# The Kakeya Problem for Circular Arcs

```@article{Hra2016TheKP,
title={The Kakeya Problem for Circular Arcs},
author={K. H{\'e}ra and Mikl{\'o}s Laczkovich},
journal={Acta Mathematica Hungarica},
year={2016},
volume={150},
pages={479-511}
}```
• Published 24 October 2016
• Mathematics
• Acta Mathematica Hungarica
We prove that if a circular arc has angle short enough, then it can be continuously moved to any prescribed position within a set of arbitrarily small area.
5 Citations

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## References

SHOWING 1-5 OF 5 REFERENCES
Closed sets with the Kakeya property
• Mathematics
• 2017
We say that a planar set \$A\$ has the Kakeya property if there exist two different positions of \$A\$ such that \$A\$ can be continuously moved from the first position to the second within a set of
Besicovitch, On Kakeya’s problem and a similar
• one, Math. Z
• 1928