منابع مشابه
A Stronger Triangle Inequality for Neutral Geometry
Bailey and Bannister [College Math. Journal, 28 (1997) 182–186] proved that a stronger triangle inequality holds in the Euclidean plane for all triangles having largest angle less than arctan( 7 ) ≈ 74◦. We use hyperbolic trigonometry to show that a stronger triangle inequality holds in the hyperbolic plane for all triangles having largest angle less than or equal to 65.87◦ .
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Given an electrical circuit each edge e of which is an isotropic conductor with a monomial conductivity function y∗ e = y r e/μ s e. In this formula, ye is the potential difference and y∗ e current in e, while μe is the resistance of e, while r and s are two strictly positive real parameters common for all edges. In 1987, Gvishiani and Gurvich [4] proved that, for every two nodes a, b of the ci...
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The geodesic distance (path length) and effective resistance are both metrics defined on the vertices of a graph. The effective resistance is a more refined measure of connectivity than the geodesic distance. For example if there are k edge disjoint paths of geodesic distance d between two vertices, then the effective resistance is no more than d k . Thus, the more paths, the closer the vertice...
متن کاملA Strong Triangle Inequality in Hyperbolic Geometry
For a triangle in the hyperbolic plane, let α, β, γ denote the angles opposite the sides a, b, c, respectively. Also, let h be the height of the altitude to side c. Under the assumption that α, β, γ can be chosen uniformly in the interval (0, π) and it is given that α + β + γ < π, we show that the strong triangle inequality a + b > c + h holds approximately 79% of the time. To accomplish this, ...
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ژورنال
عنوان ژورنال: The College Mathematics Journal
سال: 1997
ISSN: 0746-8342,1931-1346
DOI: 10.1080/07468342.1997.11973859