http://jwilson.coe.uga.edu/emt668/EMAT6680.F99/Erbas/emat6690/essay2/essay2.html WebMar 24, 2024 · The first Morley triangle , also simply known as "Morley's triangle", is the triangle constructed from pairwise intersections of the angle trisectors of a given …
Distances from Morley triangle to edges of the original triangle
http://jwilson.coe.uga.edu/emt668/EMAT6680.F99/Erbas/emat6690/essay2/essay2.html http://tecindy.com/ income protection civil service
Geometry: Morley
WebA. Bogomolny, Morley's Miracle from Interactive Mathematics Miscellany and Puzzles. Includes a long list of different proofs, in particular John Conway's proof is rather elegant. Morley's Trisection Theorem: a detailed proof at MathWorld. Morley's Theorem at MathWorld. Morley's trisector theorem at Wikipedia. © WebMorley's theorem asserts that the points of intersection of the adjacent angle trisectors of the angles of an arbitrary triangle ABC are the vertices of an equilateral triangle DEF. That triangle is known as the first Morley triangle. The points of intersection of the adjacent outer angle trisectors are the vertices of another equilateral triangle. In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank … See more There are many proofs of Morley's theorem, some of which are very technical. Several early proofs were based on delicate trigonometric calculations. Recent proofs include an algebraic proof by Alain Connes (1998, 2004) … See more The first Morley triangle has side lengths $${\displaystyle a^{\prime }=b^{\prime }=c^{\prime }=8R\sin(A/3)\sin(B/3)\sin(C/3),\,}$$ where R is the See more The centroid of the first Morley triangle is given in trilinear coordinates by Morley center = X(356) = cos(A/3) + 2 cos(B/3)cos(C/3) : cos(B/3) + 2 cos(C/3)cos(A/3) : … See more • Morleys Theorem at MathWorld • Morley's Trisection Theorem at MathPages • Morley's Theorem by Oleksandr Pavlyk, The Wolfram Demonstrations Project. See more Morley's theorem entails 18 equilateral triangles. The triangle described in the trisector theorem above, called the first Morley triangle, has … See more • Angle trisection • Hofstadter points • Morley centers See more 1. ^ Bogomolny, Alexander, Morley's Miracle, Cut-the-knot, retrieved 2010-01-02 2. ^ Bogomolny, Alexander, J. Conway's proof, Cut-the-knot, retrieved 2024-12-03 See more inception distribution