2 Feb
2020
2 Feb
'20
7:41 p.m.
On 02/02/2020 18:49, Keith F. Lynch wrote:
If a regular polygon with N sides is constructable with compass and straight-edge alone, then N expressed in binary is a palindrome followed by zero or more zeros.
Gauss proved that N has to be a product of distinct primes 2^2^n+1 times some power of 2. The power of 2 gives you zeros at the end. The other factors give you something palindromic: if some product using n<N is palindromic then multiplying by 2^2^N+1 gives you another palindrome because we're taking two copies of its bits and they are separated by just enough 0s that they can't collide. -- g