Equiangular Polygons Research Articles

The Equilateral and the Equiangular Polygon

Since an n-gon is determined by 2n − 3 conditions, and n − i conditions are involved in its being equilateral, there are still in the case of an equilateral n-gon n − 2 conditions to be determined. These n − 2 conditions cannot all be given in terms of the angles, since an infinite number of n-gons may always be described similar to, out not necessarily congruent with, any given equilateral n-gon. Hence only n − 3 of the angles of an equilateral n-gon may be assigned arbitrarily, and there must therefore be 3 independent relations connecting the angles of any equilateral n-gon. These three conditions may be obtained by projecting the perimeter of the n-gon on any three lines.