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From Euclid to Spigotry
Assignment 21 (outline 17)
Last modified: September 15, 2004
1. Show that for the heptadecagon, z2 z8 = y4 in the notation of the handout.  This means that
z2 z8 are the solutions of the quadratic equation z2 - y2 z + y4 = 0.
The diagram on the next page shows a partially completed version of Richmond's construction. The line IG,
not usually shown, is perpendicular to IE, and it is needed to get the right angle that is bisected
to construct IF.
Show that point G has coordinate y4/4. You already know that F has coordinate y2/4. Using
the same approach that Richmond used to construct z3/2 and z5/2, draw two circles to construct
z2/2 and z8/2. You will construct z2/2 accurately, but z8/2 is so close to -1 that it will be hard to get it correct because of roundoff errors in the computer-drawn diagram.