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:
“The Bostonians are really, as a race, far inferior in point of anything beyond mere intellect to any other set upon the continent of North America. They are decidedly the most servile imitators of the English it is possible to conceive.”
—Edgar Allan Poe (1809–1845)