Posts tagged 'decagon'

F.40 Regular Polygons and Nested Radicals

For a regular N-gon inscribed in a unit circle (R = 1), doubling the number of sides maps edge length E_{N/2} to E_N = sqrt(2 - sqrt(4 - E_{N/2}^2)), generating closed-form nested quadratic radicals for the 2^k, 3*2^k, 5*2^k, and 15*2^k polygon families.