In mathematics, a Kakeya set, or Besicovitch set, is any set of points in Euclidean space which contains a unit line segment in every direction. While many types of objects satisfy this property, several interesting results and questions are motivated by considering 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 within which a unit line segment can be rotated continuously through 180 degrees, returning to its original position with reversed orientation. Besicovitch showed that there are Kakeya needle sets of arbitrarily small positive measure.
Read more about Kakeya Set: Kakeya Needle Problem, Besicovitch Sets, Kakeya Needle Sets, Applications To Analysis
Famous quotes containing the word set:
“When desire, having rejected reason and overpowered judgment which leads to right, is set in the direction of the pleasure which beauty can inspire, and when again under the influence of its kindred desires it is moved with violent motion towards the beauty of corporeal forms, it acquires a surname from this very violent motion, and is called love.”
—Socrates (469–399 B.C.)