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From Euclid to Spigotry
Assignment 10 (outline 9)
Last modified: September 14, 2004
1. Another (perhaps better) way to describe the quadratrix of Hippias is by using polar coordinates.
Choose a circle of radius 1.
For a point on the quadratrix,
let q denote the angle with the
y axis (it would be more conventional
to use the x axis) and let r denote the
distance from the origin.
A point is on the quadratrix if

Show that this translates into
r = 
and find the value of r in the limit
as q approaches 0.

2. Vieta used a square as his starting point, but he could also have used a hexagon as Archimedes did.

a. Determine what formula for p this would lead to.  In the denominator you will have factors
like  and