Equable Triangles on the Eisenstein Lattice
Christian Aebi, Grant Cairns
TL;DR
This paper proves that only two equable triangles with vertices on the Eisenstein lattice exist, considering all Euclidean motions, highlighting a unique geometric property of this lattice.
Contribution
The paper establishes a complete classification of equable triangles on the Eisenstein lattice, showing only two such triangles exist up to Euclidean motions.
Findings
Only two equable triangles on the Eisenstein lattice exist.
These triangles are unique up to Euclidean motions.
The result characterizes a rare geometric configuration on this lattice.
Abstract
We show that there are only two equable triangles having vertices on the Eisenstein lattice, up to Euclidean motions.
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Taxonomy
TopicsGeometric and Algebraic Topology · advanced mathematical theories · Mathematical Dynamics and Fractals