Heptagonal triangle as the extreme triangle of Dixmier-Kahane-Nicolas inequality

On the metric triangle inequality

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

Some Collinearities in the Heptagonal Triangle

With the methods of barycentric coordinates, we establish several collinearities in the heptagonal triangle, formed by a side and two diagonals of different lengths of a regular heptagon. 1. The regular heptagon Consider a regular heptagon AA′C ′A′′BCB′ inscribed in a circle, each side of length a. The diagonals are of two kinds. Those with 3 vertices on the defining minor arc have the same len...

Triangle inequality for resistances

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...

The Poverty-Growth-Inequality Triangle

Concept Dissimilarity with Triangle Inequality

Several researchers have developed properties that ensure compatibility of a concept similarity or dissimilarity measure with the formal semantics of Description Logics. While these authors have highlighted the relevance of the triangle inequality, none of their proposed dissimilarity measures satisfy it. In this work we present a theoretical framework for dissimilarity measures with this prope...