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In Euclidean space, such a dilation is a similarity of the space. [2] Dilations change the size but not the shape of an object or figure. Every dilation of a Euclidean space that is not a congruence has a unique fixed point [3] that is called the center of dilation. [4] Some congruences have fixed points and others do not. [5]
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
List of equations in classical mechanics; Table of thermodynamic equations; List of equations in wave theory; List of electromagnetism equations; List of relativistic equations; List of equations in fluid mechanics; List of equations in gravitation; List of photonics equations; List of equations in quantum mechanics; List of equations in ...
Minkowski's theorem (geometry of numbers) Minkowski's second theorem (geometry of numbers) Minkowski–Hlawka theorem (geometry of numbers) Monsky's theorem (discrete geometry) Pick's theorem ; Pizza theorem ; Radon's theorem (convex sets) Separating axis theorem (convex geometry) Steinitz theorem (graph theory) Stewart's theorem (plane geometry)
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Klein geometry, Erlangen programme; symmetric space; space form; Maurer–Cartan form; Examples hyperbolic space; Gauss–Bolyai–Lobachevsky space; Grassmannian; Complex projective space; Real projective space; Euclidean space; Stiefel manifold; Upper half-plane; Sphere
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
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