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Miquel's Theorem
Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. It is one of several results concerning circles in Euclidean geometry due to Miquel, whose work was published in Liouville's newly founded journal ''Journal de mathématiques pures et appliquées''. Formally, let ''ABC'' be a triangle, with arbitrary points ''A´'', ''B´'' and ''C´'' on sides ''BC'', ''AC'', and ''AB'' respectively (or their extensions). Draw three circumcircles (Miquel's circles) to triangles ''AB´C´'', ''A´BC´'', and ''A´B´C''. Miquel's theorem states that these circles intersect in a single point ''M'', called the Miquel point. In addition, the three angles ''MA´B'', ''MB´C'' and ''MC´A'' (green in the diagram) are all equal, as are the three supplementary angles ''MA´C'', ''MB´A'' and ''MC´B''. - Wells refers to Miquel's theorem as the pivot theorem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miquel Circles
Miquel may refer to: * the Catalan form of the given name Michael (given name), Michael * Friedrich Anton Wilhelm Miquel (1811–1871), a Dutch botanist * Gérard Miquel (born 1946), a member of the Senate of France * Ignasi Miquel (born 1992), a Spanish football player *Joaquín Miquel (1903–1929), Spanish Olympic runner * Johann von Miquel (1828–1901), a German statesman * Miquel's theorem, a result in geometry, named after Auguste Miquel * Miquel Brown (born 1945), a Canadian actress and disco/soul singer See also *Sant Miquel (other) {{surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 1529 18th Street, Northwest in the Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the '' American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to records on JSTOR. Mission and Vision The mission of the MAA is to advance the understanding of mathematics and its impact on our world. We envision a society that values the power and beauty of mathematics and fully realizes its potential to promote human flourishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miquel Configuration
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.. Its Levi graph is the Rhombic dodecahedral graph, the skeleton of both Rhombic dodecahedron and Bilinski dodecahedron. The configuration is related to Miquel's theorem Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. It is one of several results concerning circles .... References Configurations (geometry) {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bundle Theorem
In Euclidean geometry, the bundle theorem is a statement about six circles and eight points in the Euclidean plane. In general incidence geometry, it is a similar property that a Möbius plane may or may not satisfy. According to Kahn's Theorem, it is fulfilled by "ovoidal" Möbius planes only; thus, it is the analog for Möbius planes of Desargues' Theorem for projective planes. ''Bundle theorem.'' If for eight different points A_1,A_2,A_3,A_4, B_1,B_2,B_3,B_4 five of the six quadruples Q_:=\, \ i [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford's Circle Theorems
In geometry, Clifford's theorems, named after the English geometer William Kingdon Clifford, are a sequence of theorems relating to intersections of circles. Statement The first theorem considers any four circles passing through a common point ''M'' and otherwise in general position, meaning that there are six additional points where exactly two of the circles cross and that no three of these crossing points are collinear. Every set of three of these four circles has among them three crossing points, and (by the assumption of non-collinearity) there exists a circle passing through these three crossing points. The conclusion is that, like the first set of four circles, the second set of four circles defined in this way all pass through a single point ''P'' (in general not the same point as ''M''). The second theorem considers five circles in general position passing through a single point ''M''. Each subset of four circles defines a new point ''P'' according to the first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pivot Theorem 3d
Pivot may refer to: *Pivot, the point of rotation in a lever system *More generally, the center point of any rotational system *Pivot joint, a kind of joint between bones in the body *Pivot turn, a dance move Companies *Incitec Pivot, an Australian chemicals and explosives manufacturer *Pivot Legal Society, a legal advocacy organization based in Vancouver, British Columbia *Pivot Wireless, a cell phone service, created by a joint venture between Sprint and multiple cable companies Computing *Apache Pivot, an open-source platform for building applications in Java *Microsoft Live Labs Pivot, a data search application *Morrow Pivot and Morrow Pivot II, early laptop computers *Pivot, an element of the quicksort algorithm *Pivot, now PivotX, a content management system designed for bloggers *Pivot display, a display which can change orientation *Pivot Stickfigure Animator, stick-figure animation software *Pivot table, a data summarization tool in spreadsheets *Pivotal Games, a former ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Five Circles Theorem
In geometry, the five circles theorem states that, given five circles centered on a common sixth circle and intersecting each other chainwise on the same circle, the lines joining their second intersection points forms a pentagram whose points lie on the circles themselves. See also * Clifford's circle theorems * Miquel's theorem * Six circles theorem * Seven circles theorem In geometry, the seven circles theorem is a theorem about a certain arrangement of seven circles in the Euclidean plane. Specifically, given a chain of six circles all tangent to a seventh circle and each tangent to its two neighbors, the three l ... References * External links * * {{MathWorld, title=Miquel Pentagram Theorem, urlname=MiquelsPentagramTheorem Theorems about circles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Diaz Gergonne
Joseph Diez Gergonne (19 June 1771 at Nancy, France – 4 May 1859 at Montpellier, France) was a French mathematician and logician. Life In 1791, Gergonne enlisted in the French army as a captain. That army was undergoing rapid expansion because the French government feared a foreign invasion intended to undo the French Revolution and restore Louis XVI to the throne of France. He saw action in the major battle of Valmy on 20 September 1792. He then returned to civilian life but soon was called up again and took part in the French invasion of Spain in 1794. In 1795, Gergonne and his regiment were sent to Nîmes. At this point, he made a definitive transition to civilian life by taking up the chair of "transcendental mathematics" at the new École centrale. He came under the influence of Gaspard Monge, the Director of the new École polytechnique in Paris. In 1810, in response to difficulties he encountered in trying to publish his work, Gergonne founded his own mathematics jour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Steiner
Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry. Life Steiner was born in the village of Utzenstorf, Canton of Bern. At 18, he became a pupil of Heinrich Pestalozzi and afterwards studied at Heidelberg. Then, he went to Berlin, earning a livelihood there, as in Heidelberg, by tutoring. Here he became acquainted with A. L. Crelle, who, encouraged by his ability and by that of Niels Henrik Abel, then also staying at Berlin, founded his famous ''Journal'' (1826). After Steiner's publication (1832) of his ''Systematische Entwickelungen'' he received, through Carl Gustav Jacob Jacobi, who was then professor at Königsberg University, and earned an honorary degree there; and through the influence of Jacobi and of the brothers Alexander and Wilhelm von Humboldt a new chair of geometry was founded for him at Berlin (1834). This he occupied until his death in Bern on 1 April 1863. He was described by Thomas Hirst as follows: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Quadrangle
In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four Point (geometry), points in a Plane (geometry), plane, no three of which are Collinearity, on a common line, and of the six Line (geometry), lines connecting the six pairs of points. Duality (projective geometry), Dually, a ''complete quadrilateral'' is a system of four lines, no three of which pass through the same point, and the six points of Line–line intersection, intersection of these lines. The complete quadrangle was called a tetrastigm by , and the complete quadrilateral was called a tetragram; those terms are occasionally still used. Diagonals The six lines of a complete quadrangle meet in pairs to form three additional points called the ''diagonal points'' of the quadrangle. Similarly, among the six points of a complete quadrilateral there are three pairs of points that are not already connected by line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
