The finite Kakeya problem

Chapter

Abstract

“How small can a set in the plane be in which you can turn a needle of length 1 completely around?”

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.

Keywords

Hausdorff Dimension Geometric Measure Theory Nonzero Polynomial Zero Polynomial Dimension Progress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institut für MathematikFreie Universität BerlinBerlinGermany
  2. 2.Institut für MathematikFreie Universität BerlinBerlinGermany

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