Lune (geometry)

In plane geometry, the crescent shape formed from two intersecting circles is called a lune (in gray). There are two lunes in each diagram only one of which is shaded

In plane geometry, a lune is the concave-convex area bounded by two circular arcs, while a convex-convex area is termed a lens. ^[1] The word "lune" derives from luna, the Latin word for Moon.

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 A and B are disks, then $L = A - A \cap B$ is a lune.

Example

In the 5th century BC, Hippocrates of Chios showed that certain lunes could be exactly squared by straightedge and compass.

See also

• Arbelos
• Crescent
• Gauss–Bonnet theorem

References

1. "Google Groups". Groups.google.com. Retrieved 2015-12-27.

• Weisstein, Eric W., "Lune", MathWorld.

External links

• The Five Squarable Lunes at MathPages