Difference between revisions of "Diameter"
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| − | 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]] | ||
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| + | ==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]] | ||
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| + | [[Category:Geometry]] | ||
Latest revision as of 10:01, 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 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.
