Octant of a sphere in the context of Octant (solid geometry)

Octant of a sphere in the context of Octant (solid geometry)

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⭐ Core Definition: Octant of a sphere

In geometry, an octant of a sphere is a spherical triangle with three right angles and three right sides. It is sometimes called a trirectangular (spherical) triangle. It is one face of a spherical octahedron.

For a sphere embedded in three-dimensional Euclidean space, the vectors from the sphere's center to each vertex of an octant are the basis vectors of a Cartesian coordinate system relative to which the sphere is a unit sphere. The spherical octant itself is the intersection of the sphere with one octant of space.

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Octant of a sphere in the context of Spherical triangle

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 Isaac Todhunter's textbook Spherical trigonometry for the use of colleges and Schools.Since then, significant developments have been the application of vector methods, quaternion methods, and the use of numerical methods.

View the full Wikipedia page for Spherical triangle
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LINKED FROM (PARENTS)
← Spherical triangle ← Spherical trigonometry
LINKS TO (CHILDREN)
Orthographic projection → Geometry → Spherical triangle → Right angle → Spherical octahedron → Sphere → Three-dimensional Euclidean space → Euclidean vector → Basis vector → Cartesian coordinate system → Unit sphere → Octant (solid geometry) →