Posts tagged 'pentagon'

F.23 Golden Triangles

In the acute golden isosceles triangle ABC with base AB = 1, legs AC = BC = phi, and angles 72-72-36 degrees, bisecting base angle B meets AC at D such that CD = 1, DA = phi - 1 = 1/phi, and BD = AB = 1, partitioning ABC into a smaller golden triangle BCD and a golden gnomon ABD.

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.