ClipArt ETC
Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found using Ptolemy's theorem. The lines that are bolded form a quadrilateral. Ptolemy's theorem says the square of b equals the sum of a squared and ab, which in turn gives the golden ratio.

Golden Ratio In A Pentagon

Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found…