Spherical geometry - Wikipedia
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere [a] or the n-dimensional surface of higher dimensional spheres.
Spherical Geometry | Brilliant Math & Science Wiki
Spherical geometry is the study of geometric objects located on the surface of a sphere. Spherical geometry works similarly to Euclidean geometry in that there still exist points, lines, and angles. For instance, a "line" between two points on a sphere is actually a great circle of the sphere, which is also the projection of a line in three ...
The angles of a spherical triangle are measured in the plane tangent to the sphere at the intersection of the sides forming the angle. To avoid conflict with the antipodal triangle, the triangle formed by the same great circles on the opposite side of the sphere, the sides of a spherical triangle will be restricted between 0 and π radians ...
Spherical Geometry -- from Wolfram MathWorld
2024年11月21日 · The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid geometry. In spherical geometry, straight lines are great circles, so …
Spherical Geometry: Exploring the World with Math
Spherical geometry is defined as "the study of figures on the surface of a sphere" (MathWorld), and is the three-dimensional, spherical analogue of Euclidean or planar geometry.
To get started, let S be the sphere of radius 1 centered at the origin O in three dimensional space. Using xyz coordinates, we can place O at (0; 0; 0), which means x = y = z = 0, then S is given by x2 + y2 + z2 = 1. Points will now be understood as points on S. A line is now a great circle.
Spherical geometry is a geometry where all the points lie on the surface of a sphere. Nevertheless, we can use points o the sphere and results from Euclidean geometry to develop spherical geometry. For example, the center of the sphere is the xed point from which the points in the geometry are equidis-tant. However, the center itself is not ...
If a circle is all points equidistant from a given point, what do spherical circles look like? Remember to measure distances in the spherical way, staying on the surface of the sphere. 7.
Spherical Geometry - University of Georgia
What is Spherical Geometry? The basic element of spherical geometry is the sphere, a three-dimensional surface made up of the set of all points in space at a given distance from a fixed point called the center. If we take an arbitrary plane and sphere lying in the plane, there are three possibilities for their intersections.
16: Spherical geometry - Mathematics LibreTexts
Spherical geometry studies the surface of a unit sphere. This geometry has applications in cartography, navigation, and astronomy. The spherical geometry is a close relative of the Euclidean and hy- perbolic geometries.