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Vertex (geometry) A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex ( pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra ...
Centroid. In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. [further explanation needed] The same definition extends to any object in - dimensional Euclidean space.
Octant (solid geometry) Three axial planes ( x =0, y =0, z =0) divide space into eight octants. The eight (±,±,±) coordinates of the cube vertices are used to denote them. The horizontal plane shows the four quadrants between x - and y -axis. (Vertex numbers are little-endian balanced ternary.) An octant in solid geometry is one of the eight ...
In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in perspective centrally. Denote the three vertices of one triangle by a, b and c, and those of the other by A, B and C. Axial perspectivity means that lines ab and AB meet in a point, lines ac and ...
In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle ABC, let the lines AO, BO, CO be drawn from the vertices to a common point O (not on one of the sides of ABC ), to meet opposite sides at D, E, F respectively. (The segments AD, BE, CF are known as cevians .) Then, using signed lengths of segments ,
Incircle and excircles. Incircle and excircles of a triangle. In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. [1] An excircle or escribed circle [2 ...
In geometry, an octagon (from Ancient Greek ὀκτάγωνον (oktágōnon) 'eight angles') is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} [ 1] and can also be constructed as a quasiregular truncated square, t {4}, which alternates two types of edges. A truncated octagon, t {8} is a hexadecagon, {16}.
In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8. The name derives from the fact that it is the root lattice of the E 8 root system . The norm [1] of the E 8 lattice (divided by 2) is a positive definite even unimodular quadratic form in 8 ...
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