# Golden Ratio In A Pentagon

## Description

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.

## Keywords

circle, circumscribed, divine section, extreme ratio, golden cut, golden mean, golden proportion, golden ratio, golden section, inscribed, mean ratio, medial section, ptolemy, Ptolemy's theorem, regular pentagon

## Galleries

## Source:

Florida Center for Instructional Technology *Clipart ETC* (Tampa: University of South Florida, 2007)