: Kentucky
Rating:
 
 
 
 
 

Word Count: 11382

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%%Title: %!PS-Adobe-2.0 circles.mws - [Server 1] %%Creator: Maple V Release 4 HP RISC UNIX %%DocumentFonts: Helvetica Times-Bold Times-BoldItalic Symbol Courier %%Pages: 6 %%EndComments % /sc { setrgbcolor } def % color % /stc { setrgbcolor } def % color /sc { 11 mul exch 59 mul add exch 30 mul add 100 div setgray } def % b&w /stc { pop pop pop 0 setgray } def % b&w /fsf %% stk: size font {...

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Coursehero >> Kentucky >> Kentucky >> MA 114

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%%Title: %!PS-Adobe-2.0 circles.mws - [Server 1] %%Creator: Maple V Release 4 HP RISC UNIX %%DocumentFonts: Helvetica Times-Bold Times-BoldItalic Symbol Courier %%Pages: 6 %%EndComments % /sc { setrgbcolor } def % color % /stc { setrgbcolor } def % color /sc { 11 mul exch 59 mul add exch 30 mul add 100 div setgray } def % b&w /stc { pop pop pop 0 setgray } def % b&w /fsf %% stk: size font { findfont exch scalefont setfont } def /line %% stk: width x1 y1 x2 y2 { gsave newpath 4 2 roll moveto lineto setlinewidth stroke grestore } def /underline %% stk: string ulOffset ulThickness { gsave setlinewidth 0 exch rmoveto %% stk: string dup stringwidth pop 0 rlineto stroke %% stk: string grestore show } def /pagenum %% stk: x y string { gsave 10 /Times-Roman fsf 3 1 roll moveto dup stringwidth pop %% stk: string wx 2 div neg -14 rmoveto %% stk: string show grestore } def /solid { [] 0 setdash } def /dot { [1 3] 0 setdash } def /dash { [5 5] 0 setdash } def /dashdot { [5 3 1 3] 0 setdash } def % ReEncodeSmall is copied from the Postscript Tutorial and Cookbook % Adobe Systems Inc., Addison-Wesley, page 211-212 /reencsmalldict 12 dict def /ReEncodeSmall { reencsmalldict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } {pop pop} ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /ExtraChars [ ] def /Helvetica /Helvetica-Maple ExtraChars ReEncodeSmall /Times-Bold /Times-Bold-Maple ExtraChars ReEncodeSmall /Times-BoldItalic /Times-BoldItalic-Maple ExtraChars ReEncodeSmall /Courier /Courier-Maple ExtraChars ReEncodeSmall %%EndProlog %%Page: 1 6 gsave newpath 54 720 moveto 504 0 rlineto 0 -648 rlineto -504 0 rlineto closepath clip newpath gsave 0 setgray 0.1 setlinewidth solid 12 /Helvetica-Maple fsf gsave 0 setgray 64 708.7 moveto (Sample project.) show grestore newpath 59 718 moveto 56 718 lineto 56 707.8 lineto 59 707.8 lineto stroke gsave 0 setgray 64 693.5 moveto ( \12) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 64 678.3 moveto (Problem:\12) -1.1 0.8 underline grestore 12 /Helvetica-Maple fsf gsave 0 setgray 64 662.3 moveto (Given a right triangle with vertices \(0,0\), \(0,a\) and \(b,0\). circle ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 451.4 662.3 moveto (C) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 459.4 658.7 moveto (1) show grestore Inscribe a 12 /Helvetica-Maple fsf gsave 0 setgray 463.4 662.3 moveto (, then heading off ) show grestore gsave 0 setgray 64 645.1 moveto (towards one of the acute angles \(say the vertex \(b,0\)\), inscribe an infinite chain of circles ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 64 629.1 moveto (C) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 72 625.5 moveto (n) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 76.4 629.1 moveto ( each tangent to the preceeding circle and the sides of the angle. Find the total area of ) show grestore gsave 0 setgray 64 611.9 moveto (the circles.\12) show grestore gsave 0 setgray 64 596.7 moveto (\12) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 64 580.7 moveto (Solution) -1.1 0.8 underline grestore 12 /Helvetica-Maple fsf gsave 0 setgray 107.3 580.7 moveto (: Let ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 137.3 580.7 moveto (r) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 141.9 577.1 moveto (n) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 146.3 580.7 moveto ( be the radius of the nth circle. First we get the radius ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 431.7 580.7 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 436.3 577.1 moveto (1) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 440.3 580.7 moveto ( of the 1st circle. ) show grestore gsave 0 setgray 64 562.7 moveto (Then the center is at ) show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 183.4 562.7 moveto ([) show grestore gsave 0 setgray 213.5 562.7 moveto (]) show grestore gsave 0 setgray 197.4 562.7 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 188.8 562.7 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 193.4 559.1 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 203.4 562.7 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 208 559.1 moveto (1) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 217.4 562.7 moveto (. Let \() show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 254 562.7 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 248 562.7 moveto (x) show grestore gsave 0 setgray 260 562.7 moveto (y) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 265.3 562.7 moveto (\) be the point on the hypotenuse where the circles is ) show grestore gsave 0 setgray 64 535 moveto (tangent. Then the slope of the segment from ) show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 316.8 535 moveto ([) show grestore gsave 0 setgray 346.9 535 moveto (]) show grestore gsave 0 setgray 330.8 535 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 322.2 535 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 326.8 531.4 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 336.8 535 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 341.4 531.4 moveto (1) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 350.8 535 moveto ( to \() show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 377.4 535 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 371.4 535 moveto (x) show grestore gsave 0 setgray 383.4 535 moveto (y) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 388.7 535 moveto (\) is ) show grestore gsave 0 setgray 0.7 setlinewidth solid 0.7 408 539.9 417 539.9 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 409.5 544.7 moveto (b) show grestore gsave 0 setgray 409.5 525.9 moveto (a) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 417 535 moveto (, and the slope of the ) show grestore gsave 0 setgray 64 500.6 moveto (segment from \() show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 150.6 500.6 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 144.6 500.6 moveto (b) show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 156.6 500.6 moveto (0) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 162.6 500.6 moveto (\) to \() show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 193.2 500.6 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 187.2 500.6 moveto (x) show grestore gsave 0 setgray 199.2 500.6 moveto (y) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 204.5 500.6 moveto (\) is ) show grestore 12 /Symbol fsf gsave 0 setgray 223.8 500.6 moveto (-) show grestore gsave 0 setgray 0.7 setlinewidth solid 0.7 233.3 505.5 242.3 505.5 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 234.8 510.3 moveto (a) show grestore gsave 0 setgray 234.8 491.5 moveto (b) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 242.3 500.6 moveto (. We can use this get x and y in terms of a,b, and r. grestore 12 /Courier-Maple fsf gsave 0 setgray 64 463.3 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 463.3 moveto ( restart;eq1 := \(y-r[1]\)/\(x-r[1]\)=b/a;) show grestore 12 /Times-Bold-Maple fsf \12) show gsave 0 0 1 stc 285.4 432.8 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 268.1 432.8 moveto (eq1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 335.3 432.8 moveto (=) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 302.2 437.7 332.3 437.7 line grestore gsave 0 0 1 stc 312.3 444.9 moveto (-) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 304 444.9 moveto (y) show grestore gsave 0 0 1 stc 321.8 444.9 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 326.4 441.3 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 312.7 423.7 moveto (-) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 303.7 423.7 moveto (x) show grestore gsave 0 0 1 stc 322.2 423.7 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 326.8 420.1 moveto (1) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 344.8 437.7 353.8 437.7 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 346.3 442.5 moveto (b) show grestore gsave 0 0 1 stc 346.3 423.7 moveto (a) show grestore newpath 59 702.8 moveto 56 702.8 lineto 56 419.1 lineto 59 419.1 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 406.6 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 406.6 moveto (eq2 := \(y-0\)/\(x-b\) = -a/b;) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 282 378.5 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 264.7 378.5 moveto (eq2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 329.3 378.5 moveto (=) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 298.8 383.4 326.3 383.4 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 309.9 388.2 moveto (y) show grestore 12 /Symbol fsf gsave 0 0 1 stc 309.3 369.4 moveto (-) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 300.3 369.4 moveto (x) show grestore gsave 0 0 1 stc 318.8 369.4 moveto (b) show grestore 12 /Symbol fsf gsave 0 0 1 stc 338.8 378.5 moveto (-) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 348.3 383.4 357.3 383.4 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 349.8 388.2 moveto (a) show grestore gsave 0 0 1 stc 349.8 369.4 moveto (b) show grestore newpath 59 414.1 moveto 56 414.1 lineto 56 367.2 lineto 59 367.2 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 354.7 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 354.7 moveto (sol :=solve\({eq1,eq2},{x,y}\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 185.9 322.8 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 171.9 322.8 moveto (sol) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 202.7 322.8 moveto ({) show grestore gsave 0 0 1 stc 445.4 322.8 moveto (}) show grestore gsave 0 0 1 stc 319.8 322.8 moveto (,) show grestore 12 /Symbol fsf gsave 0 0 1 stc 217.2 322.8 moveto (=) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 208.9 322.8 moveto (y) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 226.7 327.7 319.8 327.7 line grestore gsave 0 0 1 stc 228.2 334.9 moveto (a) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 237.2 334.9 moveto (\() show grestore gsave 0 0 1 stc 314.4 334.9 moveto (\)) show grestore 12 /Symbol fsf gsave 0 0 1 stc 263.2 334.9 moveto (+) show grestore gsave 0 0 1 stc 285.8 334.9 moveto (-) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 242.6 334.9 moveto (a) show grestore gsave 0 0 1 stc 251.6 334.9 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 256.2 331.3 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 272.7 334.9 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 278.8 340.4 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 295.3 334.9 moveto (b) show grestore gsave 0 0 1 stc 304.3 334.9 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 308.9 331.3 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 270 312.3 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 256.9 312.3 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 263 317.8 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 279.5 312.3 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 285.6 317.8 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 334.8 322.8 moveto (=) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 325.8 322.8 moveto (x) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 344.3 327.7 443.9 327.7 line grestore gsave 0 0 1 stc 345.8 334.9 moveto (b) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 354.8 334.9 moveto (\() show grestore gsave 0 0 1 stc 438.5 334.9 moveto (\)) show grestore 12 /Symbol fsf gsave 0 0 1 stc 360.2 334.9 moveto (-) show grestore gsave 0 0 1 stc 387.3 334.9 moveto (+) show grestore gsave 0 0 1 stc 417.4 334.9 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 366.7 334.9 moveto (a) show grestore gsave 0 0 1 stc 375.7 334.9 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 380.3 331.3 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 396.8 334.9 moveto (b) show grestore gsave 0 0 1 stc 405.8 334.9 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 410.4 331.3 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 426.9 334.9 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 433 340.4 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 390.8 312.3 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 377.7 312.3 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 383.8 317.8 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 400.3 312.3 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 406.4 317.8 moveto (2) show grestore newpath 59 362.2 moveto 56 362.2 lineto 56 310.1 lineto 59 310.1 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 295 moveto ( Now the length of the segment from \() show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 270.7 295 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 264.7 295 moveto (x) show grestore gsave 0 setgray 276.7 295 moveto (y) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 282 295 moveto (\) to ) show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 302.6 295 moveto ([) show grestore gsave 0 setgray 332.7 295 moveto (]) show grestore gsave 0 setgray 316.6 295 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 308 295 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 312.6 291.4 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 322.6 295 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 327.2 291.4 moveto (1) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 336.6 295 moveto ( is ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 355.2 295 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 359.8 291.4 moveto (1) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 363.8 295 moveto (. So, we can get one equation in ) show grestore gsave 0 setgray 64 277 moveto (a,b, and ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 110.7 277 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 115.3 273.4 moveto (1) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 119.3 277 moveto ( from this which we can solve for ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 296 277 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 300.6 273.4 moveto (1) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 304.6 277 moveto ( in terms of a and b.) show grestore 12 /Courier-Maple fsf newpath 59 305.1 moveto 56 305.1 lineto 56 274.1 lineto 59 274.1 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 261.6 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 261.6 moveto (eq3 := r[1] = simplify\(subs\(sol,sqrt\(\(x-r[1]\)^2+\(y-r[1]\)^2\)\)\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 238.6 224 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 221.3 224 moveto (eq3) show grestore 12 /Symbol fsf gsave 0 0 1 stc 267 224 moveto (=) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 255.4 224 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 260 220.4 moveto (1) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid newpath 400.6 255.3 moveto 297.9 255.3 lineto 287.2 210 lineto 281.8 228.3 lineto 276.5 223 lineto stroke grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 299.5 228.9 399.1 228.9 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 301 236.1 moveto (\() show grestore gsave 0 0 1 stc 389.6 236.1 moveto (\)) show grestore 12 /Symbol fsf gsave 0 0 1 stc 306.4 236.1 moveto (-) show grestore gsave 0 0 1 stc 333.5 236.1 moveto (+) show grestore gsave 0 0 1 stc 361 236.1 moveto (-) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 312.9 236.1 moveto (b) show grestore gsave 0 0 1 stc 321.9 236.1 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 326.5 232.5 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 343 236.1 moveto (a) show grestore gsave 0 0 1 stc 352 236.1 moveto (b) show grestore gsave 0 0 1 stc 370.5 236.1 moveto (a) show grestore gsave 0 0 1 stc 379.5 236.1 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 384.1 232.5 moveto (1) show grestore gsave 0 0 1 stc 393.6 245.1 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 346 213.5 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 332.9 213.5 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 339 219 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 355.5 213.5 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 361.6 219 moveto (2) show grestore newpath 59 269.1 moveto 56 269.1 lineto 56 211.3 lineto 59 211.3 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 197 moveto ( Solving for r,) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 183.6 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 183.6 moveto (sol2 := solve\(eq3,r[1]\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 201.4 155.5 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 181.4 155.5 moveto (sol2) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 326.4 155.5 moveto (,) show grestore 12 /Symbol fsf gsave 0 0 1 stc 236.2 155.5 moveto (+) show grestore gsave 0 0 1 stc 263.7 155.5 moveto (+) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 218.2 160.4 224.2 160.4 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 218.2 165.2 moveto (1) show grestore gsave 0 0 1 stc 218.2 146.4 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 227.2 155.5 moveto (b) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 245.7 160.4 251.7 160.4 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 245.7 165.2 moveto (1) show grestore gsave 0 0 1 stc 245.7 146.4 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 254.7 155.5 moveto (a) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 273.2 160.4 279.2 160.4 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 273.2 165.2 moveto (1) show grestore gsave 0 0 1 stc 273.2 146.4 moveto (2) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid newpath 326.4 171.2 moveto 290.6 171.2 lineto 286.4 152 lineto 284.3 159.8 lineto 282.2 157.7 lineto stroke grestore 12 /Symbol fsf gsave 0 0 1 stc 305.3 155.5 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 292.2 155.5 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 298.3 161 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 314.8 155.5 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 320.9 161 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 350.4 155.5 moveto (+) show grestore gsave 0 0 1 stc 377.9 155.5 moveto (-) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 332.4 160.4 338.4 160.4 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 332.4 165.2 moveto (1) show grestore gsave 0 0 1 stc 332.4 146.4 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 341.4 155.5 moveto (b) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 359.9 160.4 365.9 160.4 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 359.9 165.2 moveto (1) show grestore gsave 0 0 1 stc 359.9 146.4 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 368.9 155.5 moveto (a) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 387.4 160.4 393.4 160.4 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 387.4 165.2 moveto (1) show grestore gsave 0 0 1 stc 387.4 146.4 moveto (2) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid newpath 440.6 171.2 moveto 404.8 171.2 lineto 400.6 152 lineto 398.5 159.8 lineto 396.4 157.7 lineto stroke grestore 12 /Symbol fsf gsave 0 0 1 stc 419.5 155.5 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 406.4 155.5 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 412.5 161 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 429 155.5 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 435.1 161 moveto (2) show grestore newpath 59 206.3 moveto 56 206.3 lineto 56 144.2 lineto 59 144.2 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 129.9 moveto (Note: In release 3, sol2 may come up with a RootOf in it. You can get all the roots of this ) show grestore gsave 0 setgray 64 114.7 moveto (with allvalues. Just uncomment the next line.) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 101.3 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 101.3 moveto (# sol2 := allvalues\(sol2\);) show grestore newpath 59 139.2 moveto 56 139.2 lineto 56 99.7 lineto 59 99.7 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 85.4 moveto ( By inspection, we can see that r must be the second root. Let's make a function out of this.) show grestore newpath 59 94.7 moveto 56 94.7 lineto 56 32.6 lineto 59 32.6 lineto stroke grestore grestore 306 72 (Page 1) pagenum showpage %%Page: 2 6 gsave newpath 54 720 moveto 504 0 rlineto 0 -648 rlineto -504 0 rlineto closepath clip newpath gsave 0 setgray 0.1 setlinewidth solid 12 /Courier-Maple fsf gsave 0 setgray 64 710.5 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 710.5 moveto (rad := unapply\(sol2[2],a,b\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 233.5 682.4 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 216.9 682.4 moveto (rad) show grestore 12 /Symbol fsf gsave 0 0 1 stc 282.1 682.4 moveto (\256) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 250.3 682.4 moveto (\() show grestore gsave 0 0 1 stc 275.2 682.4 moveto (\)) show grestore gsave 0 0 1 stc 261.7 682.4 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 255.7 682.4 moveto (a) show grestore gsave 0 0 1 stc 267.7 682.4 moveto (b) show grestore 12 /Symbol fsf gsave 0 0 1 stc 314.9 682.4 moveto (+) show grestore gsave 0 0 1 stc 342.4 682.4 moveto (-) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 296.9 687.3 302.9 687.3 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 296.9 692.1 moveto (1) show grestore gsave 0 0 1 stc 296.9 673.3 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 305.9 682.4 moveto (b) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 324.4 687.3 330.4 687.3 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 324.4 692.1 moveto (1) show grestore gsave 0 0 1 stc 324.4 673.3 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 333.4 682.4 moveto (a) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 351.9 687.3 357.9 687.3 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 351.9 692.1 moveto (1) show grestore gsave 0 0 1 stc 351.9 673.3 moveto (2) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid newpath 405.1 698.1 moveto 369.3 698.1 lineto 365.1 678.9 lineto 363 686.7 lineto 360.9 684.6 lineto stroke grestore 12 /Symbol fsf gsave 0 0 1 stc 384 682.4 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 370.9 682.4 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 377 687.9 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 393.5 682.4 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 399.6 687.9 moveto (2) show grestore newpath 59 733.2 moveto 56 733.2 lineto 56 671.1 lineto 59 671.1 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 656.8 moveto ( Just to check if we're on the right track, let's draw the triangle and the inscribed circle. We ) show grestore gsave 0 setgray 64 641.6 moveto (make these general so that a and b can be varied.) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 628.2 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 628.2 moveto ( tri := \(a,b\) -> ) show grestore gsave 1 0 0 stc 78.4 614.1 moveto (plot\([[0,0],[b,0],[0,a],[0,0]],scaling=constrained\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 141.6 595.7 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 130.3 595.7 moveto (tri) show grestore 12 /Symbol fsf gsave 0 0 1 stc 190.2 595.7 moveto (\256) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 158.4 595.7 moveto (\() show grestore gsave 0 0 1 stc 183.3 595.7 moveto (\)) show grestore gsave 0 0 1 stc 169.8 595.7 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 163.8 595.7 moveto (a) show grestore gsave 0 0 1 stc 175.8 595.7 moveto (b) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 225 595.7 moveto (\() show grestore gsave 0 0 1 stc 487.7 595.7 moveto (\)) show grestore gsave 0 0 1 stc 205 595.7 moveto (plot) show grestore gsave 0 0 1 stc 374.4 595.7 moveto (,) show grestore gsave 0 0 1 stc 230.4 595.7 moveto ([) show grestore gsave 0 0 1 stc 370.5 595.7 moveto (]) show grestore gsave 0 0 1 stc 264.6 595.7 moveto (,) show grestore gsave 0 0 1 stc 299.4 595.7 moveto (,) show grestore gsave 0 0 1 stc 334.2 595.7 moveto (,) show grestore gsave 0 0 1 stc 235.8 595.7 moveto ([) show grestore gsave 0 0 1 stc 260.7 595.7 moveto (]) show grestore gsave 0 0 1 stc 247.2 595.7 moveto (,) show grestore gsave 0 0 1 stc 241.2 595.7 moveto (0) show grestore gsave 0 0 1 stc 253.2 595.7 moveto (0) show grestore gsave 0 0 1 stc 270.6 595.7 moveto ([) show grestore gsave 0 0 1 stc 295.5 595.7 moveto (]) show grestore gsave 0 0 1 stc 282 595.7 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 276 595.7 moveto (b) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 288 595.7 moveto (0) show grestore gsave 0 0 1 stc 305.4 595.7 moveto ([) show grestore gsave 0 0 1 stc 330.3 595.7 moveto (]) show grestore gsave 0 0 1 stc 316.8 595.7 moveto (,) show grestore gsave 0 0 1 stc 310.8 595.7 moveto (0) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 322.8 595.7 moveto (a) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 340.2 595.7 moveto ([) show grestore gsave 0 0 1 stc 365.1 595.7 moveto (]) show grestore gsave 0 0 1 stc 351.6 595.7 moveto (,) show grestore gsave 0 0 1 stc 345.6 595.7 moveto (0) show grestore gsave 0 0 1 stc 357.6 595.7 moveto (0) show grestore 12 /Symbol fsf gsave 0 0 1 stc 418.7 595.7 moveto (=) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 380.4 595.7 moveto (scaling) show grestore gsave 0 0 1 stc 428.2 595.7 moveto (constrained) show grestore newpath 59 666.1 moveto 56 666.1 lineto 56 593.5 lineto 59 593.5 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 581 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 581 moveto (circle := \(c,r\) -> plot\([c[1]+r*cos\(t\),c[2]+r*sin\(t\),t=0..2*Pi]\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 183.8 562.6 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 156.5 562.6 moveto (circle) show grestore 12 /Symbol fsf gsave 0 0 1 stc 230.3 562.6 moveto (\256) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 200.6 562.6 moveto (\() show grestore gsave 0 0 1 stc 223.4 562.6 moveto (\)) show grestore gsave 0 0 1 stc 211.3 562.6 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 206 562.6 moveto (c) show grestore gsave 0 0 1 stc 217.3 562.6 moveto (r) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 265.1 562.6 moveto (\() show grestore gsave 0 0 1 stc 461.6 562.6 moveto (\)) show grestore gsave 0 0 1 stc 245.1 562.6 moveto (plot) show grestore gsave 0 0 1 stc 270.5 562.6 moveto ([) show grestore gsave 0 0 1 stc 456.2 562.6 moveto (]) show grestore gsave 0 0 1 stc 335.3 562.6 moveto (,) show grestore gsave 0 0 1 stc 399.4 562.6 moveto (,) show grestore 12 /Symbol fsf gsave 0 0 1 stc 288.2 562.6 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 275.9 562.6 moveto (c) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 281.2 559 moveto (1) show grestore 12 /Times-BoldItalic-Maple gsave 0 0 1 stc 297.7 562.6 moveto (r) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 321.2 562.6 moveto (\() show grestore gsave 0 0 1 stc 331.4 562.6 moveto (\)) show grestore gsave 0 0 1 stc 305.3 562.6 moveto (cos) show grestore 12 /Times-BoldItalic-Maple gsave 0 0 1 stc 326.6 562.6 moveto (t) show grestore 12 /Symbol fsf gsave 0 0 1 stc 353.6 562.6 moveto (+) show grestore 12 /Times-BoldItalic-Maple gsave 0 0 1 stc 341.3 562.6 moveto (c) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 346.6 559 moveto (2) show grestore 12 /Times-BoldItalic-Maple gsave 0 0 1 stc 363.1 562.6 moveto (r) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 385.3 562.6 moveto fsf fsf fsf fsf (\() show grestore gsave 0 0 1 stc 395.5 562.6 moveto (\)) show grestore gsave 0 0 1 stc 370.7 562.6 moveto (sin) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 390.7 562.6 moveto (t) show grestore 12 /Symbol fsf gsave 0 0 1 stc 411.7 562.6 moveto (=) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 405.4 562.6 moveto (t) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 427.2 562.6 moveto ( .. ) show grestore gsave 0 0 1 stc 421.2 562.6 moveto (0) show grestore gsave 0 0 1 stc 439.2 562.6 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 448.2 562.6 moveto (p) show grestore newpath 59 588.5 moveto 56 588.5 lineto 56 558 lineto 59 558 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 545.5 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 545.5 moveto (with\(plots\);) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 69.4 527.1 moveto (animate) show grestore gsave 0 0 1 stc 115.4 527.1 moveto (animate3d) show grestore gsave 0 0 1 stc 173.4 527.1 moveto (changecoords) show grestore gsave 0 0 1 stc 248 527.1 moveto (complexplot) show grestore gsave 0 0 1 stc 314 527.1 moveto (complexplot3d) show grestore gsave 0 0 1 stc 392 527.1 moveto (conformal) show grestore gsave 0 0 1 stc 449.3 527.1 moveto (contourplot) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 109.4 527.1 moveto (,) show grestore gsave 0 0 1 stc 167.4 527.1 moveto (,) show grestore gsave 0 0 1 stc 242 527.1 moveto (,) show grestore gsave 0 0 1 stc 308 527.1 moveto (,) show grestore gsave 0 0 1 stc 386 527.1 moveto (,) show grestore gsave 0 0 1 stc 443.3 527.1 moveto (,) show grestore gsave 0 0 1 stc 506.6 527.1 moveto (,) show grestore gsave 0 0 1 stc 64 527.1 moveto ([) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 84 508.1 moveto (contourplot3d) show grestore gsave 0 0 1 stc 159.3 508.1 moveto (coordplot) show grestore gsave 0 0 1 stc 211.9 508.1 moveto (coordplot3d) show grestore gsave 0 0 1 stc 276.5 508.1 moveto (cylinderplot) show grestore gsave 0 0 1 stc 341.1 508.1 moveto (densityplot) show grestore gsave 0 0 1 stc 400.4 508.1 moveto (display) show grestore gsave 0 0 1 stc 441 508.1 moveto (display3d) show grestore gsave 0 0 1 stc 493.6 508.1 moveto (fieldplot) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 153.3 508.1 moveto (,) show grestore gsave 0 0 1 stc 205.9 508.1 moveto (,) show grestore gsave 0 0 1 stc 270.5 508.1 moveto (,) show grestore gsave 0 0 1 stc 335.1 508.1 moveto (,) show grestore gsave 0 0 1 stc 394.4 508.1 moveto (,) show grestore gsave 0 0 1 stc 435 508.1 moveto (,) show grestore gsave 0 0 1 stc 487.6 508.1 moveto (,) show grestore gsave 0 0 1 stc 534.2 508.1 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 84 489.1 moveto (fieldplot3d) show grestore gsave 0 0 1 stc 142.6 489.1 moveto (gradplot) show grestore gsave 0 0 1 stc 189.9 489.1 moveto (gradplot3d) show grestore gsave 0 0 1 stc 249.2 489.1 moveto (implicitplot) show grestore gsave 0 0 1 stc 311.2 489.1 moveto (implicitplot3d) show grestore gsave 0 0 1 stc 385.2 489.1 moveto (inequal) show grestore gsave 0 0 1 stc 428.5 489.1 moveto (listcontplot) show grestore gsave 0 0 1 stc 489.1 489.1 moveto (listcontplot3d) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 136.6 489.1 moveto (,) show grestore gsave 0 0 1 stc 183.9 489.1 moveto (,) show grestore gsave 0 0 1 stc 243.2 489.1 moveto (,) show grestore gsave 0 0 1 stc 305.2 489.1 moveto (,) show grestore gsave 0 0 1 stc 379.2 489.1 moveto (,) show grestore gsave 0 0 1 stc 422.5 489.1 moveto (,) show grestore gsave 0 0 1 stc 483.1 489.1 moveto (,) show grestore gsave 0 0 1 stc 555.7 489.1 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 84 470.1 moveto (listdensityplot) show grestore gsave 0 0 1 stc 158 470.1 moveto (listplot) show grestore gsave 0 0 1 stc 197.3 470.1 moveto (listplot3d) show grestore gsave 0 0 1 stc 248.6 470.1 moveto (loglogplot) show grestore gsave 0 0 1 stc 303.9 470.1 moveto (logplot) show grestore gsave 0 0 1 stc 343.9 470.1 moveto (matrixplot) show grestore gsave 0 0 1 stc 401.2 470.1 moveto (odeplot) show grestore gsave 0 0 1 stc 443.2 470.1 moveto (pareto) show grestore gsave 0 0 1 stc 480.5 470.1 moveto (pointplot) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 152 470.1 moveto (,) show grestore gsave 0 0 1 stc 191.3 470.1 moveto (,) show grestore gsave 0 0 1 stc 242.6 470.1 moveto (,) show grestore gsave 0 0 1 stc 297.9 470.1 moveto (,) show grestore gsave 0 0 1 stc 337.9 470.1 moveto (,) show grestore gsave 0 0 1 stc 395.2 470.1 moveto (,) show grestore gsave 0 0 1 stc 437.2 470.1 moveto (,) show grestore gsave 0 0 1 stc 474.5 470.1 moveto (,) show grestore gsave 0 0 1 stc 524.5 470.1 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 84 451.1 moveto (pointplot3d) show grestore gsave 0 0 1 stc 146 451.1 moveto (polarplot) show grestore gsave 0 0 1 stc 196.6 451.1 moveto (polygonplot) show grestore gsave 0 0 1 stc 260.6 451.1 moveto (polygonplot3d) show grestore gsave 0 0 1 stc 336.6 451.1 moveto (polyhedraplot) show grestore gsave 0 0 1 stc 410.6 451.1 moveto (replot) show grestore gsave 0 0 1 stc 445.2 451.1 moveto (rootlocus) show grestore gsave 0 0 1 stc 497.2 451.1 moveto (semilogplot) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 140 451.1 moveto (,) show grestore gsave 0 0 1 stc 190.6 451.1 moveto (,) show grestore gsave 0 0 1 stc 254.6 451.1 moveto (,) show grestore gsave 0 0 1 stc 330.6 451.1 moveto (,) show grestore gsave 0 0 1 stc 404.6 451.1 moveto (,) show grestore gsave 0 0 1 stc 439.2 451.1 moveto (,) show grestore gsave 0 0 1 stc 491.2 451.1 moveto (,) show grestore gsave 0 0 1 stc 553.8 451.1 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 84 432.1 moveto (setoptions) show grestore gsave 0 0 1 stc 139.3 432.1 moveto (setoptions3d) show grestore gsave 0 0 1 stc 206.6 432.1 moveto (spacecurve) show grestore gsave 0 0 1 stc 267.2 432.1 moveto (sparsematrixplot) show grestore gsave 0 0 1 stc 355.8 432.1 moveto (sphereplot) show grestore gsave 0 0 1 stc 413.1 432.1 moveto (surfdata) show grestore gsave 0 0 1 stc 460.4 432.1 moveto (textplot) show grestore gsave 0 0 1 stc 503 432.1 moveto (textplot3d) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 133.3 432.1 moveto (,) show grestore gsave 0 0 1 stc 200.6 432.1 moveto (,) show grestore gsave 0 0 1 stc 261.2 432.1 moveto (,) show grestore gsave 0 0 1 stc 349.8 432.1 moveto (,) show grestore gsave 0 0 1 stc 407.1 432.1 moveto (,) show grestore gsave 0 0 1 stc 454.4 432.1 moveto (,) show grestore gsave 0 0 1 stc 497 432.1 moveto (,) show grestore gsave 0 0 1 stc 551.6 432.1 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 84 413.1 moveto (tubeplot) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 125.5 413.1 moveto (]) show grestore newpath 59 553 moveto 56 553 lineto 56 410.9 lineto 59 410.9 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 396.6 moveto ( ) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 383.2 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 383.2 moveto ( inscribe := proc\(a,b\) \12) show grestore gsave 1 0 0 stc 78.4 369.1 moveto ( local r;\12) show grestore gsave 1 0 0 stc 78.4 355 moveto ( r := rad\(a,b\);\12) show grestore gsave 1 0 0 stc 78.4 340.9 moveto ( plots[display]\([tri\(a,b\),circle\([r,r],r\)]\); end;) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 121.7 322.5 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 82.4 322.5 moveto (inscribe) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 138.5 322.5 moveto (proc) show grestore gsave 0 0 1 stc 161.8 322.5 moveto (\() show grestore gsave 0 0 1 stc 183.7 322.5 moveto (\)) show grestore gsave 0 0 1 stc 520.9 322.5 moveto (end) show grestore gsave 0 0 1 stc 171.7 322.5 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 165.7 322.5 moveto (a) show grestore gsave 0 0 1 stc 177.7 322.5 moveto (b) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 190.6 322.5 moveto (local ) show grestore gsave 0 0 1 stc 222.2 322.5 moveto (;) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 217.6 322.5 moveto (r) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 298 322.5 moveto (;) show grestore gsave 0 0 1 stc 233.7 322.5 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 229.1 322.5 moveto (r) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 268.5 322.5 moveto (\() show grestore gsave 0 0 1 stc 293.4 322.5 moveto (\)) show grestore gsave 0 0 1 stc 250.5 322.5 moveto (rad) show grestore gsave 0 0 1 stc 279.9 322.5 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 273.9 322.5 moveto (a) show grestore gsave 0 0 1 stc 285.9 322.5 moveto (b) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 373.6 322.5 moveto (\() show grestore gsave 0 0 1 stc 514 322.5 moveto (\)) show grestore gsave 0 0 1 stc 328.2 322.5 moveto ([) show grestore gsave 0 0 1 stc 369.7 322.5 moveto (]) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 304.9 322.5 moveto (plots) show grestore gsave 0 0 1 stc 333.6 322.5 moveto (display) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 379 322.5 moveto ([) show grestore gsave 0 0 1 stc 508.6 322.5 moveto (]) show grestore gsave 0 0 1 stc 425.8 322.5 moveto (,) show grestore gsave 0 0 1 stc 397 322.5 moveto (\() show grestore gsave 0 0 1 stc 421.9 322.5 moveto (\)) show grestore gsave 0 0 1 stc 384.4 322.5 moveto (tri) show grestore gsave 0 0 1 stc 408.4 322.5 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 402.4 322.5 moveto (a) show grestore gsave 0 0 1 stc 414.4 322.5 moveto (b) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 459.7 322.5 moveto (\() show grestore gsave 0 0 1 stc 503.2 322.5 moveto (\)) show grestore gsave 0 0 1 stc 431.8 322.5 moveto (circle) show grestore gsave 0 0 1 stc 491.1 322.5 moveto (,) show grestore gsave 0 0 1 stc 465.1 322.5 moveto ([) show grestore gsave 0 0 1 stc 487.2 322.5 moveto (]) show grestore gsave 0 0 1 stc 475.1 322.5 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 470.5 322.5 moveto (r) show grestore gsave 0 0 1 stc 481.1 322.5 moveto (r) show grestore gsave 0 0 1 stc 497.1 322.5 moveto (r) show grestore newpath 59 405.9 moveto 56 405.9 lineto 56 320.3 lineto 59 320.3 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 307.8 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 307.8 moveto ( inscribe\(4,7\);) show grestore newpath 59 315.3 moveto 56 315.3 lineto 56 25.2 lineto 59 25.2 lineto stroke grestore grestore 306 72 (Page 2) pagenum showpage %%Page: 3 6 gsave newpath 54 720 moveto 504 0 rlineto 0 -648 rlineto -504 0 rlineto closepath clip newpath gsave 0 setgray 0.1 setlinewidth solid gsave 0 0 0 sc 0.1 setlinewidth solid gsave 0 0 0 sc 0.1 setlinewidth solid 1 0 0 sc 0.1 setlinewidth solid newpath 203.4 518.1 moveto 418.4 518.1 lineto 203.4 641 lineto 203.4 518.1 lineto stroke newpath 293.6 563.2 moveto 293.2 569.4 lineto 292.2 574.6 lineto 290.2 580.4 lineto 287.6 585.8 lineto 284.2 590.8 lineto 280.5 595.1 lineto 276.1 598.9 lineto 271.1 602.3 lineto 265.8 604.9 lineto 259.9 606.9 lineto 254.6 607.9 lineto 248.5 608.3 lineto 242.4 607.9 lineto 236.6 606.7 lineto 231.5 605 lineto 225.8 602.2 lineto 221.3 599.2 lineto 216.5 595 lineto 212.9 590.8 lineto 209.5 585.8 lineto 206.9 580.6 lineto 204.9 574.8 lineto 203.8 569.4 lineto 203.4 563.4 lineto 203.8 557.1 lineto 204.9 551.8 lineto 206.7 546.2 lineto 209.4 540.8 lineto 212.7 535.8 lineto 216.4 531.5 lineto 221.2 527.3 lineto 226 524.1 lineto 231.5 521.4 lineto 236.8 519.7 lineto 242.7 518.5 lineto 248.4 518.1 lineto 254.3 518.5 lineto 260.1 519.6 lineto 265.8 521.5 lineto 271.1 524.2 lineto 276.1 527.5 lineto 280.6 531.4 lineto 284.2 535.6 lineto 287.7 540.8 lineto 290.1 545.8 lineto 292.1 551.5 lineto 293.2 557.1 lineto 293.6 563.2 lineto stroke 0 0 0 sc 0.1 setlinewidth solid 0.1 418.4 517 418.4 519 line 0.1 412.3 517.5 412.3 518.5 line 0.1 406.1 517.5 406.1 518.5 line 0.1 400 517.5 400 518.5 line 0.1 393.8 517.5 393.8 518.5 line 0.1 387.7 517 387.7 519 line 0.1 381.5 517.5 381.5 518.5 line 0.1 375.4 517.5 375.4 518.5 line 0.1 369.3 517.5 369.3 518.5 line 0.1 363.1 517.5 363.1 518.5 line 0.1 357 517 357 519 line 0.1 350.8 517.5 350.8 518.5 line 0.1 344.7 517.5 344.7 518.5 line 0.1 338.5 517.5 338.5 518.5 line 0.1 332.4 517.5 332.4 518.5 line 0.1 326.3 517 326.3 519 line 0.1 320.1 517.5 320.1 518.5 line 0.1 314 517.5 314 518.5 line 0.1 307.8 517.5 307.8 518.5 line 0.1 301.7 517.5 301.7 518.5 line 0.1 295.6 517 295.6 519 line 0.1 289.4 517.5 289.4 518.5 line 0.1 283.3 517.5 283.3 518.5 line 0.1 277.1 517.5 277.1 518.5 line 0.1 271 517.5 271 518.5 line 0.1 264.8 517 264.8 519 line 0.1 258.7 517.5 258.7 518.5 line 0.1 252.6 517.5 252.6 518.5 line 0.1 246.4 517.5 246.4 518.5 line 0.1 240.3 517.5 240.3 518.5 line 0.1 234.1 517 234.1 519 line 0.1 228 517.5 228 518.5 line 0.1 221.8 517.5 221.8 518.5 line 0.1 215.7 517.5 215.7 518.5 line 0.1 209.6 517.5 209.6 518.5 line 0.1 199.1 518 422.8 518 line 0.1 201.6 640.9 205.2 640.9 line 0.1 202.5 634.7 204.3 634.7 line 0.1 202.5 628.6 204.3 628.6 line 0.1 202.5 622.4 204.3 622.4 line 0.1 202.5 616.3 204.3 616.3 line 0.1 201.6 610.1 205.2 610.1 line 0.1 202.5 604 204.3 604 line 0.1 202.5 597.9 204.3 597.9 line 0.1 202.5 591.7 204.3 591.7 line 0.1 202.5 585.6 204.3 585.6 line 0.1 201.6 579.4 205.2 579.4 line 0.1 202.5 573.3 204.3 573.3 line 0.1 202.5 567.1 204.3 567.1 line 0.1 202.5 561 204.3 561 line 0.1 202.5 554.9 204.3 554.9 line 0.1 201.6 548.7 205.2 548.7 line 0.1 202.5 542.6 204.3 542.6 line 0.1 202.5 536.4 204.3 536.4 line 0.1 202.5 530.3 204.3 530.3 line 0.1 202.5 524.1 204.3 524.1 line 0.1 201.6 518 205.2 518 line 0.1 203.4 515.5 203.4 643.4 line 8 /Helvetica-Maple fsf gsave 0 setgray 416.2 509.6 moveto (7) show grestore gsave 0 setgray 385.5 509.6 moveto (6) show grestore gsave 0 setgray 354.8 509.6 moveto (5) show grestore gsave 0 setgray 324.1 509.6 moveto (4) show grestore gsave 0 setgray 293.4 509.6 moveto (3) show grestore gsave 0 setgray 262.6 509.6 moveto (2) show grestore gsave 0 setgray 231.9 509.6 moveto (1) show grestore gsave 0 setgray 197.2 638.5 moveto (4) show grestore gsave 0 setgray 197.2 607.7 moveto (3) show grestore gsave 0 setgray 197.2 577 moveto (2) show grestore gsave 0 setgray 197.2 546.3 moveto (1) show grestore gsave 0 setgray 197.2 510.6 moveto (0) show grestore grestore grestore newpath 59 732.1 moveto 56 732.1 lineto 56 442 lineto 59 442 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 426.9 moveto (Good. This work fine. Now get the ratio of ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 291.4 426.9 moveto (r) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 296 423.3 moveto (n) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 300.4 426.9 moveto ( to ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 317 426.9 moveto (r) show grestore 8 /Symbol fsf gsave 0 setgray 328 423.3 moveto (-) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 321.6 423.3 moveto (n) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 334.3 423.3 moveto (1) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 338.3 426.9 moveto (. Here we can use some trig. Look at ) show grestore gsave 0 setgray 64 409.7 moveto (the right triangle whose hypotenuse is the segment n-1st and ) show grestore gsave 0 setgray 64 393.7 moveto (nth circles. The hypotenuse is ) show grestore 12 /Symbol fsf gsave 0 setgray 260.3 393.7 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 236 393.7 moveto (r) show grestore 8 /Symbol fsf connecting the centers of the gsave 0 setgray 247 390.1 moveto (-) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 240.6 390.1 moveto (n) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 253.3 390.1 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 269.8 393.7 moveto (r) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 274.4 390.1 moveto (n) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 278.8 393.7 moveto (, the angle ) show grestore 12 /Symbol fsf gsave 0 setgray 341.5 393.7 moveto (a) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 349 393.7 moveto ( on the lower right vertex is grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 64 366 moveto (.5) show grestore 12 /Symbol fsf gsave 0 setgray 109.3 375.7 moveto (\346) show grestore ) show gsave 0 setgray 109.3 356.9 moveto (\350) show grestore gsave 0 setgray 109.3 367.9 moveto (\347) show grestore gsave 0 setgray 109.3 364.7 moveto (\347) show grestore gsave 0 setgray 125.9 375.7 moveto (\366) show grestore gsave 0 setgray 125.9 356.9 moveto (\370) show grestore gsave 0 setgray 125.9 367.9 moveto (\367) show grestore gsave 0 setgray 125.9 364.7 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 76 366 moveto (arctan) show grestore gsave 0 setgray 0.7 setlinewidth solid 0.7 115.4 370.9 124.4 370.9 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 116.9 375.7 moveto (a) show grestore gsave 0 setgray 116.9 356.9 moveto (b) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 130.5 366 moveto (, and the side opposite this angle grestore 12 /Symbol fsf gsave 0 setgray 348.9 366 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 324.6 366 moveto (r) show grestore 8 /Symbol fsf gsave 0 setgray 335.6 362.4 moveto (-) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 329.2 362.4 moveto (n) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 341.9 362.4 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 358.4 366 moveto (r) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 363 362.4 moveto (n) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 367.4 366 moveto (, which is also ) show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 445.4 366 moveto (\() show grestore is ) show gsave 0 setgray 495.1 366 moveto (\)) show grestore 12 /Symbol fsf gsave 0 setgray 475.1 366 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 450.8 366 moveto (r) show grestore 8 /Symbol fsf gsave 0 setgray 461.8 362.4 moveto (-) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 455.4 362.4 moveto (n) show grestore 8 /Times-Bold-Maple fsf gsave 0 setgray 468.1 362.4 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 484.6 366 moveto (r) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 489.2 362.4 moveto (n) show grestore 12 /Times-Bold-Maple fsf gsave 0 setgray 516.6 366 moveto (\() show grestore gsave 0 setgray 531 366 moveto (\)) show grestore gsave 0 setgray 502 366 moveto (sin) show grestore 12 /Symbol fsf gsave 0 setgray 522 366 moveto (a) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 534.9 366 moveto (. ) show grestore gsave 0 setgray 64 342.1 moveto (This is eq4) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 328.7 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 328.7 moveto ( eq4 := r[n-1]-r[n]= \(r[n-1]+r[n]\)*sin\(.5*arctan\(a/b\)\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 208.6 300.6 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 191.3 300.6 moveto (eq4) show grestore 12 /Symbol fsf gsave 0 0 1 stc 271.2 300.6 moveto (=) show grestore gsave 0 0 1 stc 249.7 300.6 moveto (-) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 225.4 300.6 moveto (r) show grestore 8 /Symbol fsf gsave 0 0 1 stc 236.4 297 moveto (-) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 230 297 moveto (n) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 242.7 297 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 259.2 300.6 moveto (r) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 263.8 297 moveto (n) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 280.7 300.6 moveto (\() show grestore gsave 0 0 1 stc 330.4 300.6 moveto (\)) show grestore 12 /Symbol fsf gsave 0 0 1 stc 310.4 300.6 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 286.1 300.6 moveto (r) show grestore 8 /Symbol fsf gsave 0 0 1 stc 297.1 297 moveto (-) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 290.7 297 moveto (n) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 303.4 297 moveto (1) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 319.9 300.6 moveto (r) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 324.5 297 moveto (n) show grestore 12 /Symbol fsf gsave 0 0 1 stc 351.9 310.3 moveto (\346) show grestore gsave 0 0 1 stc 351.9 291.5 moveto (\350) show grestore gsave 0 0 1 stc 351.9 302.5 moveto (\347) show grestore gsave 0 0 1 stc 351.9 299.3 moveto (\347) show grestore gsave 0 0 1 stc 426 310.3 moveto (\366) show grestore gsave 0 0 1 stc 426 291.5 moveto (\370) show grestore gsave 0 0 1 stc 426 302.5 moveto (\367) show grestore gsave 0 0 1 stc 426 299.3 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 337.3 300.6 moveto (sin) show grestore gsave 0 0 1 stc 358 300.6 moveto (.5) show grestore 12 /Symbol fsf gsave 0 0 1 stc 403.3 310.3 moveto (\346) show grestore gsave 0 0 1 stc 403.3 291.5 moveto (\350) show grestore gsave 0 0 1 stc 403.3 302.5 moveto (\347) show grestore gsave 0 0 1 stc 403.3 299.3 moveto (\347) show grestore gsave 0 0 1 stc 419.9 310.3 moveto (\366) show grestore gsave 0 0 1 stc 419.9 291.5 moveto (\370) show grestore gsave 0 0 1 stc 419.9 302.5 moveto (\367) show grestore gsave 0 0 1 stc 419.9 299.3 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 370 300.6 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 409.4 305.5 418.4 305.5 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 410.9 310.3 moveto (a) show grestore gsave 0 0 1 stc 410.9 291.5 moveto (b) show grestore newpath 59 437 moveto 56 437 lineto 56 289.3 lineto 59 289.3 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 274.2 moveto (Solve this equation for ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 setgray 186 274.2 moveto (r) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 setgray 190.6 270.6 moveto (n) show grestore 12 /Helvetica-Maple fsf gsave 0 setgray 195 274.2 moveto ( ) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 258.8 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 258.8 moveto (sol := solve\(eq4,r[n]\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 192.9 211.9 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 178.9 211.9 moveto (sol) show grestore 12 /Symbol fsf gsave 0 0 1 stc 209.7 211.9 moveto (-) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 216.2 211.9 moveto (1.) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 228.2 216.8 443 216.8 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 229.7 230.7 moveto (r) show grestore 8 /Symbol fsf gsave 0 0 1 stc 240.7 227.1 moveto (-) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 234.3 227.1 moveto (n) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 247 227.1 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 254 240.4 moveto (\346) show grestore gsave 0 0 1 stc 254 221.6 moveto (\350) show grestore gsave 0 0 1 stc 254 232.6 moveto (\347) show grestore gsave 0 0 1 stc 254 229.4 moveto (\347) show grestore gsave 0 0 1 stc 436.9 240.4 moveto (\366) show grestore gsave 0 0 1 stc 436.9 221.6 moveto (\370) show grestore gsave 0 0 1 stc 436.9 232.6 moveto (\367) show grestore gsave 0 0 1 stc 436.9 229.4 moveto (\367) show grestore gsave 0 0 1 stc 260.1 230.7 moveto (-) show grestore gsave 0 0 1 stc 278.6 230.7 moveto (+) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 266.6 230.7 moveto (1.) show grestore 12 /Symbol fsf gsave 0 0 1 stc 302.7 240.4 moveto (\346) show grestore gsave 0 0 1 stc 302.7 221.6 moveto (\350) show grestore gsave 0 0 1 stc 302.7 232.6 moveto (\347) show grestore gsave 0 0 1 stc 302.7 229.4 moveto (\347) show grestore gsave 0 0 1 stc 430.8 240.4 moveto (\366) show grestore gsave 0 0 1 stc 430.8 221.6 moveto (\370) show grestore gsave 0 0 1 stc 430.8 232.6 moveto (\367) show grestore gsave 0 0 1 stc 430.8 229.4 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 288.1 230.7 moveto (sin) show grestore gsave 0 0 1 stc 308.8 230.7 moveto (.5000000000) show grestore 12 /Symbol fsf gsave 0 0 1 stc 408.1 240.4 moveto (\346) show grestore gsave 0 0 1 stc 408.1 221.6 moveto (\350) show grestore gsave 0 0 1 stc 408.1 232.6 moveto (\347) show grestore gsave 0 0 1 stc 408.1 229.4 moveto (\347) show grestore gsave 0 0 1 stc 424.7 240.4 moveto (\366) show grestore gsave 0 0 1 stc 424.7 221.6 moveto (\370) show grestore gsave 0 0 1 stc 424.7 232.6 moveto (\367) show grestore gsave 0 0 1 stc 424.7 229.4 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 374.8 230.7 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 414.2 235.6 423.2 235.6 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 415.7 240.4 moveto (a) show grestore gsave 0 0 1 stc 415.7 221.6 moveto (b) show grestore 12 /Symbol fsf gsave 0 0 1 stc 263.2 193.1 moveto (+) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 251.2 193.1 moveto (1.) show grestore 12 /Symbol fsf gsave 0 0 1 stc 287.3 202.8 moveto (\346) show grestore gsave 0 0 1 stc 287.3 184 moveto (\350) show grestore gsave 0 0 1 stc 287.3 195 moveto (\347) show grestore gsave 0 0 1 stc 287.3 191.8 moveto (\347) show grestore gsave 0 0 1 stc 415.4 202.8 moveto (\366) show grestore gsave 0 0 1 stc 415.4 184 moveto (\370) show grestore gsave 0 0 1 stc 415.4 195 moveto (\367) show grestore gsave 0 0 1 stc 415.4 191.8 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 272.7 193.1 moveto (sin) show grestore gsave 0 0 1 stc 293.4 193.1 moveto (.5000000000) show grestore 12 /Symbol fsf gsave 0 0 1 stc 392.7 202.8 moveto (\346) show grestore gsave 0 0 1 stc 392.7 184 moveto (\350) show grestore gsave 0 0 1 stc 392.7 195 moveto (\347) show grestore gsave 0 0 1 stc 392.7 191.8 moveto (\347) show grestore gsave 0 0 1 stc 409.3 202.8 moveto (\366) show grestore gsave 0 0 1 stc 409.3 184 moveto (\370) show grestore gsave 0 0 1 stc 409.3 195 moveto (\367) show grestore gsave 0 0 1 stc 409.3 191.8 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 359.4 193.1 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 398.8 198 407.8 198 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 400.3 202.8 moveto (a) show grestore gsave 0 0 1 stc 400.3 184 moveto (b) show grestore newpath 59 284.3 moveto 56 284.3 lineto 56 181.8 lineto 59 181.8 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 169.3 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 169.3 moveto ( collect\(sol,r[n-1]\) ;) show grestore 12 /Symbol fsf gsave 0 0 1 stc 194.3 122.4 moveto (-) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 200.8 122.4 moveto (1.) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 212.8 127.3 427.6 127.3 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 214.3 141.2 moveto (r) show grestore 8 /Symbol fsf gsave 0 0 1 stc 225.3 137.6 moveto (-) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 218.9 137.6 moveto (n) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 231.6 137.6 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 238.6 150.9 moveto (\346) show grestore gsave 0 0 1 stc 238.6 132.1 moveto (\350) show grestore gsave 0 0 1 stc 238.6 143.1 moveto (\347) show grestore gsave 0 0 1 stc 238.6 139.9 moveto (\347) show grestore gsave 0 0 1 stc 421.5 150.9 moveto (\366) show grestore gsave 0 0 1 stc 421.5 132.1 moveto (\370) show grestore gsave 0 0 1 stc 421.5 143.1 moveto (\367) show grestore gsave 0 0 1 stc 421.5 139.9 moveto (\367) show grestore gsave 0 0 1 stc 244.7 141.2 moveto (-) show grestore gsave 0 0 1 stc 263.2 141.2 moveto (+) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 251.2 141.2 moveto (1.) show grestore 12 /Symbol fsf gsave 0 0 1 stc 287.3 150.9 moveto (\346) show grestore gsave 0 0 1 stc 287.3 132.1 moveto (\350) show grestore gsave 0 0 1 stc 287.3 143.1 moveto (\347) show grestore gsave 0 0 1 stc 287.3 139.9 moveto (\347) show grestore gsave 0 0 1 stc 415.4 150.9 moveto (\366) show grestore gsave 0 0 1 stc 415.4 132.1 moveto (\370) show grestore gsave 0 0 1 stc 415.4 143.1 moveto (\367) show grestore gsave 0 0 1 stc 415.4 139.9 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 272.7 141.2 moveto (sin) show grestore gsave 0 0 1 stc 293.4 141.2 moveto (.5000000000) show grestore 12 /Symbol fsf gsave 0 0 1 stc 392.7 150.9 moveto (\346) show grestore gsave 0 0 1 stc 392.7 132.1 moveto (\350) show grestore gsave 0 0 1 stc 392.7 143.1 moveto (\347) show grestore gsave 0 0 1 stc 392.7 139.9 moveto (\347) show grestore gsave 0 0 1 stc 409.3 150.9 moveto (\366) show grestore gsave 0 0 1 stc 409.3 132.1 moveto (\370) show grestore gsave 0 0 1 stc 409.3 143.1 moveto (\367) show grestore gsave 0 0 1 stc 409.3 139.9 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 359.4 141.2 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 398.8 146.1 407.8 146.1 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 400.3 150.9 moveto (a) show grestore gsave 0 0 1 stc 400.3 132.1 moveto (b) show grestore 12 /Symbol fsf gsave 0 0 1 stc 247.8 103.6 moveto (+) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 235.8 103.6 moveto (1.) show grestore 12 /Symbol fsf gsave 0 0 1 stc 271.9 113.3 moveto (\346) show grestore gsave 0 0 1 stc 271.9 94.5 moveto (\350) show grestore gsave 0 0 1 stc 271.9 105.5 moveto (\347) show grestore gsave 0 0 1 stc 271.9 102.3 moveto (\347) show grestore gsave 0 0 1 stc 400 113.3 moveto (\366) show grestore gsave 0 0 1 stc 400 94.5 moveto (\370) show grestore gsave 0 0 1 stc 400 105.5 moveto (\367) show grestore gsave 0 0 1 stc 400 102.3 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 257.3 103.6 moveto (sin) show grestore gsave 0 0 1 stc 278 103.6 moveto (.5000000000) show grestore 12 /Symbol fsf gsave 0 0 1 stc 377.3 113.3 moveto (\346) show grestore gsave 0 0 1 stc 377.3 94.5 moveto (\350) show grestore gsave 0 0 1 stc 377.3 105.5 moveto (\347) show grestore gsave 0 0 1 stc 377.3 102.3 moveto (\347) show grestore gsave 0 0 1 stc 393.9 113.3 moveto (\366) show grestore gsave 0 0 1 stc 393.9 94.5 moveto (\370) show grestore gsave 0 0 1 stc 393.9 105.5 moveto (\367) show grestore gsave 0 0 1 stc 393.9 102.3 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 344 103.6 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 383.4 108.5 392.4 108.5 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 384.9 113.3 moveto (a) show grestore gsave 0 0 1 stc 384.9 94.5 moveto (b) show grestore newpath 59 176.8 moveto 56 176.8 lineto 56 92.3 lineto 59 92.3 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 78 moveto ( Now we can see what the common ratio is. \(Note the lead -1 above. Maple insists on writing ) show grestore newpath 59 87.3 moveto 56 87.3 lineto 56 -41.7 lineto 59 -41.7 lineto stroke grestore grestore 306 72 (Page 3) pagenum showpage %%Page: 4 6 gsave newpath 54 720 moveto 504 0 rlineto 0 -648 rlineto -504 0 rlineto closepath clip newpath gsave 0 setgray 0.1 setlinewidth solid 12 /Helvetica-Maple fsf gsave 0 setgray 64 723.9 moveto ( Now we can see what the common ratio is. \(Note the lead -1 above. Maple insists on writing ) show grestore gsave 0 setgray 64 708.7 moveto (things in this way.\)) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 695.3 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 695.3 moveto (rat := unapply\( \(1-sin\(arctan\(a/b\)/2\)\)/\(1+sin\(arctan\(a/b\)/2\)\) ) show grestore gsave 1 0 0 stc 78.4 681.2 moveto (,a,b\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 230.4 634.3 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 216.4 634.3 moveto (rat) show grestore 12 /Symbol fsf gsave 0 0 1 stc 279 634.3 moveto (\256) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 247.2 634.3 moveto (\() show grestore gsave 0 0 1 stc 272.1 634.3 moveto (\)) show grestore gsave 0 0 1 stc 258.6 634.3 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 252.6 634.3 moveto (a) show grestore gsave 0 0 1 stc 264.6 634.3 moveto (b) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 293.8 639.2 405.6 639.2 line grestore 12 /Symbol fsf gsave 0 0 1 stc 304.3 653.1 moveto (-) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 295.3 653.1 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 328.4 662.8 moveto (\346) show grestore gsave 0 0 1 stc 328.4 644 moveto (\350) show grestore gsave 0 0 1 stc 328.4 655 moveto (\347) show grestore gsave 0 0 1 stc 328.4 651.8 moveto (\347) show grestore gsave 0 0 1 stc 399.5 662.8 moveto (\366) show grestore gsave 0 0 1 stc 399.5 644 moveto (\370) show grestore gsave 0 0 1 stc 399.5 655 moveto (\367) grestore show gsave 0 0 1 stc 399.5 651.8 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 313.8 653.1 moveto (sin) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 334.5 658 340.5 658 line grestore gsave 0 0 1 stc 334.5 662.8 moveto (1) show grestore gsave 0 0 1 stc 334.5 644 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 376.8 662.8 moveto (\346) show grestore gsave 0 0 1 stc 376.8 644 moveto (\350) show grestore gsave 0 0 1 stc 376.8 655 moveto (\347) show grestore gsave 0 0 1 stc 376.8 651.8 moveto (\347) show grestore gsave 0 0 1 stc 393.4 662.8 moveto (\366) show grestore gsave 0 0 1 stc 393.4 644 moveto (\370) show grestore gsave 0 0 1 stc 393.4 655 moveto (\367) show grestore gsave 0 0 1 stc 393.4 651.8 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 343.5 653.1 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 382.9 658 391.9 658 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 384.4 662.8 moveto (a) show grestore gsave 0 0 1 stc 384.4 644 moveto (b) show grestore 12 /Symbol fsf gsave 0 0 1 stc 304.3 615.5 moveto (+) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 295.3 615.5 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 328.4 625.2 moveto (\346) show grestore gsave 0 0 1 stc 328.4 606.4 moveto (\350) show grestore gsave 0 0 1 stc 328.4 617.4 moveto (\347) show grestore gsave 0 0 1 stc 328.4 614.2 moveto (\347) show grestore gsave 0 0 1 stc 399.5 625.2 moveto (\366) show grestore gsave 0 0 1 stc 399.5 606.4 moveto (\370) show grestore gsave 0 0 1 stc 399.5 617.4 moveto (\367) show grestore gsave 0 0 1 stc 399.5 614.2 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 313.8 615.5 moveto (sin) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 334.5 620.4 340.5 620.4 line grestore gsave 0 0 1 stc 334.5 625.2 moveto (1) show grestore gsave 0 0 1 stc 334.5 606.4 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 376.8 625.2 moveto (\346) show grestore gsave 0 0 1 stc 376.8 606.4 moveto (\350) show grestore gsave 0 0 1 stc 376.8 617.4 moveto (\347) show grestore gsave 0 0 1 stc 376.8 614.2 moveto (\347) show grestore gsave 0 0 1 stc 393.4 625.2 moveto (\366) show grestore gsave 0 0 1 stc 393.4 606.4 moveto (\370) show grestore gsave 0 0 1 stc 393.4 617.4 moveto (\367) show grestore gsave 0 0 1 stc 393.4 614.2 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 343.5 615.5 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 382.9 620.4 391.9 620.4 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 384.4 625.2 moveto (a) show grestore gsave 0 0 1 stc 384.4 606.4 moveto (b) show grestore newpath 59 733.2 moveto 56 733.2 lineto 56 604.2 lineto 59 604.2 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 589.9 moveto (Now we can write the total Area of the circles.) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 576.5 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 576.5 moveto (Area := Sum\(Pi*\(rad\(a,b\)*rat\(a,b\)^i\)^2,i=0..infinity\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 165.8 529.6 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 141.8 529.6 moveto (Area) show grestore 21 /Symbol fsf gsave 0 0 1 stc 182.6 529.4 moveto (\345) show grestore 8 /Symbol fsf gsave 0 0 1 stc 187 515.3 moveto (=) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 182.8 515.3 moveto (i) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 193.3 515.3 moveto (0) show grestore 8 /Symbol fsf gsave 0 0 1 stc 187.2 546.8 moveto (\245) show grestore 12 /Symbol fsf gsave 0 0 1 stc 200.5 529.6 moveto (p) show grestore gsave 0 0 1 stc 210 539.3 moveto (\346) show grestore gsave 0 0 1 stc 210 520.5 moveto (\350) show grestore gsave 0 0 1 stc 210 531.5 moveto (\347) show grestore gsave 0 0 1 stc 210 528.3 moveto (\347) show grestore gsave 0 0 1 stc 325.8 539.3 moveto (\366) show grestore gsave 0 0 1 stc 325.8 520.5 moveto (\370) show grestore gsave 0 0 1 stc 325.8 531.5 moveto (\367) show grestore gsave 0 0 1 stc 325.8 528.3 moveto (\367) show grestore gsave 0 0 1 stc 234.1 529.6 moveto (+) show grestore gsave 0 0 1 stc 261.6 529.6 moveto (-) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 216.1 534.5 222.1 534.5 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 216.1 539.3 moveto (1) show grestore gsave 0 0 1 stc 216.1 520.5 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 225.1 529.6 moveto (b) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 243.6 534.5 249.6 534.5 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 243.6 539.3 moveto (1) show grestore gsave 0 0 1 stc 243.6 520.5 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 252.6 529.6 moveto (a) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 271.1 534.5 277.1 534.5 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 271.1 539.3 moveto (1) show grestore gsave 0 0 1 stc 271.1 520.5 moveto (2) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid newpath 324.3 545.3 moveto 288.5 545.3 lineto 284.3 526.1 lineto 282.2 533.9 lineto 280.1 531.8 lineto stroke grestore 12 /Symbol fsf gsave 0 0 1 stc 303.2 529.6 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 290.1 529.6 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 296.2 535.1 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 312.7 529.6 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 318.8 535.1 moveto (2) show grestore gsave 0 0 1 stc 330.5 543.4 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 337.5 558.1 moveto (\346) show grestore gsave 0 0 1 stc 337.5 501.7 (\350) show grestore gsave 0 0 1 stc 337.5 550.3 (\347) show grestore gsave 0 0 1 stc 337.5 542.5 (\347) show grestore gsave 0 0 1 stc 337.5 534.7 (\347) show grestore gsave 0 0 1 stc 337.5 526.9 (\347) show grestore gsave 0 0 1 stc 337.5 519.1 (\347) show grestore gsave 0 0 1 stc 337.5 511.3 (\347) show grestore gsave 0 0 1 stc 337.5 509.5 (\347) show grestore gsave 0 0 1 stc 471.4 558.1 (\366) show grestore gsave 0 0 1 stc 471.4 501.7 (\370) show grestore gsave 0 0 1 stc 471.4 550.3 (\367) show grestore gsave 0 0 1 stc 471.4 542.5 (\367) show grestore gsave moveto moveto moveto moveto moveto moveto moveto moveto moveto moveto moveto moveto 0 0 1 stc 471.4 534.7 (\367) show grestore gsave 0 0 1 stc 471.4 526.9 (\367) show grestore gsave 0 0 1 stc 471.4 519.1 (\367) show grestore gsave 0 0 1 stc 471.4 511.3 (\367) show grestore gsave 0 0 1 stc 471.4 509.5 (\367) show grestore gsave 0 0 1 stc 343.6 558.1 (\346) show grestore gsave 0 0 1 stc 343.6 501.7 (\350) show grestore gsave 0 0 1 stc 343.6 550.3 (\347) show grestore gsave 0 0 1 stc 343.6 542.5 (\347) show grestore gsave 0 0 1 stc 343.6 534.7 (\347) show grestore gsave 0 0 1 stc 343.6 526.9 (\347) show grestore gsave 0 0 1 stc 343.6 519.1 (\347) show grestore moveto moveto moveto moveto moveto moveto moveto moveto moveto moveto moveto moveto gsave 0 0 1 stc 343.6 511.3 moveto (\347) show grestore gsave 0 0 1 stc 343.6 509.5 moveto (\347) show grestore gsave 0 0 1 stc 463 558.1 moveto (\366) show grestore gsave 0 0 1 stc 463 501.7 moveto (\370) show grestore gsave 0 0 1 stc 463 550.3 moveto (\367) show grestore gsave 0 0 1 stc 463 542.5 moveto (\367) show grestore gsave 0 0 1 stc 463 534.7 moveto (\367) show grestore gsave 0 0 1 stc 463 526.9 moveto (\367) show grestore gsave 0 0 1 stc 463 519.1 moveto (\367) show grestore gsave 0 0 1 stc 463 511.3 moveto (\367) show grestore gsave 0 0 1 stc 463 509.5 moveto (\367) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 349.7 534.5 461.5 534.5 line grestore gsave 0 0 1 stc 360.2 548.4 moveto (-) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 351.2 548.4 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 384.3 558.1 moveto (\346) show grestore gsave 0 0 1 stc 384.3 539.3 moveto (\350) show grestore gsave 0 0 1 stc 384.3 550.3 moveto (\347) show grestore gsave 0 0 1 stc 384.3 547.1 moveto (\347) show grestore gsave 0 0 1 stc 455.4 558.1 moveto (\366) show grestore gsave 0 0 1 stc 455.4 539.3 moveto (\370) show grestore gsave 0 0 1 stc 455.4 550.3 moveto (\367) show grestore gsave 0 0 1 stc 455.4 547.1 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 369.7 548.4 moveto (sin) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 390.4 553.3 396.4 553.3 line grestore gsave 0 0 1 stc 390.4 558.1 moveto (1) show grestore gsave 0 0 1 stc 390.4 539.3 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 432.7 558.1 moveto (\346) show grestore gsave 0 0 1 stc 432.7 539.3 moveto (\350) show grestore gsave 0 0 1 stc 432.7 550.3 moveto (\347) show grestore gsave 0 0 1 stc 432.7 547.1 moveto (\347) show grestore gsave 0 0 1 stc 449.3 558.1 moveto (\366) show grestore gsave 0 0 1 stc 449.3 539.3 moveto (\370) show grestore gsave 0 0 1 stc 449.3 550.3 moveto (\367) show grestore gsave 0 0 1 stc 449.3 547.1 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 399.4 548.4 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 438.8 553.3 447.8 553.3 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 440.3 558.1 moveto (a) show grestore gsave 0 0 1 stc 440.3 539.3 moveto (b) show grestore 12 /Symbol fsf gsave 0 0 1 stc 360.2 510.8 moveto (+) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 351.2 510.8 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 384.3 520.5 moveto (\346) show grestore gsave 0 0 1 stc 384.3 501.7 moveto (\350) show grestore gsave 0 0 1 stc 384.3 512.7 moveto (\347) show grestore gsave 0 0 1 stc 384.3 509.5 moveto (\347) show grestore gsave 0 0 1 stc 455.4 520.5 moveto (\366) show grestore gsave 0 0 1 stc 455.4 501.7 moveto (\370) show grestore gsave 0 0 1 stc 455.4 512.7 moveto (\367) show grestore gsave 0 0 1 stc 455.4 509.5 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 369.7 510.8 moveto (sin) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 390.4 515.7 396.4 515.7 line grestore gsave 0 0 1 stc 390.4 520.5 moveto (1) show grestore gsave 0 0 1 stc 390.4 501.7 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 432.7 520.5 moveto (\346) show grestore gsave 0 0 1 stc 432.7 501.7 moveto (\350) show grestore gsave 0 0 1 stc 432.7 512.7 moveto (\347) show grestore gsave 0 0 1 stc 432.7 509.5 moveto (\347) show grestore gsave 0 0 1 stc 449.3 520.5 moveto (\366) show grestore gsave 0 0 1 stc 449.3 501.7 moveto (\370) show grestore gsave 0 0 1 stc 449.3 512.7 moveto (\367) show grestore gsave 0 0 1 stc 449.3 509.5 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 399.4 510.8 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 438.8 515.7 447.8 515.7 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 440.3 520.5 moveto (a) show grestore gsave 0 0 1 stc 440.3 501.7 moveto (b) show grestore 8 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 467.7 562.2 moveto (i) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 476.1 562.2 moveto (2) show grestore newpath 59 599.2 moveto 56 599.2 lineto 56 499.5 lineto 59 499.5 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 485.2 moveto ( This is a geometric series, which maple can sum. \(We could too.\)) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 471.8 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 471.8 moveto (form := value\(Area \);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 177.5 424.9 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 153.5 424.9 moveto (form) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 194.3 429.8 200.3 429.8 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 194.3 434.6 moveto (1) show grestore gsave 0 0 1 stc 194.3 415.8 moveto (4) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 203.3 429.8 468.4 429.8 line grestore 12 /Symbol fsf gsave 0 0 1 stc 204.8 443.7 moveto (p) show grestore gsave 0 0 1 stc 214.3 453.4 moveto (\346) show grestore gsave 0 0 1 stc 214.3 434.6 moveto (\350) show grestore gsave 0 0 1 stc 214.3 445.6 moveto (\347) show grestore gsave 0 0 1 stc 214.3 442.4 moveto (\347) show grestore gsave 0 0 1 stc 330.1 453.4 moveto (\366) show grestore gsave 0 0 1 stc 330.1 434.6 moveto (\370) show grestore gsave 0 0 1 stc 330.1 445.6 moveto (\367) show grestore gsave 0 0 1 stc 330.1 442.4 moveto (\367) show grestore gsave 0 0 1 stc 238.4 443.7 moveto (+) show grestore gsave 0 0 1 stc 265.9 443.7 moveto (-) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 220.4 448.6 226.4 448.6 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 220.4 453.4 moveto (1) show grestore gsave 0 0 1 stc 220.4 434.6 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 229.4 443.7 moveto (b) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 247.9 448.6 253.9 448.6 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 247.9 453.4 moveto (1) show grestore gsave 0 0 1 stc 247.9 434.6 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 256.9 443.7 moveto (a) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 275.4 448.6 281.4 448.6 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 275.4 453.4 moveto (1) show grestore gsave 0 0 1 stc 275.4 434.6 moveto (2) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid newpath 328.6 459.4 moveto 292.8 459.4 lineto 288.6 440.2 lineto 286.5 448 lineto 284.4 445.9 lineto stroke grestore 12 /Symbol fsf gsave 0 0 1 stc 307.5 443.7 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 294.4 443.7 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 300.5 449.2 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 317 443.7 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 323.1 449.2 moveto (2) show grestore gsave 0 0 1 stc 334.8 457.5 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 341.8 453.4 moveto (\346) show grestore gsave 0 0 1 stc 341.8 434.6 moveto (\350) show grestore gsave 0 0 1 stc 341.8 445.6 moveto (\347) show grestore gsave 0 0 1 stc 341.8 442.4 moveto (\347) show grestore gsave 0 0 1 stc 458.2 453.4 moveto (\366) show grestore gsave 0 0 1 stc 458.2 434.6 moveto (\370) show grestore gsave 0 0 1 stc 458.2 445.6 moveto (\367) show grestore gsave 0 0 1 stc 458.2 442.4 moveto (\367) show grestore gsave 0 0 1 stc 356.9 443.7 moveto (+) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 347.9 443.7 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 381 453.4 moveto (\346) show grestore gsave 0 0 1 stc 381 434.6 moveto (\350) show grestore gsave 0 0 1 stc 381 445.6 moveto (\347) show grestore gsave 0 0 1 stc 381 442.4 moveto (\347) show grestore gsave 0 0 1 stc 452.1 453.4 moveto (\366) show grestore gsave 0 0 1 stc 452.1 434.6 moveto (\370) show grestore gsave 0 0 1 stc 452.1 445.6 moveto (\367) show grestore gsave 0 0 1 stc 452.1 442.4 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 366.4 443.7 moveto (sin) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 387.1 448.6 393.1 448.6 line grestore gsave 0 0 1 stc 387.1 453.4 moveto (1) show grestore gsave 0 0 1 stc 387.1 434.6 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 429.4 453.4 moveto (\346) show grestore gsave 0 0 1 stc 429.4 434.6 moveto (\350) show grestore gsave 0 0 1 stc 429.4 445.6 moveto (\347) show grestore gsave 0 0 1 stc 429.4 442.4 moveto (\347) show grestore gsave 0 0 1 stc 446 453.4 moveto (\366) show grestore gsave 0 0 1 stc 446 434.6 moveto (\370) show grestore gsave 0 0 1 stc 446 445.6 moveto (\367) show grestore gsave 0 0 1 stc 446 442.4 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 396.1 443.7 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 435.5 448.6 444.5 448.6 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 437 453.4 moveto (a) show grestore gsave 0 0 1 stc 437 434.6 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 462.9 457.5 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 305.3 415.8 moveto (\346) show grestore gsave 0 0 1 stc 305.3 397 moveto (\350) show grestore gsave 0 0 1 stc 305.3 408 moveto (\347) show grestore gsave 0 0 1 stc 305.3 404.8 moveto (\347) show grestore gsave 0 0 1 stc 376.4 415.8 moveto (\366) show grestore gsave 0 0 1 stc 376.4 397 moveto (\370) show grestore gsave 0 0 1 stc 376.4 408 moveto (\367) show grestore gsave 0 0 1 stc 376.4 404.8 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 290.7 406.1 moveto (sin) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 311.4 411 317.4 411 line grestore gsave 0 0 1 stc 311.4 415.8 moveto (1) show grestore gsave 0 0 1 stc 311.4 397 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 353.7 415.8 moveto (\346) show grestore gsave 0 0 1 stc 353.7 397 moveto (\350) show grestore gsave 0 0 1 stc 353.7 408 moveto (\347) show grestore gsave 0 0 1 stc 353.7 404.8 moveto (\347) show grestore gsave 0 0 1 stc 370.3 415.8 moveto (\366) show grestore gsave 0 0 1 stc 370.3 397 moveto (\370) show grestore gsave 0 0 1 stc 370.3 408 moveto (\367) show grestore gsave 0 0 1 stc 370.3 404.8 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 320.4 406.1 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 359.8 411 368.8 411 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 361.3 415.8 moveto (a) show grestore gsave 0 0 1 stc 361.3 397 moveto (b) show grestore newpath 59 494.5 moveto 56 494.5 lineto 56 394.8 lineto 59 394.8 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 380.5 moveto (Make a function out of this.) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 367.1 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 367.1 moveto (area := unapply\(form,a,b\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 153.2 320.2 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 131.3 320.2 moveto (area) show grestore 12 /Symbol fsf gsave 0 0 1 stc 201.8 320.2 moveto (\256) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 170 320.2 moveto (\() show grestore gsave 0 0 1 stc 194.9 320.2 moveto (\)) show grestore gsave 0 0 1 stc 181.4 320.2 moveto (,) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 175.4 320.2 moveto (a) show grestore gsave 0 0 1 stc 187.4 320.2 moveto (b) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 216.6 325.1 222.6 325.1 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 216.6 329.9 moveto (1) show grestore gsave 0 0 1 stc 216.6 311.1 moveto (4) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 225.6 325.1 490.7 325.1 line grestore 12 /Symbol fsf gsave 0 0 1 stc 227.1 339 moveto (p) show grestore gsave 0 0 1 stc 236.6 348.7 moveto (\346) show grestore gsave 0 0 1 stc 236.6 329.9 moveto (\350) show grestore gsave 0 0 1 stc 236.6 340.9 moveto (\347) show grestore gsave 0 0 1 stc 236.6 337.7 moveto (\347) show grestore gsave 0 0 1 stc 352.4 348.7 moveto (\366) show grestore gsave 0 0 1 stc 352.4 329.9 moveto (\370) show grestore gsave 0 0 1 stc 352.4 340.9 moveto (\367) show grestore gsave 0 0 1 stc 352.4 337.7 moveto (\367) show grestore gsave 0 0 1 stc 260.7 339 moveto (+) show grestore gsave 0 0 1 stc 288.2 339 moveto (-) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 242.7 343.9 248.7 343.9 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 242.7 348.7 moveto (1) show grestore gsave 0 0 1 stc 242.7 329.9 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 251.7 339 moveto (b) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 270.2 343.9 276.2 343.9 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 270.2 348.7 moveto (1) show grestore gsave 0 0 1 stc 270.2 329.9 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 279.2 339 moveto (a) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 297.7 343.9 303.7 343.9 line grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 297.7 348.7 moveto (1) show grestore gsave 0 0 1 stc 297.7 329.9 moveto (2) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid newpath 350.9 354.7 moveto 315.1 354.7 lineto 310.9 335.5 lineto 308.8 343.3 lineto 306.7 341.2 lineto stroke grestore 12 /Symbol fsf gsave 0 0 1 stc 329.8 339 moveto (+) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 316.7 339 moveto (a) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 322.8 344.5 moveto (2) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 339.3 339 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 345.4 344.5 moveto (2) show grestore gsave 0 0 1 stc 357.1 352.8 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 364.1 348.7 moveto (\346) show grestore gsave 0 0 1 stc 364.1 329.9 moveto (\350) show grestore gsave 0 0 1 stc 364.1 340.9 moveto (\347) show grestore gsave 0 0 1 stc 364.1 337.7 moveto (\347) show grestore gsave 0 0 1 stc 480.5 348.7 moveto (\366) show grestore gsave 0 0 1 stc 480.5 329.9 moveto (\370) show grestore gsave 0 0 1 stc 480.5 340.9 moveto (\367) show grestore gsave 0 0 1 stc 480.5 337.7 moveto (\367) show grestore gsave 0 0 1 stc 379.2 339 moveto (+) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 370.2 339 moveto (1) show grestore 12 /Symbol fsf gsave 0 0 1 stc 403.3 348.7 moveto (\346) show grestore gsave 0 0 1 stc 403.3 329.9 moveto (\350) show grestore gsave 0 0 1 stc 403.3 340.9 moveto (\347) show grestore gsave 0 0 1 stc 403.3 337.7 moveto (\347) show grestore gsave 0 0 1 stc 474.4 348.7 moveto (\366) show grestore gsave 0 0 1 stc 474.4 329.9 moveto (\370) show grestore gsave 0 0 1 stc 474.4 340.9 moveto (\367) show grestore gsave 0 0 1 stc 474.4 337.7 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 388.7 339 moveto (sin) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 409.4 343.9 415.4 343.9 line grestore gsave 0 0 1 stc 409.4 348.7 moveto (1) show grestore gsave 0 0 1 stc 409.4 329.9 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 451.7 348.7 moveto (\346) show grestore gsave 0 0 1 stc 451.7 329.9 moveto (\350) show grestore gsave 0 0 1 stc 451.7 340.9 moveto (\347) show grestore gsave 0 0 1 stc 451.7 337.7 moveto (\347) show grestore gsave 0 0 1 stc 468.3 348.7 moveto (\366) show grestore gsave 0 0 1 stc 468.3 329.9 moveto (\370) show grestore gsave 0 0 1 stc 468.3 340.9 moveto (\367) show grestore gsave 0 0 1 stc 468.3 337.7 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 418.4 339 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 457.8 343.9 466.8 343.9 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 459.3 348.7 moveto (a) show grestore gsave 0 0 1 stc 459.3 329.9 moveto (b) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 485.2 352.8 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 327.6 311.1 moveto (\346) show grestore gsave 0 0 1 stc 327.6 292.3 moveto (\350) show grestore gsave 0 0 1 stc 327.6 303.3 moveto (\347) show grestore gsave 0 0 1 stc 327.6 300.1 moveto (\347) show grestore gsave 0 0 1 stc 398.7 311.1 moveto (\366) show grestore gsave 0 0 1 stc 398.7 292.3 moveto (\370) show grestore gsave 0 0 1 stc 398.7 303.3 moveto (\367) show grestore gsave 0 0 1 stc 398.7 300.1 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 313 301.4 moveto (sin) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 333.7 306.3 339.7 306.3 line grestore gsave 0 0 1 stc 333.7 311.1 moveto (1) show grestore gsave 0 0 1 stc 333.7 292.3 moveto (2) show grestore 12 /Symbol fsf gsave 0 0 1 stc 376 311.1 moveto (\346) show grestore gsave 0 0 1 stc 376 292.3 moveto (\350) show grestore gsave 0 0 1 stc 376 303.3 moveto (\347) show grestore gsave 0 0 1 stc 376 300.1 moveto (\347) show grestore gsave 0 0 1 stc 392.6 311.1 moveto (\366) show grestore gsave 0 0 1 stc 392.6 292.3 moveto (\370) show grestore gsave 0 0 1 stc 392.6 303.3 moveto (\367) show grestore gsave 0 0 1 stc 392.6 300.1 moveto (\367) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 342.7 301.4 moveto (arctan) show grestore gsave 0 0 1 sc 0.7 setlinewidth solid 0.7 382.1 306.3 391.1 306.3 line grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 383.6 311.1 moveto (a) show grestore gsave 0 0 1 stc 383.6 292.3 moveto (b) show grestore newpath 59 389.8 moveto 56 389.8 lineto 56 290.1 lineto 59 290.1 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 277.6 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 277.6 moveto (area\(4.,11.\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 274.7 259.2 moveto (5.386806700) show grestore 12 /Symbol fsf gsave 0 0 1 stc 340.7 259.2 moveto (p) show grestore newpath 59 285.1 moveto 56 285.1 lineto 56 257 lineto 59 257 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 242.7 moveto ( Now lets draw a picture of the triangle and the first few, say m, grestore 12 /Courier-Maple fsf gsave 0 setgray 64 229.3 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 229.3 moveto (a := 4. : b := 7.: m := 7: r[1] := rad\(a,b\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 275.4 210.9 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 266.8 210.9 moveto (r) show grestore 8 /Times-Bold-Maple fsf gsave 0 0 1 stc 271.4 207.3 moveto (1) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 292.2 210.9 moveto (1.468871126) show circles.) show grestore newpath 59 252 moveto 56 252 lineto 56 206.3 lineto 59 206.3 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 193.8 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 193.8 moveto (for i from 2 to m do r[i] := rat\(a,b\)^\(i-1\)*r[1] od:) show grestore newpath 59 201.3 moveto 56 201.3 lineto 56 192.2 lineto 59 192.2 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 179.7 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 179.7 moveto (x1 := evalf\(r[1]\);) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 277.1 161.3 moveto ( := ) show grestore 12 /Times-BoldItalic-Maple fsf gsave 0 0 1 stc 265.1 161.3 moveto (x1) show grestore 12 /Times-Bold-Maple fsf gsave 0 0 1 stc 293.9 161.3 moveto (1.468871126) show grestore newpath 59 187.2 moveto 56 187.2 lineto 56 159.1 lineto 59 159.1 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 144.8 moveto ( Get the x coordinate of the center of the ith circle i from 2 to m,\12) show grestore gsave 0 setgray 64 129.6 moveto ( use some trig.) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 116.2 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 116.2 moveto (for i from 2 to m do x.i := evalf\(x.\(i-1\) + ) show grestore gsave 1 0 0 stc 78.4 102.1 moveto (\(r[i]+r[i-1]\)*cos\(arctan\(a/b\)/2\)\) od:) show grestore newpath 59 154.1 moveto 56 154.1 lineto 56 100.5 lineto 59 100.5 lineto stroke 12 /Courier-Maple fsf gsave 0 setgray 64 88 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 88 moveto ( for i from 1 to m do cir.i := circle\([x.i,r[i]],r[i]\) od:) show grestore newpath 59 95.5 moveto 56 95.5 lineto 56 86.4 lineto 59 86.4 lineto stroke newpath 59 81.4 moveto 56 81.4 lineto 56 -208.7 lineto 59 -208.7 lineto stroke grestore grestore 306 72 (Page 4) pagenum showpage %%Page: 5 6 gsave newpath 54 720 moveto 504 0 rlineto 0 -648 rlineto -504 0 rlineto closepath clip newpath gsave 0 setgray 0.1 setlinewidth solid 12 /Courier-Maple fsf gsave 0 setgray 64 710.5 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 710.5 moveto ( display\([tri\(a,b\),cir1,cir2,cir3,cir4,cir5 ,cir6,cir7]\);) show grestore gsave 0 0 0 sc 0.1 setlinewidth solid gsave 0 0 0 sc 0.1 setlinewidth solid 1 0 0 sc 0.1 setlinewidth solid newpath 203.4 504 moveto 418.4 504 lineto 203.4 626.9 lineto 203.4 504 lineto stroke newpath 293.6 549.1 moveto 293.2 555.3 lineto 292.2 560.5 lineto 290.2 566.3 lineto 287.6 571.7 lineto 284.2 576.7 lineto 280.5 581 lineto 276.1 584.8 lineto 271.1 588.2 lineto 265.8 590.8 lineto 259.9 592.8 lineto 254.6 593.8 lineto 248.5 594.2 lineto 242.4 593.8 lineto 236.6 592.6 lineto 231.5 590.9 lineto 225.8 588.1 lineto 221.3 585.1 lineto 216.5 580.9 lineto 212.9 576.7 lineto 209.5 571.7 lineto 206.9 566.5 lineto 204.9 560.7 lineto 203.8 555.3 lineto 203.4 549.3 lineto 203.8 543 lineto 204.9 537.7 lineto 206.7 532.1 lineto 209.4 526.7 lineto 212.7 521.7 lineto 216.4 517.4 lineto 221.2 513.2 lineto 226 510 lineto 231.5 507.3 lineto 236.8 505.6 lineto 242.7 504.4 lineto 248.4 504 lineto 254.3 504.4 lineto 260.1 505.5 lineto 265.8 507.4 lineto 271.1 510.1 lineto 276.1 513.4 lineto 280.6 517.3 lineto 284.2 521.5 lineto 287.7 526.7 lineto 290.1 531.7 lineto 292.1 537.4 lineto 293.2 543 lineto 293.6 549.1 lineto stroke newpath 344.6 530.7 moveto 344.4 534.3 lineto 343.7 537.4 lineto 342.6 540.8 lineto 341 544.1 lineto 339 547 lineto 336.8 549.5 lineto 334.2 551.8 lineto 331.3 553.8 lineto 328.1 555.3 lineto 324.7 556.5 lineto 321.5 557.1 lineto 317.9 557.4 lineto 314.3 557.1 lineto 310.9 556.4 lineto 307.8 555.4 lineto 304.5 553.7 lineto 301.8 552 lineto 299 549.5 lineto 296.8 547 lineto 294.8 544 lineto 293.3 540.9 lineto 292.1 537.5 lineto 291.5 534.3 lineto 291.2 530.8 lineto 291.5 527.1 lineto 292.1 523.9 lineto 293.2 520.6 lineto 294.8 517.4 lineto 296.7 514.5 lineto 298.9 511.9 lineto 301.8 509.4 lineto 304.6 507.6 lineto 307.9 506 lineto 311 504.9 lineto 314.5 504.2 lineto 317.8 504 lineto 321.4 504.2 lineto 324.7 504.9 lineto 328.2 506 lineto 331.3 507.6 lineto 334.2 509.6 lineto 336.9 511.9 lineto 339 514.3 lineto 341.1 517.4 lineto 342.5 520.4 lineto 343.7 523.7 lineto 344.4 527.1 lineto 344.6 530.7 lineto stroke newpath 374.8 519.8 moveto 374.6 521.9 lineto 374.2 523.8 lineto 373.6 525.8 lineto 372.6 527.7 lineto 371.4 529.5 lineto 370.1 530.9 lineto 368.6 532.3 lineto 366.9 533.4 lineto 365 534.4 lineto 363 535.1 lineto 361.1 535.4 lineto 359 535.6 lineto 356.8 535.4 lineto 354.8 535 lineto 353 534.4 lineto 351 533.4 lineto 349.4 532.4 lineto 347.8 530.9 lineto 346.5 529.5 lineto 345.3 527.7 lineto 344.4 525.9 lineto 343.7 523.8 lineto 343.3 521.9 lineto 343.2 519.8 lineto 343.3 517.7 lineto 343.7 515.8 lineto 344.3 513.8 lineto 345.3 511.9 lineto 346.4 510.2 lineto 347.7 508.7 lineto 349.4 507.2 lineto 351.1 506.1 lineto 353 505.2 lineto 354.8 504.5 lineto 356.9 504.1 lineto 358.9 504 lineto 361 504.1 lineto 363 504.5 lineto 365 505.2 lineto 366.9 506.1 lineto 368.6 507.3 lineto 370.2 508.7 lineto 371.4 510.1 lineto 372.7 511.9 lineto 373.5 513.7 lineto 374.2 515.7 lineto 374.6 517.6 lineto 374.8 519.8 lineto stroke newpath 392.6 513.3 moveto 392.5 514.6 lineto 392.3 515.7 lineto 391.9 516.9 lineto 391.3 518 lineto 390.6 519.1 lineto 389.9 519.9 lineto 389 520.7 lineto 387.9 521.4 lineto 386.8 522 lineto 385.6 522.4 lineto 384.5 522.6 lineto 383.2 522.7 lineto 382 522.6 lineto 380.8 522.3 lineto 379.7 522 lineto 378.5 521.4 lineto 377.6 520.8 lineto 376.6 519.9 lineto 375.9 519.1 lineto 375.2 518 lineto 374.6 516.9 lineto 374.2 515.7 lineto 374 514.6 lineto 373.9 513.4 lineto 374 512.1 lineto 374.2 511 lineto 374.6 509.8 lineto 375.1 508.7 lineto 375.8 507.7 lineto 376.6 506.8 lineto 377.6 505.9 lineto 378.6 505.2 lineto 379.7 504.7 lineto 380.8 504.3 lineto 382 504.1 lineto 383.2 504 lineto 384.4 504.1 lineto 385.6 504.3 lineto 386.8 504.7 lineto 387.9 505.3 lineto 388.9 505.9 lineto 389.9 506.8 lineto 390.6 507.6 lineto 391.3 508.7 lineto 391.9 509.7 lineto 392.3 510.9 lineto 392.5 512.1 lineto 392.6 513.3 lineto stroke newpath 403.1 509.5 moveto 403.1 510.3 lineto 403 510.9 lineto 402.7 511.6 lineto 402.4 512.3 lineto 402 512.9 lineto 401.5 513.4 lineto 401 513.9 lineto 400.4 514.3 lineto 399.7 514.6 lineto 399 514.9 lineto 398.4 515 lineto 397.6 515 lineto 396.9 515 lineto 396.1 514.8 lineto 395.5 514.6 lineto 394.8 514.3 lineto 394.3 513.9 lineto 393.7 513.4 lineto 393.2 512.9 lineto 392.8 512.3 lineto 392.5 511.6 lineto 392.3 510.9 lineto 392.1 510.3 lineto 392.1 509.5 lineto 392.1 508.8 lineto 392.3 508.1 lineto 392.5 507.4 lineto 392.8 506.8 lineto 393.2 506.2 lineto 393.7 505.6 lineto 394.3 505.1 lineto 394.9 504.7 lineto 395.5 504.4 lineto 396.2 504.2 lineto 396.9 504 lineto 397.6 504 lineto 398.3 504 lineto 399 504.2 lineto 399.7 504.4 lineto 400.4 504.7 lineto 401 505.1 lineto 401.5 505.6 lineto 402 506.1 lineto 402.4 506.8 lineto 402.7 507.4 lineto 402.9 508.1 lineto 403.1 508.8 lineto 403.1 509.5 lineto stroke newpath 409.4 507.3 moveto 409.3 507.7 lineto 409.3 508.1 lineto 409.1 508.5 lineto 408.9 508.9 lineto 408.7 509.3 lineto 408.4 509.6 lineto 408.1 509.8 lineto 407.7 510.1 lineto 407.4 510.3 lineto 406.9 510.4 lineto 406.5 510.5 lineto 406.1 510.5 lineto 405.7 510.5 lineto 405.2 510.4 lineto 404.9 510.3 lineto 404.5 510.1 lineto 404.1 509.9 lineto 403.8 509.6 lineto 403.5 509.3 lineto 403.3 508.9 lineto 403.1 508.5 lineto 402.9 508.1 lineto 402.9 507.7 lineto 402.8 507.3 lineto 402.9 506.8 lineto 402.9 506.4 lineto 403.1 506 lineto 403.3 505.6 lineto 403.5 505.3 lineto 403.8 505 lineto 404.1 504.7 lineto 404.5 504.4 lineto 404.9 504.2 lineto 405.3 504.1 lineto 405.7 504 lineto 406.1 504 lineto 406.5 504 lineto 406.9 504.1 lineto 407.4 504.2 lineto 407.7 504.4 lineto 408.1 504.7 lineto 408.4 505 lineto 408.7 505.3 lineto 408.9 505.6 lineto 409.1 506 lineto 409.3 506.4 lineto 409.3 506.8 lineto 409.4 507.3 lineto stroke newpath 413.1 505.9 moveto 413 506.2 lineto 413 506.4 lineto 412.9 506.7 lineto 412.8 506.9 lineto 412.7 507.1 lineto 412.5 507.3 lineto 412.3 507.5 lineto 412.1 507.6 lineto 411.9 507.7 lineto 411.6 507.8 lineto 411.4 507.8 lineto 411.1 507.9 lineto 410.9 507.8 lineto 410.6 507.8 lineto 410.4 507.7 lineto 410.2 507.6 lineto 410 507.5 lineto 409.8 507.3 lineto 409.6 507.1 lineto 409.5 506.9 lineto 409.3 506.7 lineto 409.3 506.4 lineto 409.2 506.2 lineto 409.2 505.9 lineto 409.2 505.7 lineto 409.3 505.4 lineto 409.3 505.2 lineto 409.5 505 lineto 409.6 504.8 lineto 409.8 504.6 lineto 410 504.4 lineto 410.2 504.3 lineto 410.4 504.1 lineto 410.6 504.1 lineto 410.9 504 lineto 411.1 504 lineto 411.4 504 lineto 411.6 504.1 lineto 411.9 504.1 lineto 412.1 504.3 lineto 412.3 504.4 lineto 412.5 504.6 lineto 412.7 504.7 lineto 412.8 505 lineto 412.9 505.2 lineto 413 505.4 lineto 413 505.7 lineto 413.1 505.9 lineto stroke 0 0 0 sc 0.1 setlinewidth solid 0.1 418.4 502.9 418.4 504.9 line 0.1 412.3 503.4 412.3 504.4 line 0.1 406.1 503.4 406.1 504.4 line 0.1 400 503.4 400 504.4 line 0.1 393.8 503.4 393.8 504.4 line 0.1 387.7 502.9 387.7 504.9 line 0.1 381.5 503.4 381.5 504.4 line 0.1 375.4 503.4 375.4 504.4 line 0.1 369.3 503.4 369.3 504.4 line 0.1 363.1 503.4 363.1 504.4 line 0.1 357 502.9 357 504.9 line 0.1 350.8 503.4 350.8 504.4 line 0.1 344.7 503.4 344.7 504.4 line 0.1 338.5 503.4 338.5 504.4 line 0.1 332.4 503.4 332.4 504.4 line 0.1 326.3 502.9 326.3 504.9 line 0.1 320.1 503.4 320.1 504.4 line 0.1 314 503.4 314 504.4 line 0.1 307.8 503.4 307.8 504.4 line 0.1 301.7 503.4 301.7 504.4 line 0.1 295.6 502.9 295.6 504.9 line 0.1 289.4 503.4 289.4 504.4 line 0.1 283.3 503.4 283.3 504.4 line 0.1 277.1 503.4 277.1 504.4 line 0.1 271 503.4 271 504.4 line 0.1 264.8 502.9 264.8 504.9 line 0.1 258.7 503.4 258.7 504.4 line 0.1 252.6 503.4 252.6 504.4 line 0.1 246.4 503.4 246.4 504.4 line 0.1 240.3 503.4 240.3 504.4 line 0.1 234.1 502.9 234.1 504.9 line 0.1 228 503.4 228 504.4 line 0.1 221.8 503.4 221.8 504.4 line 0.1 215.7 503.4 215.7 504.4 line 0.1 209.6 503.4 209.6 504.4 line 0.1 199.1 503.9 422.8 503.9 line 0.1 201.6 626.8 205.2 626.8 line 0.1 202.5 620.6 204.3 620.6 line 0.1 202.5 614.5 204.3 614.5 line 0.1 202.5 608.3 204.3 608.3 line 0.1 202.5 602.2 204.3 602.2 line 0.1 201.6 596 205.2 596 line 0.1 202.5 589.9 204.3 589.9 line 0.1 202.5 583.8 204.3 583.8 line 0.1 202.5 577.6 204.3 577.6 line 0.1 202.5 571.5 204.3 571.5 line 0.1 201.6 565.3 205.2 565.3 line 0.1 202.5 559.2 204.3 559.2 line 0.1 202.5 553 204.3 553 line 0.1 202.5 546.9 204.3 546.9 line 0.1 202.5 540.8 204.3 540.8 line 0.1 201.6 534.6 205.2 534.6 line 0.1 202.5 528.5 204.3 528.5 line 0.1 202.5 522.3 204.3 522.3 line 0.1 202.5 516.2 204.3 516.2 line 0.1 202.5 510 204.3 510 line 0.1 201.6 503.9 205.2 503.9 line 0.1 203.4 501.4 203.4 629.3 line 8 /Helvetica-Maple fsf gsave 0 setgray 416.2 495.5 moveto (7) show grestore gsave 0 setgray 385.5 495.5 moveto (6) show grestore gsave 0 setgray 354.8 495.5 moveto (5) show grestore gsave 0 setgray 324.1 495.5 moveto (4) show grestore gsave 0 setgray 293.4 495.5 moveto (3) show grestore gsave 0 setgray 262.6 495.5 moveto (2) show grestore gsave 0 setgray 231.9 495.5 moveto (1) show grestore gsave 0 setgray 197.2 624.4 moveto (4) show grestore gsave 0 setgray 197.2 593.6 moveto (3) show grestore gsave 0 setgray 197.2 562.9 moveto (2) show grestore gsave 0 setgray 197.2 532.2 moveto (1) show grestore gsave 0 setgray 197.2 496.5 moveto (0) show grestore grestore grestore newpath 59 718 moveto 56 718 lineto 56 427.9 lineto 59 427.9 lineto stroke 12 /Helvetica-Maple fsf gsave 0 setgray 64 413.6 moveto ( We can make a word out this.) show grestore 12 /Courier-Maple fsf gsave 0 setgray 64 400.2 moveto (> ) show grestore 12 /Courier-Maple fsf gsave 1 0 0 stc 78.4 400.2 moveto (drawem := proc\(a,b,m\)\12) show grestore gsave 1 0 0 stc 78.4 386.1 moveto ( local i,r,x,cir,ar;\12) show grestore gsave 1 0 0 stc 78.4 372 moveto ( r[1] := evalf\(rad\(a,b\)\);\12) show grestore gsave 1 0 0 stc 78.4 357.9 moveto ( for i from 2 to m do r[i]:= evalf\(rat\(a,b\)^\(i-1\)*r[1] \)od:\12) show grestore gsave 1 0 0 stc 78.4 343.8 moveto ( x[1] := r[1]:\12) show grestore gsave 1 0 0 stc 78.4...

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Kentucky - MA - 114
# The Drinking Bird Problem# # # A familiar object of amusement is a glass "bird" which apparently# drinks from a glass of water.# # Picture of the bird# # # Something about how the bird works# # The bird is basically a baromometer
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws9_1.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws9_1 %DVIPSParameters: dpi=300, comments removed %DVIPSSou
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws9_2.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws9_2 %DVIPSParameters: dpi=300, comments removed %DVIPSSou
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws9_3.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws9_3 %DVIPSParameters: dpi=300, comments removed %DVIPSSou
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws11_1.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws11_1 %DVIPSParameters: dpi=300, comments removed %DVIPSS
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws11_2.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws11_2 %DVIPSParameters: dpi=300, comments removed %DVIPSS
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws11_3.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws11_3 %DVIPSParameters: dpi=300, comments removed %DVIPSS
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws11_4.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws11_4 %DVIPSParameters: dpi=300, comments removed %DVIPSS
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws11_5.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws11_5 %DVIPSParameters: dpi=300, comments removed %DVIPSS
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws11_6.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws11_6 %DVIPSParameters: dpi=300, comments removed %DVIPSS
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws12_1.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws12_1.dvi -o ws12_1.ps %DVIPSParameters: dpi=300, comment
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws12_2.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws12_2.dvi -o ws12_2.ps %DVIPSParameters: dpi=300, comment
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws12_3.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws12_3.dvi -o ws12_3.ps %DVIPSParameters: dpi=300, comment
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws12_4.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws12_4.dvi -o ws12_4.ps %DVIPSParameters: dpi=300, comment
Kentucky - MA - 114
# Lab Project II# Two identical jars of boiling water, labeled A and B, stand beside# two identical jars of ice water , labeled C and D, in a room whose# temperature remains constant. The contents of jars A and C are# immediately mixed. Jars
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: proj2.dvi %Pages: 4 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips proj2 %DVIPSParameters: dpi=300, comments removed %DVIPSSou
Kentucky - MA - 114
# # Center of mass of a solid of revolution# # If y *`=` *f(x) >= 0 for a <= x *`<=` b, then let S be the solid of# revolution obtained by rotating# the region under the graph of f around the x axis. We know how to# express the volume of S a
Kentucky - MA - 114
# Arclength # # Thm. If f' is continuous on [a,b], then the graph# of f over the interval has length > len = Int(sqrt(1+(diff(f(x),x)^2),x=a.b); b /
Kentucky - MA - 114
# Homework from Ostobee Zorn# # 8.3 Arclength# # #2 Verify that the arclength formula gives the correct# answer for the length of the graph of y = mx +b from# x =0 to x = 1.# # Solution: The correct answer is the distance from (0,b)# to
Kentucky - MA - 114
# Present Value # # In the continuous compound interest formula, # A = P*e^(rt),# P is referred to as the 'present value' of A t years from# now if money grows at 100r percent yearly with continuous# compounding of interest. So for exampl
Kentucky - MA - 114
# Ostobee Zorn Chapter 9# # 9.1 #7 The hint is not needed.# > with(student);Warning, new definition for D[D, Diff, Doubleint, Int, Limit, Lineint, Product, Sum, Tripleint, changevar, combine, completesquare, distance, equate, extrema
Kentucky - MA - 114
-# Notes on project 2:# # This problem involves ideas like those needed in project 2.# # Given a right triangle with legs a and b. Inscribe a circle c1, then# heading off towards one of the acute angles, inscribe an infinite # chain of ci
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws1.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws1 %DVIPSParameters: dpi=300, comments removed %DVIPSSource:
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws2.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips -p1 -l1 ws2 %DVIPSParameters: dpi=300, comments removed %DVIP
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: ws3.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips ws3 %DVIPSParameters: dpi=300, comments removed %DVIPSSource:
Kentucky - MA - 114
# Ostobee Zorn vol 2> # P. 46, no 3. # # This problem asks for the left, tight, and midpint regular estimates of an intgral, which the book abbreviates# as # > L[n] = Sum(f(x[i])*Delta[n],i=0.n-1);M[n] = Sum(f(x[i]+x[i+1])/2)*Delta[n],i
Kentucky - MA - 114
> # NOTES ON MA114 HOMEWORK 5.1-5.3# # # # p.12, no 7# # The car's velocity at time t is 60-20*t. # > Int(60-20*t,t=0.4);\> int(60-20*t,t=0.4);\# Since this number is positive and east is the positive direction the# # net effect of th
Kentucky - MA - 114
# Calculus II - notes 9/11# # Ostobee Zorn# # 11. page 47 # Evaluate limit 2/n *sum(2*j/n)^3,j=1.n) as n goes to infinity.> s := n -> 2/n *sum(2*j/n)^3,j=1.n); > n - /
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: hw3.dvi %Pages: 6 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips hw3 %DVIPSParameters: dpi=300, comments removed %DVIPSSource:
Kentucky - MA - 114
# 7.1 > with(student);[D, Diff, Doubleint, Int, Limit, Lineint, Product, Sum, Tripleint, changevar, combine, completesquare, distance, equate, extrema, integrand, intercept, intparts, isolate, leftbox, leftsum, makeproc, maximiz
Kentucky - MA - 114
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: skills1.dvi %Pages: 4 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips skills1 %DVIPSParameters: dpi=300, comments removed %DVIP