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Miquel's theorem is a result in geometry, named after Auguste Miquel, [1] concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides.
Miquel configuration Rhombic dodecahedral graph. In geometry, the Miquel configuration is a configuration of eight points and six circles in the Euclidean plane, with four points per circle and three circles through each point. [1] Its Levi graph is the Rhombic dodecahedral graph, the skeleton of both Rhombic dodecahedron and Bilinski dodecahedron.
Minlos's theorem (functional analysis) Miquel's theorem ; Mirsky–Newman theorem (group theory) Mitchell's embedding theorem (category theory) Mittag-Leffler's theorem (complex analysis) Modigliani–Miller theorem (finance theory) Modularity theorem (number theory) Mohr–Mascheroni theorem ; Monge's theorem
Theorem (Miquel): For the Möbius plane (,) the following is true: If for any 8 points P 1 , . . . , P 8 {\displaystyle P_{1},...,P_{8}} which can be assigned to the vertices of a cube such that the points in 5 faces correspond to concyclical quadruples than the sixth quadruple of points is concyclical, too.
Truncating a single vertex from a cube produces a simple polyhedron (one with three edges per vertex) that cannot be realized as an ideal polyhedron: by Miquel's six circles theorem, if seven of the eight vertices of a cube are ideal, the eighth vertex is also ideal, and so the vertices created by truncating it cannot be ideal.
Mrs. Miniver's problem-- MSU Faculty of Mechanics and Mathematics-- MTD-f-- Mu Alpha Theta-- MU puzzle-- Muckenhoupt weights-- Mueller calculus-- Muhammad ibn Musa al-Khwarizmi-- Muirhead's inequality-- Muisca numerals-- Mukhopadhyaya theorem-- Muller–Schupp theorem-- Muller's method-- Multi-adjoint logic programming-- Multi-armed bandit ...
A complete quadrangle (at left) and a complete quadrilateral (at right).. In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points.
The clique graph of a graph is the intersection graph of its maximal cliques. Closely related concepts to complete subgraphs are subdivisions of complete graphs and complete graph minors . In particular, Kuratowski's theorem and Wagner's theorem characterize planar graphs by forbidden complete and complete bipartite subdivisions and minors ...