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In 2000, Bernard Gibert proposed a generalization of the Lester Theorem involving the Kiepert hyperbola of a triangle. His result can be stated as follows: Every circle with a diameter that is a chord of the Kiepert hyperbola and perpendicular to the triangle's Euler line passes through the Fermat points. [11] [12]
Ordinary trigonometry studies triangles in the Euclidean plane .There are a number of ways of defining the ordinary Euclidean geometric trigonometric functions on real numbers, for example right-angled triangle definitions, unit circle definitions, series definitions [broken anchor], definitions via differential equations [broken anchor], and definitions using functional equations.
The special case in which the subgraph is a triangle is known as the triangle removal lemma. [2] The graph removal lemma can be used to prove Roth's theorem on 3-term arithmetic progressions, [3] and a generalization of it, the hypergraph removal lemma, can be used to prove Szemerédi's theorem. [4] It also has applications to property testing. [5]
In plane geometry, the Conway circle theorem states that when the sides meeting at each vertex of a triangle are extended by the length of the opposite side, the six endpoints of the three resulting line segments lie on a circle whose centre is the incentre of the triangle.
Ceva's theorem, case 1: the three lines are concurrent at a point O inside ABC Ceva's theorem, case 2: the three lines are concurrent at a point O outside ABC. In Euclidean geometry, Ceva's theorem is a theorem about triangles.
SCIP-Jack (Software for solving the Steiner tree problem in graphs and 14 variants, e.g., prize-collecting Steiner tree problem; free for non-commercial use) Fortran subroutine for finding the Steiner vertex of a triangle (i.e., Fermat point), its distances from the triangle vertices, and the relative vertex weights.
WASHINGTON (Reuters) -President-elect Donald Trump cannot ignore a law requiring Chinese-based ByteDance to divest its popular short video app TikTok in the U.S. by early next year or face a ban ...
Langley's Adventitious Angles Solution to Langley's 80-80-20 triangle problem. Langley's Adventitious Angles is a puzzle in which one must infer an angle in a geometric diagram from other given angles. It was posed by Edward Mann Langley in The Mathematical Gazette in 1922. [1] [2]
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