WOLFRAM|DEMONSTRATIONS PROJECT

The Lunes of Hippocrates

​
P
area of left lune = 0.2601
area of right lune = 0.5531
area of triangle = 0.8132
total area of the lunes = area of the triangle
The triangle in the semicircle has a right angle at
P
. The sum of the areas of the two lunes (or crescents) is equal to the area of the triangle.