A Kakeya set in set containing a line segment
of length 1 in every direction .
The definition specifies the presence of the segments ;
continuous rotation of a needle within the set
is the separate requirement in the Kakeya needle
problem .
Choudhuri (2026) proved that every Kakeya set in Hausdorff dimension
at least
See also Hausdorff Dimension ,
Kakeya Maximal Conjecture ,
Kakeya Maximal Function ,
Kakeya Needle Problem ,
Line
Segment ,
Perron Tree
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References Choudhuri, M. R. "New Bound on the Hausdorff Dimension of Kakeya Sets in https://arxiv.org/abs/2610.12480 . Wolff,
T. H. Lectures
on Harmonic Analysis. https://doi.org/10.1090/ulect/029 . Referenced
on Wolfram|Alpha Kakeya Set
Cite this as:
Weisstein, Eric W. "Kakeya Set." From
MathWorld https://mathworld.wolfram.com/KakeyaSet.html
Subject classifications
is a set containing a line segment
of length 1 in every direction.
The definition specifies the presence of the segments;
continuous rotation of a needle within the set
is the separate requirement in the Kakeya needle
problem.
has Hausdorff dimension
at least 
.
The argument combines the three-dimensional Kakeya theorem with a planebrush estimate.
."
30 Aug 2026.