The octant of a sphere is a spherical triangle with three right angles.
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 navigation.
The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook Spherical trigonometry for the use of colleges and Schools.[1]
Since then, significant developments have been the application of vector methods, quaternion methods, and the use of numerical methods.
^Todhunter, I. (1886). Spherical Trigonometry (5th ed.). MacMillan. Archived from the original on 2020-04-14. Retrieved 2013-07-28.
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Sphericaltrigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles...
tables of sine values, and used them to solve problems in trigonometry and sphericaltrigonometry. In the 2nd century AD, the Greco-Egyptian astronomer Ptolemy...
author on trigonometry was Bhaskara II in the 12th century. Bhaskara II developed sphericaltrigonometry, and discovered many trigonometric results. Bhaskara...
geodesy, spherical geometry and the metrical tools of sphericaltrigonometry are in many respects analogous to Euclidean plane geometry and trigonometry, but...
and allows the exact calculation (hisab) of the qibla using a sphericaltrigonometric formula that takes the coordinates of a location and of the Kaaba...
to trigonometry: Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles. Trigonometry defines...
postulate. In sphericaltrigonometry, angles are defined between great circles. Sphericaltrigonometry differs from ordinary trigonometry in many respects...
development of trigonometry. He "innovated new trigonometric functions, created a table of cotangents, and made some formulas in sphericaltrigonometry." These...
circles (all of which are closed) and the problems reduce to ones in sphericaltrigonometry. However, Newton (1687) showed that the effect of the rotation of...
coordinates when needed. Spherical coordinate system Sphericaltrigonometry Transcendent angle Green, Robin Michael (1985). Spherical Astronomy. Cambridge...
natural logarithms of trigonometric functions.: Ch. III The book also has a discussion of theorems in sphericaltrigonometry, usually known as Napier's...
In sphericaltrigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles...
others. He developed trigonometry and constructed trigonometric tables, and he solved several problems of sphericaltrigonometry. With his solar and lunar...
and location on Earth. It relies on the mathematical methods of sphericaltrigonometry and the measurements of astrometry. This is the oldest branch of...
of a more general formula in sphericaltrigonometry, the law of haversines, that relates the sides and angles of spherical triangles. The first table of...
the angles and sides are analogous to those of sphericaltrigonometry; the length scale for both spherical geometry and hyperbolic geometry can for example...
imaginary trigonometric functions, Frank (1909) and Varićak (1910) used hyperbolic functions, Bateman and Cunningham (1909–1910) used spherical wave transformations...
treatise on sphericaltrigonometry, Hodges, Figgis, & co. Papadopoulos, Athanase (2014), "On the works of Euler and his followers on spherical geometry"...
a great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Euclidean space....
Hague) was a Dutch mathematician famous for his published work on sphericaltrigonometry. In 1638 he moved to The Hague to become tutor of William II, Prince...
tetrahedrons and n-simplices. In sphericaltrigonometry, triangles on the surface of a sphere are studied. The spherical triangle identities are written...
p>=1 Wikimedia Commons has media related to Spherical polyhedra. Spherical geometry Sphericaltrigonometry Polyhedron Projective polyhedron Toroidal polyhedron...
in the center. The resulting tesselation has 4 × 6=24 spherical triangles (it is the spherical disdyakis cube). These groups are finite, which corresponds...
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for...
this definition, the galactic poles and equator can be found from sphericaltrigonometry and can be precessed to other epochs; see the table. The IAU recommended...
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