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This is a Quantitative Study study.

October 13, 2025Open Access

On generalized disc-polygons in plane convex bodies with a higher degree of smoothness

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This research demonstrates power series expansions for vertices and area in random convex polygons, indicating advancements in geometric probability.

The study reveals power series expansions for the expected number of vertices in random L-convex polygons.
It extends prior asymptotic formulas, enhancing understanding of convex structures and their properties.
Analysis incorporates random L-convex polygons formed by random points in planar convex bodies, with implications for floating bodies.
Results provide insights into the relationship between smooth boundaries and geometric probabilities in convex forms.

Fodor et al. (2025) studied this question.

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This research demonstrates power series expansions for vertices and area in random convex polygons, indicating advancements in geometric probability.