More configurations on elliptic curves

We construct elliptic $(3 r_{s}, s r_{3})$ configurations for all integers $r \geq s \geq 1$ . This solves an open problem of Branko Grünbaum. The configurations which we build have mirror symmetry and even $D_{3}$ symmetry if $r$ is a multiple of $3$ . The configurations are dynamic in the sense that the points can be moved along the elliptic curve in such a way that all line incidences are preserved.

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Keywords

configurations, elliptic curves

Mathematical Subject Classification

Primary: 51A05, 51A20

Milestones

Received: 26 January 2023

Accepted: 12 March 2024

Published: 31 May 2024

Authors

Marco Bramato
Department of Mathematics ETH Zürich Zürich Switzerland

Lorenz Halbeisen
Department of Mathematics ETH Zürich Zürich Switzerland

Norbert Hungerbühler
Department of Mathematics ETH Zürich Zürich Switzerland

Vol. 21, No. 1, 2024

Marco Bramato, Lorenz Halbeisen and Norbert Hungerbühler

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors