Methods for counting the intersections of slopes in the flat torus

نویسندگان
Pinheiro, Leonardo ID 1
Richer, Cameron ID 2
Burke, John ID 3
Burke, Maitland ID 4

1 Department of Mathematical Sciences, Rhode Island College, 600 Mt. Pleasant Ave. Providence, RI 02908

2 Department of Mathematical Sciences, Rhode Island College, 600 Mt. Pleasant Ave. Providence, RI 02908

3 Department of Mathematical Sciences, Rhode Island College, 600 Mt. Pleasant Ave. Providence, RI 02908

4 Department of Mathematical Sciences, Rhode Island College, 600 Mt. Pleasant Ave. Providence, RI 02908

doi
10.22108/toc.2023.135546.2023
چکیده

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.

کلیدواژه‌ها
Torus, intersection of curves, counting methods