|
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] |
Clifford Circle Theorems
Clifford may refer to: People *Clifford (name), an English given name and surname, includes a list of people with that name *William Kingdon Clifford *Baron Clifford *Baron Clifford of Chudleigh *Baron de Clifford *Clifford baronets *Clifford family (bankers) *Jaryd Clifford *Justice Clifford (other) *Lord Clifford (other) Arts, entertainment, and media *''Clifford the Big Red Dog'', a series of children's books **Clifford (character), the central character of ''Clifford the Big Red Dog'' **Clifford the Big Red Dog (2000 TV series), ''Clifford the Big Red Dog'' (2000 TV series), 2000 animated TV series **''Clifford's Puppy Days'', 2003 animated TV series **''Clifford's Really Big Movie'', 2004 animated movie **Clifford the Big Red Dog (2019 TV series), ''Clifford the Big Red Dog'' (2019 TV series), 2019 animated TV series **Clifford the Big Red Dog (film), ''Clifford the Big Red Dog'' (film), 2021 live-action movie *Clifford (film), ''Clifford'' (film), a 1994 fil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Kingdon Clifford
William Kingdon Clifford (4 May 18453 March 1879) was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modelled to new positions. Clifford algebras in general and geometric algebra in particular have been of ever increasing importance to mathematical physics, geometry, and computing. Clifford was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression ''mind-stuff''. Biography Born at Exeter, England, Exeter, William Clifford showed great promise at school. He went on to King's College London (at age 15) and Trinity College, Cambridge, where he was elected fellow in 1868, after being second Wrangler (Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with r=0 (a single point) is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a '' disc''. A circle may also be defined as a special ki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Position
In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the ''general case'' situation, as opposed to some more special or coincidental cases that are possible, which is referred to as special position. Its precise meaning differs in different settings. For example, generically, two lines in the plane intersect in a single point (they are not parallel or coincident). One also says "two generic lines intersect in a point", which is formalized by the notion of a generic point. Similarly, three generic points in the plane are not collinear; if three points are collinear (even stronger, if two coincide), this is a degenerate case. This notion is important in mathematics and its applications, because degenerate cases may require an exceptional treatment; for example, when stating general theorems or giving precise statements thereof, and when writing computer programs (see '' generic compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homersham Cox (mathematician)
Homersham Cox (1857–1918) was an English mathematician. Life He was the son of Homersham Cox (1821–1897) and brother of Harold Cox and was educated at Tonbridge School (1870–75). At Trinity College, Cambridge, he graduated B.A. as 4th wrangler in 1880, and MA in 1883. He became a fellow in 1881. His younger sister Margaret, described him as a man often completely lost in his thoughts. He was married to Amy Cox. Later they separated and she started working as a governess in Russia in 1907. Cox wrote four papers applying algebra to physics, and then turned to mathematics education with a book on arithmetic in 1885. His ''Principles of Arithmetic'' included binary numbers, prime numbers, and permutations. Contracted to teach mathematics at Muir Central College, Cox became a resident of Allahabad, Uttar Pradesh from 1891 till his death in 1918. He was married to Amy Cox, by whom he had a daughter, Ursula Cox. Work on non-Euclidean geometry 1881–1883 he publishe ... [...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] |
Miquel's Six Circles 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] |
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, movies/videos, moving images, and millions of books. In addition to its archiving function, the Archive is an activist organization, advocating a free and open Internet. , the Internet Archive holds over 35 million books and texts, 8.5 million movies, videos and TV shows, 894 thousand software programs, 14 million audio files, 4.4 million images, 2.4 million TV clips, 241 thousand concerts, and over 734 billion web pages in the Wayback Machine. The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East Orange, New Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Publicationes Mathematicae Debrecen
''Publicationes Mathematicae Debrecen'' is a Hungarian mathematical journal, edited and published in Debrecen, at the Mathematical Institute of the University of Debrecen. It was founded by Alfréd Rényi, Tibor Szele Tibor Szele (Debrecen, 21 June 1918 – Szeged, 5 April 1955) Hungarian mathematician, working in combinatorics and abstract algebra. After graduating at the Debrecen University, he became a researcher at the Szeged University in 1946, then ..., and Ottó Varga in 1950. The current editor-in-chief is Lajos Tamássy. External links * The journal'homepageOn-line papers Mathematics journals University of Debrecen {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
