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.
[2] Formally, a lune is the relative complement of one disk in another (where they intersect but neither is a subset of the other).
In 1771 Leonhard Euler gave a general approach and obtained a certain equation to the problem.
In 1933 and 1947 it was proven by Nikolai Chebotaryov and his student Anatoly Dorodnov that these five are the only squarable lunes.