University of IsfahanTransactions on Combinatorics2251-865713420241201Methods for counting the intersections of slopes in the flat torus3053172777310.22108/toc.2023.135546.2023ENJohnBurkeDepartment of Mathematical Sciences,
Rhode Island College,
600 Mt. Pleasant Ave.
Providence, RI 02908MaitlandBurkeDepartment of Mathematical Sciences,
Rhode Island College,
600 Mt. Pleasant Ave.
Providence, RI 02908LeonardoPinheiroDepartment of Mathematical Sciences,
Rhode Island College,
600 Mt. Pleasant Ave.
Providence, RI 02908CameronRicherDepartment of Mathematical Sciences,
Rhode Island College,
600 Mt. Pleasant Ave.
Providence, RI 02908Journal Article20221108We define slopes in the flat torus as the set of equivalence classes of the solutions of linear equations in $\mathbb{R}^2$. The definition is equivalent to that of closed geodesics in the flat torus passing through the equivalence class of the point $(0,0)$. In this paper we derive formulas for counting the number of points in the intersection of multiple slopes in the flat torus.https://toc.ui.ac.ir/article_27773_5c824a257fe0d279edecdab4f38dbfe4.pdf