Equable kites, trapezoids and cyclic quadrilaterals on the Eisenstein Lattice

Document Type : Research Paper

Authors

1 Collè€ge Calvin Geneva, Switzerland

2 Department of Mathematical and Physical Sciences, La Trobe University Melbourne, Australia

Abstract

We show that on the Eisenstein lattice, up to Euclidean motions, there is only one infinite family of equable kites, which is given by the Pell-like equation $3x^2-2=y^2$, and only one single equable trapezoid, which also happens to be the only equable cyclic quadrilateral.

Keywords

Main Subjects


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Articles in Press, Corrected Proof
Available Online from 14 December 2024
  • Receive Date: 11 February 2024
  • Revise Date: 13 October 2024
  • Accept Date: 14 December 2024
  • Published Online: 14 December 2024