- Source: 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.
Uniquely among spherical triangles, the octant is its own polar triangle.
The octant can be parametrized using a rational quartic Bézier triangle.
The solid angle subtended by a spherical octant is π/2 sr, one-eight of the solid angle of a sphere.
See also
Trirectangular tetrahedron
Notes
Kata Kunci Pencarian:
- Octant of a sphere
- Octant
- Spherical trigonometry
- Right angle
- Octant (solid geometry)
- Planck's law
- Solid angle
- Midpoint circle algorithm
- Gauss–Bonnet theorem
- Waterman butterfly projection
