Constructible polygonsI 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?

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Constructible polygonsI know certain polygons can be constructed while others cannot. Here is Gauss&#039; 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?

pokajalaq1 · Accepted Answer

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

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?

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