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Home > Art, Film & Photography > Spherical Trigonometry: Great Circle, Angle Excess, Spherical Geometry, Spherical Trigonometry, Haversine Formula, Great-Circle Distance
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Spherical Trigonometry: Great Circle, Angle Excess, Spherical Geometry, Spherical Trigonometry, Haversine Formula, Great-Circle Distance

Spherical Trigonometry: Great Circle, Angle Excess, Spherical Geometry, Spherical Trigonometry, Haversine Formula, Great-Circle Distance


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About the Book

Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Great Circle, Angle Excess, Spherical Geometry, Spherical Trigonometry, Haversine Formula, Great-Circle Distance, Versor, Triangle Group, Schwarz Triangle, Spherical Polyhedron, Spherical Law of Cosines, Small Circle. Excerpt: Angle excess, also known as spherical excess is the amount by which the sum of the angles of a polygon on a sphere exceeds the sum of the angles of a polygon with the same number of sides in a plane . For instance, a plane triangle has an angle sum of 180; an octant is a spherical triangle with 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. In 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 in hyperbolic geometry and is likewise proportional to area. See also (online edition) References (URLs online) A hyperlinked version of this chapter is at The great-circle distance or orthodromic distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere's interior). Because spherical geometry is rather different from ordinary Euclidean geometry, the equations for distance take on a different form. The distance between two points in Euclidean...


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Product Details
  • ISBN-13: 9781155497747
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Great Circle, Angle Excess, Spherical Geometry, Spherical Trigonometry, Haversine Formula, Great-Circle Distance
  • Width: 229 mm
  • ISBN-10: 1155497740
  • Publisher Date: 04 May 2010
  • Binding: Paperback
  • Spine Width: 4 mm
  • Weight: 100 gr


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