This preview shows page 1. Sign up to view the full content.
Unformatted text preview: show that the equation of the quadratrix in polar coordinates is r sin = 2 a. (b) Show that if P is on the arc of the circle in the Frst quadrant, then the angle POA can be trisected as follows: let F be the intersection of OP with the quadratrix, and let FH be the vertical line segment to the xaxis. If F is onethird the way from H to F along this segment, and F L is a horizontal segment with L on the quadratrix, then show that LOA = 1 3 POA . (c) i. Show that if the quadratrix intersects OA at G , then OG = 2 a . (You can use calculus here: in the proof by Dinostratus ( ca. 390320 BC ), it is done by contradiction, using only Euclidean geometry.) ii. Conclude from this that CA : OA = OA : OG. iii. Show how, in light of this, we can construct a line segment equal in length to CA . iv. Show that a rectangle with one side equal to twice this line segment and the other equal to a has the same area as the circle of radius a ....
View
Full
Document
This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Conic Sections

Click to edit the document details