Definition of Spherical excess. Meaning of Spherical excess. Synonyms of Spherical excess

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Definition of Spherical excess

Spherical excess
Excess Ex*cess", n. [OE. exces, excess, ecstasy, L. excessus a going out, loss of self-possession, fr. excedere, excessum, to go out, go beyond: cf. F. exc[`e]s. See Exceed.] 1. The state of surpassing or going beyond limits; the being of a measure beyond sufficiency, necessity, or duty; that which exceeds what is usual or prover; immoderateness; superfluity; superabundance; extravagance; as, an excess of provisions or of light. To gild refined gold, to paint the lily, To throw a perfume on the violet, . . . Is wasteful and ridiculous excess. --Shak. That kills me with excess of grief, this with excess of joy. --Walsh. 2. An undue indulgence of the appetite; transgression of proper moderation in natural gratifications; intemperance; dissipation. Be not drunk with wine, wherein is excess. --Eph. v. 18. Thy desire . . . leads to no excess That reaches blame. --Milton. 3. The degree or amount by which one thing or number exceeds another; remainder; as, the difference between two numbers is the excess of one over the other. Spherical excess (Geom.), the amount by which the sum of the three angles of a spherical triangle exceeds two right angles. The spherical excess is proportional to the area of the triangle.

Meaning of Spherical excess from wikipedia

- Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles...
- Look up excess or excessive in Wiktionary, the free dictionary. Excess may refer to: Angle excess, in spherical trigonometry Insurance excess, similar...
- radiometric quantities radiant intensity and radiance Calculating spherical excess E of a spherical triangle The calculation of potentials by using the boundary...
- The amount by which the sum of the angles exceeds 180° is called the spherical excess, denoted as Ε or Δ. Specifically, the sum of the angles is 180° × (1...
- Spherical geometry or spherics (from Ancient Gr**** σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of...
- the spherical triangle exceed the corresponding angles of the planar triangle by approximately one third of the spherical excess (the spherical excess is...
- spherical excess or solid angle measure. The angle measure of a complete great circle is 2 π {\displaystyle 2\pi } radians, and the spherical excess of...
- {\displaystyle \Omega =q\theta -(q-2)\pi .\,} This follows from the spherical excess formula for a spherical polygon and the fact that the vertex figure of the polyhedron...
- dividing squared side length by the spherical excess E , {\displaystyle E,} we obtain a non-vanishing ratio, the spherical trigonometry relation: tan 2 ⁡ 1...
- (coordinated) points. In geodetic operations the observations are adjusted for spherical excess and projection variations. Precise angular measurements between lines...