The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle. It is the shortest distance between two points on the surface of a sphere, measured along t
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so t
In mathematics, a spherical conic or sphero-conic is a curve on the sphere, the intersection of the sphere with a concentric elliptic cone. It is the spherical analog of a conic section (ellipse, para
Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2-dimensional surface and other terms like "ball" or "solid sphere"
A Lénárt sphere is a educational manipulative and writing surface for exploring spherical geometry, invented by Hungarian István Lénárt as a modern replacement for a spherical blackboard. It can be us
A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs of great circles on a sphere. It is measured by the angle between the planes containing the arcs (which
Legendre's theorem on spherical triangles
In geometry, Legendre's theorem on spherical triangles, named after Adrien-Marie Legendre, is stated as follows: Let ABC be a spherical triangle on the unit sphere with small sides a, b, c. Let A'B'C'
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation, it is a special case of a more general formula
Pentagramma mirificum (Latin for miraculous pentagram) is a star polygon on a sphere, composed of five great circle arcs, all of whose internal angles are right angles. This shape was described by Joh
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 f
In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangl
Trigonometry of a tetrahedron
The trigonometry of a tetrahedron explains the relationships between the lengths and various types of angles of a general tetrahedron.
Solution of triangles
Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The tria
Spherical law of cosines
In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from p
In mathematics, a versor is a quaternion of norm one (a unit quaternion). The word is derived from Latin versare = "to turn" with the suffix -or forming a noun from the verb (i.e. versor = "the turner
In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere (spherical tiling), possibly overlapping, through reflections in its edges. They
In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and d