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In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians.
Теорема Рауса Теорема Рауса
Теорема Рауса определяет отношение между площадями заданного треугольника и треугольника, образованного тремя попарно пересекающимися чевианами. Википедия
Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians.
Routh's Theorem states that \[[GHI]=\dfrac{(rst-1)^2}{(rs+r+1)(st+s+1)(tr+t+1)}[ABC]\] [asy] unitsize(5); defaultpen(fontsize(10)
15 июл. 2020 г. · This theorem of geometry is attributed to Edward John Routh (1831–1907) who gave this in a slightly different form in his 1891 book titled A ...
If the sides of a triangle are divided in the ratios lambda:1, mu:1, and nu:1, the cevians form a central triangle whose area is A=((lambdamunu-1)^2)/(( ...
Here is the Proof of Routh's Theorem to find the area of the triangle formed by pairwise intersections of three Cevians of the triangle.
In mathematics, the Routh–Hurwitz theorem gives a test to determine whether all roots of a given polynomial lie in the left-half complex plane.
8 окт. 2023 г. · In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of ...
This paper presents a proof of Routh's theorem for polynomials with real coefficients, determining the number of roots in the right half plane (RHP).
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