Difference between revisions of "Diameter"

m
m
 
(2 intermediate revisions by 2 users not shown)
Line 1: Line 1:
A '''diameter''' of a [[circle]] is a [[chord]] of that circle which passes through the [[center]].  Thus a diameter divides the circle into two regions of equal [[area]].
+
A '''diameter''' of a [[circle]] is a [[chord]] of that circle which passes through the [[center]].  Thus a diameter divides the circle into two regions of equal [[area]] called [[semicircle]]s.
  
 
[[Image:Diameter.PNG|center]]
 
[[Image:Diameter.PNG|center]]
 +
 +
 +
==Diameter of a set==
 +
The diameter of more general [[set]]s can also be defined.  In any given [[metric space]] (that is, anywhere you can measure [[distance]]s between [[point]]s such as normal Euclidean 3-D space, the surface of the Earth, or any [[real number|real]] [[vector space]]) the diameter of a [[bounded]] set of points is the [[supremum]] of the distances between pairs of points.  In the case where the set of points is a circle, the diameter is the length of the diameter of the circle.
  
 
[[Category:Definition]]
 
[[Category:Definition]]
 +
 +
[[Category:Geometry]]

Latest revision as of 11:01, 15 February 2009

A diameter of a circle is a chord of that circle which passes through the center. Thus a diameter divides the circle into two regions of equal area called semicircles.

Diameter.PNG


Diameter of a set

The diameter of more general sets can also be defined. In any given metric space (that is, anywhere you can measure distances between points such as normal Euclidean 3-D space, the surface of the Earth, or any real vector space) the diameter of a bounded set of points is the supremum of the distances between pairs of points. In the case where the set of points is a circle, the diameter is the length of the diameter of the circle.