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Fuhrmann Triangle
The Fuhrmann triangle, named after Wilhelm Fuhrmann (1833–1904), is special triangle based on a given arbitrary triangle. For a given triangle \triangle ABC and its circumcircle the midpoints of the arcs over triangle sides are denoted by M_a, M_b, M_c . Those midpoints get reflected at the associated triangle sides yielding the points M^\prime_a, M^\prime_b, M^\prime_c , which forms the ''Fuhrmann triangle''. Roger A. Johnson: ''Advanced Euclidean Geometry''. Dover 2007, , pp. 228–229, 300 (originally published 1929 with Houghton Mifflin Company (Boston) as ''Modern Geometry'').Ross Honsberger: ''Episodes in Nineteenth and Twentieth Century Euclidean Geometry''. MAA, 1995, pp49-52 The circumcircle of Fuhrmann triangle is the Fuhrmann circle. Furthermore the Furhmann triangle is similar to the triangle formed by the mid arc points, that is \triangle M^\prime_c M^\prime_b M^\prime_a \sim \triangle M_a M_b M_c . For the area of the Fuhrmann triangle the following fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuhrmann Triangle
The Fuhrmann triangle, named after Wilhelm Fuhrmann (1833–1904), is special triangle based on a given arbitrary triangle. For a given triangle \triangle ABC and its circumcircle the midpoints of the arcs over triangle sides are denoted by M_a, M_b, M_c . Those midpoints get reflected at the associated triangle sides yielding the points M^\prime_a, M^\prime_b, M^\prime_c , which forms the ''Fuhrmann triangle''. Roger A. Johnson: ''Advanced Euclidean Geometry''. Dover 2007, , pp. 228–229, 300 (originally published 1929 with Houghton Mifflin Company (Boston) as ''Modern Geometry'').Ross Honsberger: ''Episodes in Nineteenth and Twentieth Century Euclidean Geometry''. MAA, 1995, pp49-52 The circumcircle of Fuhrmann triangle is the Fuhrmann circle. Furthermore the Furhmann triangle is similar to the triangle formed by the mid arc points, that is \triangle M^\prime_c M^\prime_b M^\prime_a \sim \triangle M_a M_b M_c . For the area of the Fuhrmann triangle the following fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuhrmann Triangle2
Fuhrmann or Fuhrman may refer to: Surname * Bärbel Fuhrmann (born 1940), retired German swimmer * Emma Fuhrmann (born 2001), American film actress and model * Ernst Fuhrmann (1918-1995), chairman of Porsche AG in the 1970s * Irene Fuhrmann (born 1980), Austrian former football player * Joel Fuhrman (born 1953), American physician advocating a "micronutrient-rich diet" * Mark Fuhrman (born 1952), former detective of the Los Angeles Police Department, investigator in the O.J. Simpson murder case * Louis P. Fuhrmann (1868–1931), Mayor of the City of Buffalo, New York * Manfred Fuhrmann (1925-2005), German philologist * Otto Fuhrmann (1871-1945), Swiss parasitologist who specialized in the field of helminthology * Petra Fuhrmann (1955–2019), Austrian politician * Susan Fuhrmann Susan Elizabeth Fuhrmann (born 30 July 1986), known as "the Fuhrmannator", is an Australian retired international netball player. Early life Susan Fuhrmann was born and raised in Katoomba, New Sou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilhelm Fuhrmann
Wilhelm Ferdinand Fuhrmann (28 February 1833 – 11 June 1904) was a German mathematician. The Fuhrmann circle and the Fuhrmann triangle are named after him.Roger A. Johnson: ''Advanced Euclidean Geometry''. Dover 2007, , pp. 228–229, 300 (originally published 1929 with Houghton Mifflin Company (Boston) as ''Modern Geometry''). Biography Fuhrmann was born on 28 February 1833 in Burg bei Magdeburg. Fuhrmann had shortly worked as sailor before he returned to school and attended the Altstadt Gymnasium in Königsberg, where his teachers noticed his interest and talent in mathematics and geography. He graduated in 1853 and went on to study mathematics and physics at the University of Königsberg. One of his peers later remembered him as the most talented and diligent student of his class. Fuhrmann however despite his talent did not pursue a career at the university, instead he became a math and science teacher at the Burgschule in Königsberg after his graduation. He j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circumcircle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm. Even if a polygon has a circumscribed circle, it may be different from its minimum bounding circle. For example, for an obtuse triangle, the minimum bounding circle has the longest sid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuhrmann Circle
__notoc__ In geometry, the Fuhrmann circle of a triangle, named after the German Wilhelm Fuhrmann (1833–1904), is the circle that has as a diameter the line segment between the orthocenter H and the Nagel point N. This circle is identical with the circumcircle of the Fuhrmann triangle. The radius of the Fuhrmann circle of a triangle with sides ''a'', ''b'', and ''c'' and circumradius ''R'' is : R\sqrt, which is also the distance between the circumcenter and incenter. Aside from the orthocenter the Fuhrmann circle intersects each altitude of the triangle in one additional point. Those points all have the distance 2r from their associated vertices of the triangle. Here r denotes the radius of the triangles incircle.Ross Honsberger: ''Episodes in Nineteenth and Twentieth Century Euclidean Geometry''. MAA, 1995, pp49-52/ref> Notes Further reading *Nguyen Thanh Dung"The Feuerbach Point and the Fuhrmann Triangle" ''Forum Geometricorum'', Volume 16 (2016), pp. 299–311. * J. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Theorem In Geometry
In geometry, Euler's theorem states that the distance ''d'' between the circumcenter and incenter of a triangle is given by d^2=R (R-2r) or equivalently \frac + \frac = \frac, where R and r denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively). The theorem is named for Leonhard Euler, who published it in 1765. However, the same result was published earlier by William Chapple in 1746. From the theorem follows the Euler inequality: R \ge 2r, which holds with equality only in the equilateral case. Stronger version of the inequality A stronger version is \frac \geq \frac \geq \frac+\frac+\frac-1 \geq \frac \left(\frac+\frac+\frac \right) \geq 2, where a, b, and c are the side lengths of the triangle. Euler's theorem for the escribed circle If r_a and d_a denote respectively the radius of the escribed circle opposite to the vertex A and the distance between its center and the center of the circumscribed circl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
