cos(2pi/n) is constructible iff n=2^r p_1 p_2 cdots p_k, where each pi is a Fermat prime. Can this is be used to determine the constructibility of a regular p_2 polygon? If so how and what would be the cos(2pi/n) here?

logosdepmpe

logosdepmpe

Answered question

2022-08-11

Constructible polygons
I know certain polygons can be constructed while others cannot. Here is Gauss' Theorem on Constructions:
cos ( 2 π / n ) is constructible iff n = 2 r p 1 p 2 · · · p k , where each p i is a Fermat prime.
Can this is be used to determine the constructibility of a regular p 2 polygon? If so how and what would be the cos ( 2 π / n ) here?

Answer & Explanation

pokajalaq1

pokajalaq1

Beginner2022-08-12Added 18 answers

Explanation:
The p i have to be distinct Fermat primes, so a regular polygon with p 2 sides is constructible only when p = 2.

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