# Kakeya Set

## 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