Lune of Hippocrates

Drawing the Lune of Hippocrates

Isosceles Triangle

1. Draw a right-angled isosceles triangle AOB.

Triangle and Arc

2. With center O, plot an arc between points AB.

Lune of Hippocrates

3. At Point M, which is the midpoint of the hypotenuse in triangle AOB, draw another arc between points AB.

The outside, in green, is the lune of Hippocrates.

Area of the Lune

Area of the lune = area of the semicircle − area of circular segment.

Area of the lune = area of the semicircle − (area sector − area of triangle)

Area of the Lune of Hippocrates Formula

Lune of Hippocrates Formula