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From Euclid to Spigotry
Assignment 7 (topic 7)
Last modified: September 14, 2004
You can do everything on this piece of paper and hand it in.

1. Here is a line segment of length 1.
In the space below, using your compass
and a marked ruler, construct a segment of length 
. Measure its length and the length
of the given segment, cube the ratio
using a calculator, and see how close
to 2 the result is.

2. If you try to trisect a 60 degree angle (3q = 60 degrees), and let y = cos q, what
cubic equation with integer coefficients is satisfied by y? (Note: at the top of p. 34, Bold is using x = 2 cos q to get a simpler cubic equation.)
According to the theorem that Bold cites in the last paragraph on p. 34, what are the only candidates for rational roots of this cubic?  Try them and show that they all fail.