Area on a sphere bounded by two semicircles joined at antipodal points
For the plane geometry region, see Lune (geometry).
This article is about the surface. For the volume, see Spherical wedge.
The two great circles are shown as thin black lines, whereas the spherical lune (shown in green) is outlined in thick black lines. This geometry also defines lunes of greater angles: {2}π-θ, and {2}2π-θ.
In spherical geometry, a spherical lune (or biangle) is an area on a sphere bounded by two half great circles which meet at antipodal points.[1] It is an example of a digon, {2}θ, with dihedral angle θ.[2] The word "lune" derives from luna, the Latin word for Moon.
^Davis, Elwyn H. (1999). "Area of spherical triangles". The Mathematics Teacher. 92 (2): 150–153. doi:10.5951/MT.92.2.0150. JSTOR 27970882.
In spherical geometry, a sphericallune (or biangle) is an area on a sphere bounded by two half great circles which meet at antipodal points. It is an...
in transforming polyhedra. A sphericallune is a digon whose two vertices are antipodal points on the sphere. A spherical polyhedron constructed from such...
In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a sphericallune (termed the wedge's base). The angle...
In spherical geometry, an n-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite...
Lune of Hippocrates, in geometry, a plane region bounded by arcs of circles and amenable to quadrature Sphericallune, a 3-dimensional lune Ted Lune (1920–1968)...
In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded...
polygons may have any number of sides greater than 1. Two-sided spherical polygons—lunes, also called digons or bi-angles—are bounded by two great-circle...
technique for the measurement of the specific surface area of materials Spherical area Surface integral Weisstein, Eric W. "Surface Area". MathWorld. "Schwarz's...
hosohedra. On a spherical surface, the regular polyhedron {2, n} is represented as n abutting lunes, with interior angles of 2π/n. All these lunes share two...
dual, a hosohedron, {2,1} has two antipodal vertices at the poles, one 360° lune face, and one edge (meridian) between the two vertices. Look up monogon in...
or torus. For example, digon can be realised non-degenerately as a sphericallune. A monogon {1} could also be realised on the sphere as a single point...
allowed; for example, a spherical triangle degenerates to an underspecified lune if two of the vertices are antipodal. The point antipodal to a given point...
squares as five cubes. Two clusters of faces of the bilunabirotunda, the lunes (each lune featuring two triangles adjacent to opposite sides of one square),...
classical convex polytopes may be considered tessellations, or tilings, of spherical space. Tessellations of euclidean and hyperbolic space may also be considered...
small set of axioms. He also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour. In addition to the Elements...
astronomical position calculated from an ephemeris is often given in the spherical polar coordinate system of right ascension and declination, together with...
April 9, 1860, when Scott recorded someone singing the song "Au Clair de la Lune" ("By the Light of the Moon") on the device. However, the device was not...
proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality. A variety...
the Apocalypse is the Virgin of Guadalupe. The crescent shape is a type of lune, the latter consisting of a circular disk with a portion of another disk...
regular tilings, the hosohedra, {2,n} with 2 vertices at the poles, and lune faces, and the dual dihedra, {n,2} with 2 hemispherical faces and regularly...
1949, p. 149), (Korevaar 2004, p. 10) and (Lune 1986, p. 2, §1.1 "Tauber's first theorem"). See also (Lune 1986, p. 2, §1.1 "Tauber's first theorem")...
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