Generalization of Heron's and Brahmagupta's equalities to any cyclic polygon

DOI10.1007/s00010-020-00771-wzbMath1473.52002OpenAlexW3125897951MaRDI QIDQ822777

Paolo Dulio, Enrico Laeng

Publication date: 23 September 2021

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-020-00771-w

zbMATH Keywords

areasymmetric functioninradiuscyclic polygonincircle

Mathematics Subject Classification ID

Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (2) dimensions (including convex curves) (52A10)

Cites Work

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• The geometry of cyclic hyperbolic polygons
• Areas of polygons inscribed in a circle
• Random cyclic polygons from Dirichlet distributions and approximations of \(\pi\)
• On the areas of cyclic and semicyclic polygons
• The area of cyclic polygons: recent progress on Robbins' conjectures
• A Variational Principle for Cyclic Polygons with Prescribed Edge Lengths
• Geometric constructibility of cyclic polygons and a limit theorem
• Inscribed polygons and Heron polynomials
• Areas of Polygons Inscribed in a Circle

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