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.