Number Theory

    

Euclidean Curvatures in the Full Modular Group Tessellation of the Upper Half-Plane

Authors: Hans Montanus

The successive action of the generators of the full modular group SL(2, Z) on thefundamental domain produces a tessellation of the upper half-plane H. Each tile is acurved triangle whose boundaries are circular arcs. We will analyze the curvatures ofthe boundaries from a flat space point of view. All Euclidean curvatures are integer.We will show that these integer curvatures are either odd or multiples of 8, and thatevery odd number and every multiple of 8 occurs as a curvature.

Comments: 8 Pages.

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[v1] 2026-04-08 12:18:49

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