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Brokard's Theorem
Brokard's theorem (also known as Brocard's theorem) is a theorem in projective geometry. It is commonly used in Olympiad mathematics. It is named after French mathematician Henri Brocard. Statement Brokard's theorem. The points ''A'', ''B'', ''C'', and ''D'' lie in this order on a circle \omega with center ''O''. Lines ''AC'' and ''BD'' intersect at ''P'', ''AB'' and ''DC'' intersect at ''Q'', and ''AD'' and ''BC'' intersect at ''R''. Then ''O'' is the orthocenter of \triangle PQR. Furthermore, ''QR'' is the polar of ''P'', ''PQ'' is the polar of ''R'', and ''PR'' is the polar of ''Q'' with respect to \omega. An equivalent formulation of Brokard's theorem states that the orthocenter of the diagonal triangle of a cyclic quadrilateral is the circumcenter of the cyclic quadrilateral. See also * Orthocenter * Power of a point * Pole and polar In geometry, a pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given ... [...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 A university () is an educational institution, institution of tertiary education and research which awards academic degrees in several Discipline (academia), academic disciplines. ''University'' is derived from the Latin phrase , which roughly ..., 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 11 Dupont in the Dupont Circle, Washington, D.C., 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 re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''projective space'') and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "Point at infinity, points at infinity") to Euclidean points, and vice versa. Properties meaningful for projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix and translation (geometry), translations (the affine transformations). The first issue for geometers is what kind of geometry is adequate for a novel situation. Unlike in Euclidean geometry, the concept of an angle does not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Olympiad Mathematics
A mathematical olympiad is a mathematical competition where participants are examined by problem solving and may win medals depending on their performance. Usually aimed at pre-university students, much of olympiad mathematics consists of elementary mathematics, though solutions may involve the use of calculus or higher-level mathematics. The biggest mathematics olympiad is the International Mathematical Olympiad. Among their objectives, they serve the purpose of identifying talented or gifted students in mathematics, who often receive opportunities for scholarships at universities.https://unesdoc.unesco.org/ark:/48223/pf0000110203 In a sense, they measure some mathematical abilities of the students. History The concept of mathematics competitions dates back to the late 19th century. A one-off competition for 70 primary school students was held in Bucharest in May 1885, but little is known about it. A better-documented Eötvös Competition in Hungary became one of the earlies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
