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]]. | + | {{asy image|<asy>unitsize(40pt);draw(unitcircle,black);pair O = (0,0);pair A = (-1,0);pair B = (1,0);draw(A--O--B);label("$O$",O,S);label("$A$",A,W);label("$B$",B,E);</asy>|right|This circle has diameter <math>AB</math><br />since center <math>O</math> lies on <math>AB</math>.}} |
| + | 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. | ||
| − | [[ | + | ==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]] | ||
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| + | {{stub}} | ||
Latest revision as of 19:12, 16 January 2025
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  since center  lies on .
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![[asy]unitsize(40pt);draw(unitcircle,black);pair O = (0,0);pair A = (-1,0);pair B = (1,0);draw(A--O--B);label("$O$",O,S);label("$A$",A,W);label("$B$",B,E);[/asy]](http://latex.artofproblemsolving.com/b/9/3/b93e62ca8e3b80b26714b654f32b62488bb1f155.png)
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.
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