lune

In geometry, a lune is a shape on a plane or sphere bounded by two intersecting arcs or great circles. The term "lune" comes from the Latin word for "moon".1

Historically, mathematicians like Hippocrates of Chios explored the concept of "squaring the lune," which means expressing the area of a lune as a rectilinear area. In a specific case, the combined area of two lunes created around the sides of a right triangle was found to be exactly equal to the area of the triangle itself. This discovery was significant because it showed that curved shapes could sometimes be measured with straight-edged geometry, a concept that fueled attempts to solve the even more challenging problem of "squaring the circle".2