Research investigates perimeter deviation in random spherical disc-polygons, indicating unique spherical geometric properties.
We consider the asymptotic behaviour of the expectation of the perimeter deviation of a uniform random spherical disc–polygon in a spherical spindle convex disc with smooth boundary. We also introduce the notion of duality on the sphere, define a model of random circumscribed disc–polygons, and determine some asymptotic results about them.
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Nagy et al. (2026) studied this question.
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