Lune (geometry)

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Lune" geometry – news · newspapers · books · scholar · JSTOR (July 2021) (Learn how and when to remove this message)

In plane geometry, the crescent shape formed by two intersecting circles is called a lune. In each diagram, two lunes are present, and one is shaded in grey.

In plane geometry, a lune (from Latin luna 'moon') is the concave-convex region bounded by two circular arcs.^[1] It has one boundary portion for which the connecting segment of any two nearby points moves outside the region and another boundary portion for which the connecting segment of any two nearby points lies entirely inside the region. A convex-convex region is termed a lens.^[2]

Formally, a lune is the relative complement of one disk in another (where they intersect but neither is a subset of the other). Alternatively, if ${\displaystyle A}$ and ${\displaystyle B}$ are disks, then ${\displaystyle A\smallsetminus A\cap B}$ is a lune.