cp's OEIS Frontend

Starting with a golden triangle whose base is of length 1 and whose sides are of length phi = (1+sqrt(5))/2, create the next golden triangle at the base of the previous triangle, i.e., sides length = 1 and base length = phi-1, and so on. a(n) is the floor of the curvature (inverse of the radius) of the circle inscribed in the n-th triangle.

The golden triangles created by this process are the same as the golden triangles inscribed in a logarithmic spiral.

The logarithmic spiral can be approximated by circular arcs of radii 1, phi-1, (phi-1)^2, ... which are the sides of bisected golden gnomons and center located at their related apex. The sequence whose n-th term is the curvature (rounded down) of the n-th such circular arc is A014217. See illustration in link.

a(n) is the curvature (rounded down) of circles inscribed in minor segment where chord length equal to sagitta length starting from a unit circle, the next iterations are nested down at scale factor 4/5. The curvature of circles inscribed in major segment would be A065565: floor((5/4)^n). See illustrations.