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Chapter12Sec6ShowCode

Chapter12Sec6ShowCode - Initialization Cells(Code Needed...

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Initialization Cells (Code Needed for Most Plot3D Statements) In[42]:= ticks @ min_,max_ D : = Join @ Table @8 i,If @ i 0, ,Style @ i,12 DD , 8 0.01,0 << , 8 i,Ceiling @ min D ,Floor @ max D , 2 <D , H * Numbered ticks * L Table @8 j, , 8 0.01,0 << , 8 j,Round @ min D ,Round @ max - 1 D ,1 <DD H * Un - numbered ticks * L H * 2D Options * L SetOptions @ Plot, ImageSize fi 350, AxesOrigin fi 8 0,0 < , AspectRatio fi 1, AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks D ; H * 3D Options * L SetOptions @ Plot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False,AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; SetOptions @ ContourPlot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False,AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; SetOptions @ ParametricPlot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False,AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None,
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ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; SetOptions @ RegionPlot3D, ImageSize fi 600, BoxRatios fi 1,Boxed fi False,AxesOrigin fi 8 0,0,0 < , AxesStyle fi Directive @ Medium, Bold D , Ticks fi ticks, Mesh fi None, ViewPoint fi 8 2,0.9,1 < , ViewVertical fi 8 0,0,1 < D ; Chapter 12 : Vectors and the Geometry of Space 2 Chapter12Sec6.nb
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Section 12.6: Cylinders and Quadric Surfaces Cylinders ª Definition A cylinder is a surface that consists of all lines (called rulings ) that are parallel to a given line and pass through a given plane (i.e. 2D) curve. Chapter12Sec6.nb 3
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In[48]:= GraphicsGrid @8 8 Show @ ContourPlot3D @ x^2 + y^2 9, 8 x, - 4.5, 4.5 < , 8 y, - 4.5, 4.5 < , 8 z, - 5, 5 < D , Graphics3D @ Text @ Style @ x, Large D , 8 5.2,0,0 <DD , H * Label the x - axis * L Graphics3D @ Text @ Style @ y, Large D , 8 0,5,0 <DD , H * Label the y - axis * L Graphics3D @ Text @ Style @ z, Large D , 8 0,0,6.2 <DD , H * Label the z - axis * L PlotLabel -> Style @ "Circular Cylinder", Large D H * Label the plot * L D , Show @ ContourPlot3D @ z y^2 - 3, 8 x, - 4.5, 4.5 < , 8 y, - 4.5, 4.5 < , 8 z, - 5, 5 < D , Graphics3D @ Text @ Style @ x, Large D , 8 5.2,0,0 <DD , H * Label the x - axis * L Graphics3D @ Text @ Style @ y, Large D , 8 0,5,0 <DD , H * Label the y - axis * L Graphics3D @ Text @ Style @ z, Large D , 8 0,0,6.2 <DD , H * Label the z - axis * L PlotLabel -> Style @ "Parabolic Cylinder", Large D H * Label the plot * L D < < , ImageSize fi 600 D Out[48]= Circular Cylinder x y z - 4 - 2 2 4 - 4 - 2 2 4 - 5 - 3 - 1 1 3 5 Parabolic Cylinder x y z - 4 - 2 2 4 - 4 - 2 2 4 - 5 - 3 - 1 1 3 5 4 Chapter12Sec6.nb
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Quadric Surfaces ª Definition A quadric surface is the graph of a second-degree equation in three variables, x, y, z . The most general such equation is Ax 2 + By 2 + Cz 2 + Dxy + Eyz + Fxz + Gx + Hy + Iz = J , where A,B,C,D,E,F,G,H,I,J are constants. In[49]:= GraphicsGrid @8 8 Show @ ContourPlot3D @ x^2 + y^2 9 + z^2 4 1, 8 x, - 3.5, 3.5 < , 8 y, - 3.5, 3.5 < , 8 z, - 3,3 < , Mesh fi 3 H * Draws the grid on the surface * L D , Graphics3D @ Text @ Style @ x, Large D , 8 4.2,0,0 <DD , H * Label the x - axis * L Graphics3D @ Text @ Style @ y, Large D , 8 0,4,0 <DD , H * Label the y - axis * L Graphics3D @ Text @ Style @ z, Large D , 8 0,0.6,3.2 <DD , H * Label the z - axis * L PlotLabel -> Style @ "Ellipsoid", Medium D H * Label the plot * L D , Show @ ContourPlot3D @ z 4x^2 + y^2, 8 x, - 2.5, 2.5 < , 8 y, - 3.5, 3.5 < , 8 z, - 2, 5 < , Mesh fi 3 D , Graphics3D @ Text @ Style @ x, Large D , 8 3.2,0,0 <DD , H * Label the x - axis * L Graphics3D @ Text @ Style @ y, Large D , 8 0,3.8,0 <DD , H * Label the y - axis * L
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