%0 Journal Article
%T Methods for counting the intersections of slopes in the flat torus
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Burke, John
%A Burke, Maitland
%A Pinheiro, Leonardo
%A Richer, Cameron
%D 2024
%\ 12/01/2024
%V 13
%N 4
%P 305-317
%! Methods for counting the intersections of slopes in the flat torus
%K Torus
%K intersection of curves
%K counting methods
%R 10.22108/toc.2023.135546.2023
%X We 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.
%U https://toc.ui.ac.ir/article_27773_5c824a257fe0d279edecdab4f38dbfe4.pdf