Kakeya Set

(Discrete Geometry)

Logo of Kakeya set
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Discrete Geometry since 1917
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What is Kakeya set?

In mathematics, a Kakeya set, or Besicovitch set, is a set of points in Euclidean space which contains a unit line segment in every direction. For instance, a disk of radius 1/2 in the Euclidean plane, or a ball of radius 1/2 in three-dimensional space, forms a Kakeya set. Much of the research in this area has studied the problem of how small such sets can be. Besicovitch showed that there are Besicovitch sets of measure zero. A Kakeya needle set (sometimes also known as a Kakeya set) is a (Besicovitch) set in the plane with a stronger property, that a unit line segment can be rotated continuously through 180 degrees within it, returning to its original position with reversed orientation. Again, the disk of radius 1/2 is an example of a Kakeya needle set.

Technology Types

conjecturediscrete geometryharmonic analysishypothesisreal analysisspeculation

Synonyms

Besicovitch setKakeya conjectureKakeya dimension conjectureKakeya maximal functionKakeya maximal function conjectureKakeya maximal operatorKakeya needle problemKakeya needle setKakeya problem

Translations

Conjunto Kakeya (es)Problème de l'aiguille de Kakeya (fr)Задача об иголке (ru)挂谷集合 (zh)掛谷集合 (ja)

Tech Info


Source: [object Object]
 — Date merged: 11/6/2021, 1:32:47 PM
 — Date scraped: 5/20/2021, 5:56:11 PM