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Steiner Point (triangle)
In triangle geometry, the Steiner point is a particular point associated with a triangle. It is a triangle center and it is designated as the center X(99) in Clark Kimberling's Encyclopedia of Triangle Centers. Jakob Steiner (1796–1863), Swiss mathematician, described this point in 1826. The point was given Steiner's name by Joseph Neuberg in 1886. Definition The Steiner point is defined as follows. (This is not the way in which Steiner defined it.) :Let be any given triangle. Let be the circumcenter and be the symmedian point of triangle . The circle with as diameter is the Brocard circle of triangle . The line through perpendicular to the line intersects the Brocard circle at another point . The line through perpendicular to the line intersects the Brocard circle at another point . The line through perpendicular to the line intersects the Brocard circle at another point . (The triangle is the Brocard triangle of triangle .) Let be the line through parallel t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non-Collinearity, collinear, determine a unique triangle and simultaneously, a unique Plane (mathematics), plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted. Types of triangle The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concurrent Lines
In geometry, lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point. They are in contrast to parallel lines. Examples Triangles In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors: * A triangle's altitudes run from each vertex and meet the opposite side at a right angle. The point where the three altitudes meet is the orthocenter. * Angle bisectors are rays running from each vertex of the triangle and bisecting the associated angle. They all meet at the incenter. * Medians connect each vertex of a triangle to the midpoint of the opposite side. The three medians meet at the centroid. * Perpendicular bisectors are lines running out of the midpoints of each side of a triangle at 90 degree angles. The three perpendicular bisectors meet at the circumcenter. Other sets of lines associated with a triangle are concurrent as well. For example: * Any median ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tarry Point
In geometry, the Tarry point for a triangle is a point of concurrency of the lines through the vertices of the triangle perpendicular to the corresponding sides of the triangle's first Brocard triangle . The Tarry point lies on the other endpoint of the diameter of the circumcircle drawn through the Steiner point. The point is named for Gaston Tarry. See also *Concurrent lines In geometry, lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point. They are in contrast to parallel lines. Examples Triangles In a triangle, four basic types of sets of concurrent lines are ... Notes Triangle centers {{Elementary-geometry-stub ... [...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] |
Tarry Point Construction
Tarry is a surname. Notable people with the surname include: * Chris Tarry (born 1970), a Canadian guitarist * Ellen Tarry (1906–2008), African-American journalist, author and centenarian * Gaston Tarry (1843–1913), a French mathematician * Michael Tarry (died 2013), a Canadian popular singer * Sam Tarry (born 1982), a British politician * Sasura Hussein Tarry (elected 2007), a Kenyan politician See also * McCallum and Tarry (formed 1999), an artistic combination * Prouhet–Tarry–Escott problem, in mathematics * Tarry, a minor planet * '' Tarry Flynn'', a novel by Patrick Kavanagh * Tarry Park, Indiana, an unincorporated community * Tarry point In geometry, the Tarry point for a triangle is a point of concurrency of the lines through the vertices of the triangle perpendicular to the corresponding sides of the triangle's first Brocard triangle . The Tarry point lies on the other end ..., in geometry, named after Gaston Tarry * '' Tarry v Ashton'', an Englis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simson Line
In geometry, given a triangle and a point on its circumcircle, the three closest points to on lines , , and are collinear. The line through these points is the Simson line of , named for Robert Simson. The concept was first published, however, by William Wallace in 1799. The converse is also true; if the three closest points to on three lines are collinear, and no two of the lines are parallel, then lies on the circumcircle of the triangle formed by the three lines. Or in other words, the Simson line of a triangle and a point is just the pedal triangle of and that has degenerated into a straight line and this condition constrains the locus of to trace the circumcircle of triangle . Equation Placing the triangle in the complex plane, let the triangle with unit circumcircle have vertices whose locations have complex coordinates , , , and let P with complex coordinates be a point on the circumcircle. The Simson line is the set of points satisfyingTodor Zaharinov, "Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Center Of Mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ross Honsberger
Ross Honsberger (1929–2016) was a Canadian mathematician and author on recreational mathematics. Life Honsberger studied mathematics at the University of Toronto, with a bachelor's degree, and then worked for ten years as a teacher in Toronto, before continuing his studies at the University of Waterloo (master's degree). Since 1964 he had been on the faculty of mathematics, where he later became a professor emeritus. He dealt with combinatorics and optimization, especially with mathematics education. He developed education courses, for example, on combinatorial geometry, held frequently lectures for students and math teachers, and was editor of the ''Ontario Secondary School Mathematics Bulletin''. He wrote numerous books on elementary mathematics (geometry, number theory, combinatorics, probability theory), and recreational mathematics (often at the Mathematical Association of America, MAA), with him in his own words using the book by Hans Rademacher and Otto Toeplitz of nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steiner Circumellipse
In geometry, the Steiner ellipse of a triangle, also called the Steiner circumellipse to distinguish it from the Steiner inellipse, is the unique circumellipse ( ellipse that touches the triangle at its vertices) whose center is the triangle's centroid.Weisstein, Eric W. "Steiner Circumellipse." From MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/SteinerCircumellipse.html Named after Jakob Steiner, it is an example of a circumconic. By comparison the circumcircle of a triangle is another circumconic that touches the triangle at its vertices, but is not centered at the triangle's centroid unless the triangle is equilateral. The area of the Steiner ellipse equals the area of the triangle times \frac, and hence is 4 times the area of the Steiner inellipse. The Steiner ellipse has the least area of any ellipse circumscribed about the triangle. The Steiner ellipse is the scaled Steiner inellipse (factor 2, center is the centroid). Hence both ellipses are similar ( ... [...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] |
Steiner Point Construction 02 , the professional wrestling "tag team" of real-life brothers Rick and Scott Steiner
{{disambiguation, geo ...
Steiner may refer to: Felix Steiner, German Waffen SS-commander Surname *Steiner (surname) Other uses *Steiner, Michigan, a village in the United States * Steiner, Mississippi * Steiner Studios, film and television production studio in New York City * Steiner's theorem, used to determine the mass moment of inertia around an axis. Also known as parallel axis theorem See also * Poncelet–Steiner theorem *Steiner point (other) * Steiner surface *Steiner system, a type of block design *Steiner tree *Waldorf education, also called Steiner education *The Steiner Brothers The Steiner Brothers are an American professional wrestling tag team consisting of brothers Robert "Rick Steiner" Rechsteiner and Scott "Scott Steiner" Rechsteiner. The brothers wrestled as amateurs at the University of Michigan. The team ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brocard Triangle
In geometry, the Brocard triangle of a triangle is a triangle formed by the intersection of lines from a vertex to its corresponding Brocard point and a line from another vertex to its corresponding Brocard point and the other two points constructed using different combinations of vertices and Brocard points. This triangle is also called the first Brocard triangle, as further triangles can be formed by forming the Brocard triangle of the Brocard triangle and continuing this pattern. The Brocard triangle is inscribed in the Brocard circle. It is named for Henri Brocard. See also *Henri Brocard *Brocard points In geometry, Brocard points are special points within a triangle. They are named after Henri Brocard (1845–1922), a French mathematician. Definition In a triangle ''ABC'' with sides ''a'', ''b'', and ''c'', where the vertices are labeled '' ... Notes Triangles {{Elementary-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
