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Consider a geodesic triangle on a surface of constant curvature and subdivideit recursively into 4 triangles by joining the midpoints of its edges. We showthe existence of a uniform $\delta>0$ such that, at any step of thesubdivision, all the triangle angles lie in the interval $(\delta, \pi-\delta)$. Additionally, we exhibit stabilising behaviours for both angles andlengths as this subdivision progresses.

Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature