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In trigonometry, the Snellius–Pothenot problem is a problem first described in the context of planar surveying.Given three known points A, B, C, an observer at an unknown point P observes that the line segment AC subtends an angle α and the segment CB subtends an angle β; the problem is to determine the position of the point P.
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and ...
Spherical trigonometry on Math World. Intro to Spherical Trig. Includes discussion of The Napier circle and Napier's rules; Spherical Trigonometry — for the use of colleges and schools by I. Todhunter, M.A., F.R.S. Historical Math Monograph posted by Cornell University Library. Triangulator – Triangle solver. Solve any plane triangle ...
Spherical trigonometry was studied by early Greek mathematicians such as Theodosius of Bithynia, a Greek astronomer and mathematician who wrote Spherics, a book on the geometry of the sphere, [2] and Menelaus of Alexandria, who wrote a book on spherical trigonometry called Sphaerica and developed Menelaus' theorem. [3] [4]
Theory and Problems of Differential and Integral Calculus; in Si Metric Units, J.C. Ault (Adapter) Theory And Problems of Mathematics of Finance; Theory And Problems of Matrices; Theory and Problems of Modern Algebra; Theory and Problems of Plane and Spherical Trigonometry; Theory and Problems of Projective Geometry
In spherical trigonometry, the law of cosines (also called the cosine rule for sides [1]) is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry. Spherical triangle solved by the law of cosines.
An area formula for spherical triangles analogous to the formula for planar triangles. Given a fixed base , an arc of a great circle on a sphere, and two apex points and on the same side of great circle , Lexell's theorem holds that the surface area of the spherical triangle is equal to that of if and only if lies on the small-circle arc , where and are the points antipodal to and , respectively.
As can be seen from Fig. 1, these problems involve solving the triangle NAB given one angle, α 1 for the direct problem and λ 12 = λ 2 − λ 1 for the inverse problem, and its two adjacent sides. For a sphere the solutions to these problems are simple exercises in spherical trigonometry , whose solution is given by formulas for solving a ...