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Clawson Point
The Clawson point is a special point in a planar triangle defined by the trilinear coordinates \tan(\alpha):\tan(\beta):\tan(\gamma) ( Kimberling number X(19)), where \alpha, \beta, \gamma are the interior angles at the triangle vertices A, B, C. It is named after John Wentworth Clawson, who published it 1925 in the American Mathematical Monthly. Geometrical constructions There are at least two ways to construct the Clawson point, which also could be used as coordinate free definitions of the point. In both cases you have two triangles, where the three lines connecting their according vertices meet in a common point, which is the Clawson point. Construction 1 For a given triangle \triangle ABC let \triangle H_aH_bH_c be its orthic triangle and \triangle T_aT_bT_c the triangle formed by the outer tangents to its three excircles. These two triangles are similar and the Clawson point is their center of similarity, therefore the three lines T_aH_a, T_bH_b, T_cH_c connecting thei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clawson Punkt3
Clawson may refer to: * Clawson (surname) *The travel cost method of economic valuation, also called the Clawson method Places ;In the United States * Clawson, Idaho, an unincorporated community *Clawson, Michigan, a city *Clawson, Utah, a town ;Elsewhere *Long Clawson Long Clawson is a village and former civil parish, now included in that of Clawson, Hose and Harby, in the Melton district and the county of Leicestershire, England. Being in the Vale of Belvoir, the village is enclosed by farmland with rich so ..., a small village in Leicestershire, England, United Kingdom See also * Clawson codes, an alphanumeric system of prioritizing and classifying 911 medical calls {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trilinear Coordinates
In geometry, the trilinear coordinates of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. Trilinear coordinates are an example of homogeneous coordinates. The ratio is the ratio of the perpendicular distances from the point to the sides (extended if necessary) opposite vertices and respectively; the ratio is the ratio of the perpendicular distances from the point to the sidelines opposite vertices and respectively; and likewise for and vertices and . In the diagram at right, the trilinear coordinates of the indicated interior point are the actual distances (, , ), or equivalently in ratio form, for any positive constant . If a point is on a sideline of the reference triangle, its corresponding trilinear coordinate is 0. If an exterior point is on the opposite side of a sideline from the interior of the triangle, its trilinear coordinate associated with that sideline is negative. It is impossible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encyclopedia Of Triangle Centers
The Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "centers" associated with the geometry of a triangle. It is maintained by Clark Kimberling, Professor of Mathematics at the University of Evansville. , the list identifies 52,440 triangle centers. Each point in the list is identified by an index number of the form ''X''(''n'')—for example, ''X''(1) is the incenter. The information recorded about each point includes its trilinear and barycentric coordinates and its relation to lines joining other identified points. Links to The Geometer's Sketchpad diagrams are provided for key points. The Encyclopedia also includes a glossary of terms and definitions. Each point in the list is assigned a unique name. In cases where no particular name arises from geometrical or historical considerations, the name of a star is used instead. For example, the 770th point in the list is named ''point Acamar''. The first 10 points listed in the Encyclopedia ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wentworth Clawson
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope John ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' 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. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incircle And Excircles Of A Triangle
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 in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Center Of Similarity
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clark Kimberling
Clark Kimberling (born November 7, 1942 in Hinsdale, Illinois) is a mathematician, musician, and composer. He has been a mathematics professor since 1970 at the University of Evansville. His research interests include triangle centers, integer sequences, and hymnology. Kimberling received his PhD in mathematics in 1970 from the Illinois Institute of Technology, under the supervision of Abe Sklar. Since at least 1994, he has maintained a list of triangle centers and their properties. In its current on-line form, the Encyclopedia of Triangle Centers, this list comprises tens of thousands of entries. He has contributed to ''The Hymn'', the journal of the Hymn Society in the United States and Canada; and in the '' Canterbury Dictionary of Hymnology''. Kimberling's golden triangle Robert C. Schoen has defined a "golden triangle" as a triangle with two of its sides in the golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clawson Punkt2
Clawson may refer to: * Clawson (surname) *The travel cost method of economic valuation, also called the Clawson method Places ;In the United States * Clawson, Idaho, an unincorporated community *Clawson, Michigan, a city *Clawson, Utah, a town ;Elsewhere *Long Clawson Long Clawson is a village and former civil parish, now included in that of Clawson, Hose and Harby, in the Melton district and the county of Leicestershire, England. Being in the Vale of Belvoir, the village is enclosed by farmland with rich so ..., a small village in Leicestershire, England, United Kingdom See also * Clawson codes, an alphanumeric system of prioritizing and classifying 911 medical calls {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perspective Center
Two figures in a plane are perspective from a point ''O'', called the center of perspectivity if the lines joining corresponding points of the figures all meet at ''O''. Dually, the figures are said to be perspective from a line if the points of intersection of corresponding lines all lie on one line. The proper setting for this concept is in projective geometry where there will be no special cases due to parallel lines since all lines meet. Although stated here for figures in a plane, the concept is easily extended to higher dimensions. Terminology The line which goes through the points where the figure's corresponding sides intersect is known as the axis of perspectivity, perspective axis, homology axis, or archaically, perspectrix. The figures are said to be perspective from this axis. The point at which the lines joining the corresponding vertices of the perspective figures intersect is called the center of perspectivity, perspective center, homology center, pole, or archaica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Émile Lemoine
Émile Michel Hyacinthe Lemoine (; 22 November 1840 – 21 February 1912) was a French civil engineer and a mathematician, a geometer in particular. He was educated at a variety of institutions, including the Prytanée National Militaire and, most notably, the École Polytechnique. Lemoine taught as a private tutor for a short period after his graduation from the latter school. Lemoine is best known for his proof of the existence of the Lemoine point (or the symmedian point) of a triangle. Other mathematical work includes a system he called ''Géométrographie'' and a method which related algebraic expressions to geometric objects. He has been called a co-founder of modern triangle geometry, as many of its characteristics are present in his work. For most of his life, Lemoine was a professor of mathematics at the École Polytechnique. In later years, he worked as a civil engineer in Paris, and he also took an amateur's interest in music. During his tenure at the École Polytechniq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
