# Pythagoras, semicircles and lunes - Lesson+Exploration

- Author:
- Simona Riva

- Topic:
- Area, Circle, Rectangle, Right Triangles, Triangles

A

*lune*is a*bidimensional surface*bounded by*two arcs*of a*circle*having*different radii*.*Hippocrates of Chios*, the founder of the Athenian school of geometry, who lived in Athens in 450-420 a.C, was the first mathematician to study the problem of*squaring the lunes*, and he showed that the*ratio of the areas of two circles is equal to the ratio of the squares constructed on their diameters*. This result is named*squaring*because it shows that a*curvilinear area*is*equivalent*to another one,*bounded by segments*, so it can be easily calculated and built with compass and straightedge. The GeoGebra applet shows a result derived from the theorem stated above.