Circle — This article is about the shape and mathematical concept. For other uses, see Circle (disambiguation). Circle illustration showing a radius, a diameter, the centre and the circumference … Wikipedia
Riemannian manifold — In Riemannian geometry, a Riemannian manifold ( M , g ) (with Riemannian metric g ) is a real differentiable manifold M in which each tangent space is equipped with an inner product g in a manner which varies smoothly from point to point. The… … Wikipedia
Circle packing theorem — Example of the circle packing theorem on K5, the complete graph on five vertices, minus one edge. The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane … Wikipedia
Riemannian geometry — noun (mathematics) a non Euclidean geometry that regards space as like a sphere and a line as like a great circle Bernhard Riemann pioneered elliptic geometry • Syn: ↑elliptic geometry • Topics: ↑mathematics, ↑math, ↑maths … Useful english dictionary
Unit circle — In mathematics, a unit circle is a circle with a unit radius, i.e., a circle whose radius is 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in… … Wikipedia
List of circle topics — This list of circle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or concretely in physical space. It does not include metaphors like inner circle or circular reasoning in… … Wikipedia
Great circle — For fictional interstellar organization called Great Circle, see Andromeda (novel). A great circle divides the sphere in two equal hemispheres A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a… … Wikipedia
Great-circle distance — The great circle distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere s interior). Because spherical geometry is rather… … Wikipedia
List of formulas in Riemannian geometry — This is a list of formulas encountered in Riemannian geometry.Christoffel symbols, covariant derivativeIn a smooth coordinate chart, the Christoffel symbols are given by::Gamma {ij}^m=frac12 g^{km} left( frac{partial}{partial x^i} g {kj}… … Wikipedia
Systolic geometry — In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner, and developed by Mikhail Gromov and others, in its arithmetic, ergodic, and topological manifestations.… … Wikipedia
