Conway's Nightmare: Brahmagupta and Butterflies

2022/01/19 by Richard Evan Schwartz, Schwartz, Richard Evan
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2201.07743

openalex publication_date 2022/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note gives a very succinct conceptual proof of Brahmagupta's formula for cyclic quadrilaterals, and then a long discussion about how the proof is inspired by ideas from modern mathematics.

Related

• Two generalizations of the Butterfly Theorem
• A porism for cyclic quadrilaterals, butterfly theorems, and hyperbolic geometry
• Brahmagupta quadrilaterals with equal perimeters and equal areas
• From Stokes' formula to cyclic Hochschild cocycles on classical symbols
• Rank of elliptic curves associated to the Brahmagupta quadrilaterals