The picture by Dr. Reza Sarhangi (taken from MSRI web site) describes the construction of a regular 17-gon. The famous mathematician Carl Friedrich Gauss (1777-1855) discovered this construction in 1796 when he was eighteen years old.
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This page contains syllabus and problems of the workshop WSE187 (Spring 2005) in mathematics organized
by Dusa McDuff and Valentina Kiritchenko. In this workshop, we explore constructions using
a compass and a ruler. What
regular n-gons can be constructed using only a compass and a ruler?
Since complex numbers are essential for solving this
problem we review complex numbers and some of their applications.
For instance, using complex numbers we
show that the regular 5-gon is constructible, but the regular
7-gon is not. And how to construct a regular 15-gon? The picture by Dr. Reza Sarhangi (taken from MSRI web site) describes the construction of a regular 17-gon. The famous mathematician Carl Friedrich Gauss (1777-1855) discovered this construction in 1796 when he was eighteen years old. |
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February 17,22
We explore some basic constructions using a compass and a ruler. We construct
an equilateral triangle, a square and a regular octagon. We show that if lengths 1, a and b
are constructible, then so are ab, a/b and the square root of a.
February 24, March 1
We study complex numbers and their relation to regular polygons. We see how solving the
equation x^5=1 helps to
construct a regular pentagon.
March 3,8
Projects