Spherical Excess

spherical excess

[′sfir·ə·kəl ek′ses] (mathematics) The sum of the angles of a spherical triangle, minus 180°.

Spherical Excess

the difference between the sum of the angles of a spherical triangle and 180°—that is, the amount by which the sum is greater than the sum of the angles of a plane triangle.

The sum of the angles of a triangle formed by three geodesies on a surface of positive curvature—that is, on a convex surface—is always greater than two right angles and is equal to

π + ʃʃ K dS

where K is the total curvature of the surface and dS is the element of area of the surface. The spherical excess of a spherical triangle formed by great circles on a sphere of radius R is

where S is the area of the triangle. In the case of small spherical triangles on the surface of the earth, the quantity ∊, in seconds of arc, is given by the formula

Here, a and b are the lengths of two sides of the triangle, and C is the angle between the two sides.

单词	spherical excess
释义	spherical excess spherical excess n. The difference between the sum of the angles of a spherical triangle and the sum of the angles of a plane triangle. Spherical Excess spherical excess [′sfir·ə·kəl ek′ses] (mathematics) The sum of the angles of a spherical triangle, minus 180°. Spherical Excess the difference between the sum of the angles of a spherical triangle and 180°—that is, the amount by which the sum is greater than the sum of the angles of a plane triangle. The sum of the angles of a triangle formed by three geodesies on a surface of positive curvature—that is, on a convex surface—is always greater than two right angles and is equal to π + ʃʃ K dS where K is the total curvature of the surface and dS is the element of area of the surface. The spherical excess of a spherical triangle formed by great circles on a sphere of radius R is where S is the area of the triangle. In the case of small spherical triangles on the surface of the earth, the quantity ∊, in seconds of arc, is given by the formula Here, a and b are the lengths of two sides of the triangle, and C is the angle between the two sides. ThesaurusSeespherical trigonometry
随便看	functional area records manager functional area representative function(al) area requirement functional area requirements specification functional areas functional area segment specification functional area services functional area sponsor functional area strategic plan functional area subsystem functional area supervisor functional area team functional arguments functional asplenia functional assessment functional assessment completion notice functional assessment conduct notice functional assessment measure functional assessment observation form functional assessment of academic behavior functional assessment of anorexia/cachexia therapy functional assessment of cancer therapy fatigue functional assessment of cancer therapy-general functional assessment of cancer therapy - head and neck functional assessment of cancer therapy prostate module