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Equal Parallelians Point
In geometry, the equal parallelians point (also called congruent parallelians point) is a special point associated with a Plane (geometry), plane triangle. It is a triangle center and it is denoted by ''X''(192) in Clark Kimberling's Encyclopedia of Triangle Centers. There is a reference to this point in one of Peter Yff's notebooks, written in 1961. Definition The equal parallelians point of triangle is a point in the plane of such that the three line segments through parallel to the extended side, sidelines of and having endpoints on these sidelines have equal lengths. Trilinear coordinates The trilinear coordinates of the equal parallelians point of triangle are bc(ca+ab-bc) \ : \ ca(ab+bc-ca) \ : \ ab(bc+ca-ab) Construction for the equal parallelians point Let be the anticomplementary triangle of triangle . Let the internal bisectors of the angles at the vertices of meet the opposite sidelines at respectively. Then the lines concur at the equal parallelians p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
