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In spherical geometry, the basic concepts are point and great circle. However, two great circles on a plane intersect in two antipodal points, unlike coplanar lines in Elliptic geometry . In the extrinsic 3-dimensional picture, a great circle is the intersection of the sphere with any plane through the center.
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 ...
The basic elements of Euclidean plane geometry are points and lines. On the sphere, points are defined in the usual sense. On the sphere, points are defined in the usual sense. The analogue of the "line" is the geodesic , which is a great circle ; the defining characteristic of a great circle is that the plane containing all its points also ...
Small circle of a sphere. In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical radius) from a given point on the sphere (the pole or spherical center).
Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle ) is called the reference plane (sometimes fundamental plane ).
The Lénárt sphere was invented by István Lénárt in Hungary in the early 1990s and its use is described in his 2003 book comparing planar and spherical geometry. [ 4 ] The Lénárt sphere is widely used throughout Europe in university courses on non-Euclidean geometry and geographic information systems (GIS).