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The finite Kakeya problem

  • Martin Aigner
  • Günter M. Ziegler
Chapter

Abstract

This beautiful question was posed by the Japanese mathematician Sōichi Kakeya in 1917. It gained immediate prominence and, together with its higher-dimensional analogs, helped initiate a whole new field, today called geometric measure theory. To be precise, by “turning around” Kakeya had a continuous motion in mind that returns the needle to the original position with its ends reversed, like a Samurai whirling his pole. Any such motion takes place in a compact subset of the plane.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 1
  1. 1.Institut für MathematikFreie Universität BerlinBerlinGermany

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