Menelaus relation and Fay's trisecant formula are associativity equations

TL;DR

This paper reveals that the Menelaus relation and Fay's trisecant formula function as associativity conditions for structure constants in specific three-dimensional algebras, linking classical geometry with algebraic structures.

Contribution

It demonstrates that classical geometric relations serve as associativity equations in algebra, providing a novel algebraic interpretation of these geometric formulas.

Findings

Menelaus relation acts as an associativity condition

Fay's trisecant formula is analogous to WDVV equations

Establishes a connection between geometry and algebraic structures

Abstract

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.