Originally published at: Why did this famous mathematician want a 17-sided shape on his tombstone? - Boing Boing
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I tried performing the construction once- it ain’t easy. Honestly i think i came pretty close, but when you have to walk the line segment around 17 times, the error adds up!
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For those curious…
If you can make a 3-gon and a 5-gon, and you do so in the same circle, you can find the length needed to make a 15-gon. With that sort of trick one can reduce to p^n-gons where p is prime.
Gauss figured out that you can make a p-gon iff p is 1 more than a power of 2. This is basically because one’s trying to find the complex numbers solving z^p=1, but not z=1, so one faces a polynomial of degree p-1. Why power of 2? Because intersecting a line with a circle, or circle with circle, lets you find square roots of numbers you already have. Then fourth roots, eighth roots, …
I had a homework problem once to invent the construction, but not to actually carry it out. Supposedly there’s a satchel in Gottingen full of the details of the 65537-gon.
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