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This is a list of formulas encountered in Riemannian geometry. Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.
Shape Area Perimeter/Circumference Meanings of symbols Square: is the length of a side Rectangle (+)is length, is breadth Circle: or : where is the radius and is the diameter ...
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugural lecture "Ueber die Hypothesen, welche der Geometrie zu Grunde liegen" ("On the Hypotheses on which Geometry is Based"). [1] It is a very broad and abstract generalization of the differential geometry of surfaces in R 3.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
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