Encyclopedia > Ball (mathematics)

  Article Content

Ball (mathematics)

In mathematics, in a metric space, a ball is a set containing all points within a specified distance of a given point.

The set is often written as Br(p), meaning the ball of radius r centred on a point p. This is defined as:

Br(p) = { x | d(x,p) < r }
where d is the distance function or metric.

If the less-than symbol (<) is replaced by a less-than-or-equal-to (≤), the above definition becomes that of a closed ball. This is usually notated by adding an overscore[?] to the B.

If r = 1, then it is called a unit ball.

A set is bounded if it is contained in a ball.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Lake Ronkonkoma, New York

... units at an average density of 546.4/km² (1,414.4/mi²). The racial makeup of the town is 93.53% White, 1.36% African American, 0.15% Native American, 2.41% Asian, ...

 
 
 
This page was created in 25.2 ms