Side Lengths of Equiangular Polygons (as seen by a coding theorist)

Abstract

A tuple a = (a₁,…,a_n) of positive real numbers is said to be equiangular if there is an equiangular polygon with consecutive side lengths a₁,…,a_n. It is well known that a is equiangular if and only if the polynomial a(x) = a₁ + a₂x + … + a_n-1x^n-2 + a_nx^n-1 vanishes at . Here we dispense with complex numbers and borrow an idea from the theory of cyclic codes to prove that a is equiangular if and only if a(x) is divisible by .