October 3, 2025Open Access

An improved lower bound for star-shaped Kakeya sets

Key Points

The improved lower bound for star-shaped Kakeya sets is π/98.
Cunningham's original bound of π/108 has been shown to be suboptimal.
The analysis involves a mathematical reassessment of Kakeya sets in the Euclidean plane.
This finding has implications for theoretical mathematics, particularly in geometry.

Abstract

In 1971, Cunningham proved that every star-shaped Kakeya set E² satisfies |E| π/108. In this paper, we show that Cunningham's bound is not optimal and can be improved to |E| π/98.

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Sanbai Li (Sat,) studied this question.

www.synapsesocial.com/papers/68e02f3cf0e39f13e7fa24dc — DOI: https://doi.org/10.48550/arxiv.2509.05711

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An improved lower bound for star-shaped Kakeya sets

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