Iterated Medial Triangle Subdivision in Surfaces of Constant Curvature

07/08/2021

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by   Florestan Brunck, et al.

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Consider a geodesic triangle on a surface of constant curvature and subdivide it recursively into 4 triangles by joining the midpoints of its edges. We show the existence of a uniform δ>0 such that, at any step of the subdivision, all the triangle angles lie in the interval (δ, π -δ). Additionally, we exhibit stabilising behaviours for both angles and lengths as this subdivision progresses.