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Soddy Circles Of A Triangle
In geometry, the Soddy circles of a triangle are two circles associated with any triangle in the plane. Their centers are the Soddy centers of the triangle. They are all named for Frederick Soddy, who rediscovered Descartes' theorem on the radii of mutually tangent quadruples of circles. Any triangle has three externally tangent circles centered at its vertices. Two more circles, its Soddy circles, are tangent to the three circles centered at the vertices; their centers are called Soddy centers. The line through the Soddy centers is the Soddy line of the triangle. These circles are related to many other notable features of the triangle. They can be generalized to additional triples of tangent circles centered at the vertices in which one circle surrounds the other two. Construction Let A, B, C be the three vertices of a triangle, and let a, b, c be the lengths of the opposite sides, and s = \tfrac12(a + b + c) be the semiperimeter. Then the three circles centered at A, B, C have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outer Soddy Center As Equal Detour Point
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Excircle
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. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. The center of the incircle, called the incenter, can be found as the intersection of the three internal angle bisectors. The center of an excircle is the intersection of the internal bisector of one angle (at vertex , for example) and the external bisectors of the other two. The center of this excircle is called the excenter relative to the vertex , or the excenter of . Because the internal bisector of an angle is perpendicular to its external bisector, it follows that the center of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cut-the-knot
Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet Union, Soviet-born Israeli Americans, Israeli-American mathematician. He was Professor Emeritus of Mathematics at the University of Iowa, and formerly research fellow at the Moscow Institute of Electronics and Mathematics, senior instructor at Hebrew University and software consultant at Ben Gurion University. He wrote extensively about arithmetic, probability, algebra, geometry, trigonometry and mathematical games. He was known for his contribution to heuristics and mathematics education, creating and maintaining the mathematically themed educational website ''Cut-the-Knot'' for the Mathematical Association of America (MAA) Online. He was a pioneer in mathematical education on the internet, having started ''Cut-the-Knot'' in October 1996. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forum Geometricorum
''Forum Geometricorum: A Journal on Classical Euclidean Geometry'' was a peer-reviewed open-access academic journal that specialized in mathematical research papers on Euclidean geometry. Founded in 2001, it was published by Florida Atlantic University and was indexed by Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ... and .. Its founding editor-in-chief was Paul Yiu, a professor of mathematics at Florida Atlantic. In 2019, Forum Geometricorum published what was later announced to be its final issue, and stopped accepting submissions, after the retirement of Yiu. Prior issues are still available. Volumes for 2001 to 2009 can be accessed as a single searchable file (see below). Individual articles up to 2019 are available from Internet Archive (see below). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Geometry
The ''Journal of Geometry'' is a triannual peer-reviewed scientific journal covering geometry, broadly considered. In particular this includes "foundations of geometry, geometric algebra, finite geometries, combinatorial geometry, and special geometries". It was established in 1971 by Walter Benz and is published by Birkhäuser. The editors-in-chief are Hans Havlicek (Technische Universität Wien) and Alexander Kreuzer (Universität Hamburg). Abstracting and indexing The journal is abstracted and indexed in EBSCO databases, Emerging Sources Citation Index, Scopus, and zbMATH Open zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru .... References External links * {{Authority control, state=collapsed Geometry journals Academic journals established in 1971 Triannual journals Eng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The American Mathematical Monthly
''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. The editor-in-chief is Vadim Ponomarenko (San Diego State University). The journal gives the Lester R. Ford Award annually to "authors of articles of expository excellence" published in the journal. Editors-in-chief The following persons are or have been editor-in-chief: See also *''Mathematics Magazine'' *''Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circumcenter
In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertices. The center of this circle is called the circumcenter of the triangle, and its radius is called the circumradius. The circumcenter is the point of intersection between the three perpendicular bisectors of the triangle's sides, and is a triangle center. More generally, an -sided polygon with all its vertices on the same circle, also called the circumscribed circle, is called a cyclic polygon, or in the special case , a cyclic quadrilateral. All rectangles, isosceles trapezoids, right kites, and regular polygons are cyclic, but not every polygon is. Straightedge and compass construction The circumcenter of a triangle can be constructed by drawing any two of the three perpendicular bisectors. For three non-collinear points, these two lines cannot be parallel, and the circumcenter is the point where they cross. Any point on the bisector is equidistant from th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthocenter
The orthocenter of a triangle, usually denoted by , is the point (geometry), point where the three (possibly extended) altitude (triangle), altitudes intersect. The orthocenter lies inside the triangle if and only if the triangle is acute triangle, acute. For a right triangle, the orthocenter coincides with the vertex (geometry), vertex at the right angle. For an equilateral triangle, all triangle center, triangle centers (including the orthocenter) coincide at its centroid. Formulation Let denote the vertices and also the angles of the triangle, and let a = \left, \overline\, b = \left, \overline\, c = \left, \overline\ be the side lengths. The orthocenter has trilinear coordinatesClark Kimberling's Encyclopedia of Triangle Centers \begin & \sec A:\sec B:\sec C \\ &= \cos A-\sin B \sin C:\cos B-\sin C \sin A:\cos C-\sin A\sin B, \end and Barycentric coordinates (mathematics), barycentric coordinates \begin & (a^2+b^2-c^2)(a^2-b^2+c^2) : (a^2+b^2-c^2)(-a^2+b^2+c^2) : (a^2- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Longchamps Point
In geometry, the de Longchamps point of a triangle is a triangle center named after French mathematician Gaston Albert Gohierre de Longchamps. It is the reflection of the orthocenter of the triangle about the circumcenter.. Definition Let the given triangle have vertices A, B, and C, opposite the respective sides a, b, and c, as is the standard notation in triangle geometry. In the 1886 paper in which he introduced this point, de Longchamps initially defined it as the center of a circle \Delta orthogonal to the three circles \Delta_a, \Delta_b, and \Delta_c, where \Delta_a is centered at A with radius a and the other two circles are defined symmetrically. De Longchamps then also showed that the same point, now known as the de Longchamps point, may be equivalently defined as the orthocenter of the anticomplementary triangle of ABC, and that it is the reflection of the orthocenter of ABC around the circumcenter. The Steiner circle of a triangle is concentric with the nine-po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Excenter
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. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides. The center of the incircle, called the incenter, can be found as the intersection of the three internal angle bisectors. The center of an excircle is the intersection of the internal bisector of one angle (at vertex , for example) and the external bisectors of the other two. The center of this excircle is called the excenter relative to the vertex , or the excenter of . Because the internal bisector of an angle is perpendicular to its external bisector, it follows that the center of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homothetic Center
In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contraction of one another. If the center is external, the two figures are directly similar to one another; their angles have the same rotational sense. If the center is internal, the two figures are scaled mirror images of one another; their angles have the opposite sense. General polygons If two geometric figures possess a homothetic center, they are similar to one another; in other words they must have the same angles at corresponding points and differ only in their relative scaling. The homothetic center and the two figures need not lie in the same plane; they can be related by a projection from the homothetic center. Homothetic centers may be external or internal. If the center is internal, the two geometric figures are scaled mirror images of one another; in technical languag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
