Cyclic polygons in classical geometry
Ren Guo, Nilg\"un S\"onmez
TL;DR
This paper unifies formulas related to side lengths, diagonals, and circumcircle radii of cyclic polygons across Euclidean, hyperbolic, and spherical geometries, providing a comprehensive framework.
Contribution
It introduces a unified approach to formulas of cyclic polygons applicable in multiple geometries, enhancing understanding and computation.
Findings
Unified formulas for cyclic polygons across geometries
Extension of classical Euclidean formulas to hyperbolic and spherical cases
Simplified computation of polygon properties in different geometries
Abstract
Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.
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Taxonomy
TopicsMathematics and Applications · Computational Geometry and Mesh Generation · History and Theory of Mathematics