Digon

A lune, also spherical Zweieck, Kugelzweiseit, ball spline or gore is in the spherical geometry ( spherical geometry ) a set of points, which is bounded by two great circles. On the globe forms as the two meridians area enclosed by a lune, with north and south poles of the earth are the corners.

The two corners of any Kugelzweiecks lie on the sphere exactly opposite. The side lengths are respectively 180 °. The two interior angles are equal.

Applies to the area of ​​the Kugelzweiecks (the surface of the entire sphere):

Here are

• The size of an interior angle ( in degrees)
• R is the radius of the sphere.

Is given in radians, can the formula be written as:

For example, on the earth's surface has a lune which is delimited by two adjacent meridians ( So = 1 ° ), the surface