Triangle angles and sides in progression and the diophantine equation x^2+3y^2 =z^2
Konstantine Zelator
TL;DR
This paper provides a complete parametric description of integer-sided triangles with one angle of sixty degrees, contributing to the understanding of geometric configurations satisfying specific Diophantine equations.
Contribution
It offers a novel, comprehensive parametric characterization of triangles with integer sides and a sixty-degree angle, linking geometry with Diophantine equations.
Findings
Explicit parametric formulas for such triangles
Connection between triangle properties and the equation x^2+3y^2=z^2
Complete classification of these triangles
Abstract
The main result of this paper, is the complete parametric description of the family of triangles which have integer sidelengths and with one angle being sixty degrees.
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Taxonomy
TopicsMathematics and Applications · Algebraic Geometry and Number Theory · History and Theory of Mathematics