Golden Triangle and Spiral

In a golden triangle, i.e. an isosceles triangle whose ratio side/base is [math]\phi[/math], and having angles of 36°, 72°, 72°, subtracting a golden gnomon - that is an isosceles triangle having sides equal to the golden ratio of the longest triangle side - you obtain a golden triangle. Therefore it is possible to decompose the given triangle into an infinite sequence of triangles having the same property, fixing a direction and determining the intersection of the base angle bisector with the opposite side of each triangle. Drawing circumference arcs having width equal to the vertex angle of the gnomon, 108°, you obtain a golden logarithmic spiral.

The Golden Spiral