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17-gon

John Fredsted 2243
February 04 2008
2

Searching for something completely different (it sounds almost like Monty Python), yesterday I stumbled over the conversion of trigonometric expressions to radicals, see ?convert,radical, and I became intrigued: would Maple be able to convert cos(2*Pi/17) to radicals? It was not.

Gauss was the first to show that the 17-gon could be constructed using compass and straightedge. The expression 16*cos(2*Pi/17) in terms of radicals can be found at the Wikipedia page Heptadecagon.

It made me wonder: what are the limitations of the Maple conversion of trigonometric expressions to radicals?
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