Golden Gnomon

The golden gnomon is the obtuse isosceles triangle whose ratio of side to base lengths is given by , where  is the golden ratio. Such a triangle has angles of -- and can be constructed from a regular pentagon as illustrated above in red. The corresponding 36-72-72 triangle with side-to-base ratio  is a golden triangle.

Golden triangles and gnomons can be dissected into smaller triangles that are golden gnomons and golden triangles (Livio 2003, p. 79).

REFERENCES:

Livio, M. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books, p. 79, 2002.