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Brahmagupta quadrilaterals are lattice quadrilaterals

Susan H. Marshall and Brooke Tortorelli
Vol. 17 (2024), No. 4, 593–602
DOI: 10.2140/involve.2024.17.593
Abstract

A Brahmagupta quadrilateral is a cyclic quadrilateral with integer side lengths, integer diagonals, and integer area. We show that every Brahmagupta quadrilateral can be placed in the xy-plane so that its vertices have integer coordinates, generalizing a similar result for Heronian triangles (triangles with integer side lengths and integer area).

Keywords
Brahmagupta quadrilateral, Gaussian integers
Mathematical Subject Classification
Primary: 51M04
Milestones
Received: 29 May 2022
Revised: 26 May 2023
Accepted: 27 May 2023
Published: 2 October 2024

Communicated by Joshua Cooper
Authors
Susan H. Marshall
Department of Mathematics
Monmouth University
West Long Branch, NJ
United States
Brooke Tortorelli
Department of Mathematics
Monmouth University
West Long Branch, NJ
United States
© 2024 MSP (Mathematical Sciences Publishers).