Exploring the lunes of Hippocrates in a dynamic geometry environment

Abstract

These classroom notes offer methods of solving the quadrature of lunes, that is, the area of croissant-shaped plane figures bounded by two intersecting non-congruent circular arcs, using Hippocrates of Chios’ area conservation and similarity arguments. I also offer a method of using history in the classroom with students via dynamic geometry snapshots presented in a manner that complements the analytic and the visual approaches.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ The word ‘trapezium’ is used elsewhere in the article.