- Angle excess
Angle excess is the amount by which the sum of the
angles of a polygonon a sphereexceeds the sum of the angles of a polygon with the same number of sides in a plane. For instance, a plane trianglehas an angle sum of 180°; an octantis a spherical trianglewith three right angles, so its angle sum is 270°, and its angle excess is 90°. The angle excess of any polygon on a sphere is proportional to the polygon's area, with the proportionality constant being the reciprocal of the square of the sphere's radius.
surveying, one checks whether the angles and distances form a closed polygon, and by how much it is off. If the area is sufficiently large, the polygon will not close no matter how accurately measured if it is calculated on a plane. The area of a polygon whose angle excess is 1 second of arc, which is the precision (though not necessarily the accuracy) of surveying, is 393 square kilometres, or about 20 kilometres square.
Angle deficit is defined similarly on a
pseudosphere, and is likewise proportional to area in hyperbolic geometry.
Wikimedia Foundation. 2010.
Look at other dictionaries:
Angle of Climb — In aerodynamics, angle of climb is the ratio between distance travelled over the ground and altitude gained. The angle of climb can be expressed as the angle between a plane horizontal to the earth s surface and the actual flight path followed by … Wikipedia
Angle grinder — An angle grinder is a handheld power tool used for cutting, grinding and polishing.Angle grinders can be powered by an electric motor, petrol engine or compressed air. The motor drives a geared head at a right angle on which is mounted an… … Wikipedia
Solid angle — The solid angle, Ω , is the angle in three dimensional space that an object subtends at a point. It is a measure of how big that object appears to an observer looking from that point. For instance, a small object nearby could subtend the same… … Wikipedia
Spherical excess — Spherical Spher ic*al, Spheric Spher ic, a. [L. sphaericus, Gr. ???: cf. F. sph[ e]rique.] 1. Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body. [1913 Webster] 2. Of or pertaining to a sphere. [1913 Webster] 3 … The Collaborative International Dictionary of English
Lead angle — Lead Lead, n. 1. The act of leading or conducting; guidance; direction; as, to take the lead; to be under the lead of another. [1913 Webster] At the time I speak of, and having a momentary lead, . . . I am sure I did my country important service … The Collaborative International Dictionary of English
Spherical angle — Spherical Spher ic*al, Spheric Spher ic, a. [L. sphaericus, Gr. ???: cf. F. sph[ e]rique.] 1. Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body. [1913 Webster] 2. Of or pertaining to a sphere. [1913 Webster] 3 … The Collaborative International Dictionary of English
The Zenith Angle — Infobox Book name = The Zenith Angle title orig = translator = image caption = author = Bruce Sterling illustrator = cover artist = country = United States language = English series = genre = Science fiction publisher = Del Ray release date = May … Wikipedia
Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… … Wikipedia
Solide de Platon — En géométrie euclidienne, un solide de Platon est un polyèdre régulier et convexe. Entre les polygones réguliers et convexes de la géométrie plane, et les polyèdres réguliers convexes de l’espace à trois dimensions, il y a une analogie, mais… … Wikipédia en Français
Steradian — The steradian (symbol: sr) is the SI unit of solid angle. It is used to describe two dimensional angular spans in three dimensional space, analogous to the way in which the radian describes angles in a plane. The name is derived from the Greek… … Wikipedia