Lune (mathematics)
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, a lune is either of two figures, both shaped roughly like a crescent Moon. The word "lune" derives from luna, the Latin word for Moon.In plane geometry, a lune is a concave area bounded by two arcs. The corresponding convex shape is a lens.In spherical geometry, a lune is an area on a sphere bounded by two half great circles, which is also called a digon or a diangle or (in German) a Zweieck. Great circles are the largest possible circles on a sphere; eac...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, a lune is either of two figures, both shaped roughly like a crescent Moon. The word "lune" derives from luna, the Latin word for Moon.In plane geometry, a lune is a concave area bounded by two arcs. The corresponding convex shape is a lens.In spherical geometry, a lune is an area on a sphere bounded by two half great circles, which is also called a digon or a diangle or (in German) a Zweieck. Great circles are the largest possible circles on a sphere; each great circle divides the surface of the sphere into two equal halves. Two great circles always intersect at two polar opposite points. Common examples of great circles are lines of longitude (meridians), which meet at the North and South Poles. Thus, the area between two meridians of longitude is a lune. The area of a spherical lune is 2 R2, where R is the radius of the sphere and is the dihedral angle between the two half great circles. When this angle equals 2 i.e., when the second half great circle has moved a full circle, and the lune in between covers the sphere the area formula for the spherical lune gives 4 R2, the surface area of the sphere.
