Hyperbolic triangles of the maximum area with two fixed sides
Jane I. Alekseeva
TL;DR
This paper investigates the problem of determining the hyperbolic triangle with two fixed sides that has the maximum area within Lobachevskii geometry, extending a classical Euclidean problem into hyperbolic space.
Contribution
It provides a solution to the hyperbolic analog of the maximum area triangle problem with two fixed sides, which was previously studied only in Euclidean geometry.
Findings
Identifies the conditions for maximum area hyperbolic triangles with fixed sides.
Derives explicit formulas for the maximum area in hyperbolic geometry.
Extends classical geometric optimization problems into non-Euclidean contexts.
Abstract
The aim of this paper is to consider the Lobachevskii geometry analog of a well-known Euclidian problem; namely: to find a triangle with two fixed sides and the maximum area
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Taxonomy
TopicsMathematics and Applications · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · Mathematical Control Systems and Analysis