Radius
1780815
220856674
2008-06-21T23:06:40Z
122.106.242.51
/* Circles */
{{otheruses}}
== Circles ==
[[Image:CIRCLE 1.svg|thumb|Circle illustration]]
In classical [[geometry]], a '''radius''' (plural: radii) of a [[circle]] or [[sphere]] is any [[line segment]] from its center to its [[perimeter]]. By extension, '''''the'' radius''' of a circle or sphere is the [[length]] of any such segment. The radius is half the [[diameter]]. In science and engineering the term [[Radius_of_curvature|radius of curvature]] is commonly used as a synonym for radius.
More generally—in [[geometry]], [[engineering]], [[graph theory]], and many other contexts—the radius of something (e.g., a [[cylinder (geometry)|cylinder]], a [[polygon]], a [[graph theory|graph]], or a mechanical part) is the [[distance]] from its [[center (geometry)|center]] or [[axis of symmetry]] to its outermost points. In this case, the radius may be more than half the diameter.
The relationship between the radius and the [[circumference]] of a circle is <math>r=\frac{c}{2\pi}</math>.
To compute the radius of a circle going through three points <math> P_1, P_2, P_3</math>, the following formula can be used:
: <math>r=\frac{|P_1-P_3|}{2\sin\theta}</math>
where <math>\theta</math> is the angle <math> \angle P_1 P_2 P_3.</math>
A more simple way to find the length of the radius is:
: <math>r=\frac{diameter}{2}</math>
A radius may also be applied to [[arithmetic]]. Where 4,5,6,7,8,9 and 10 can be in a three number radius of 7.
== Polygons ==
Regular polygons are sometimes said to have a radius, defined as the distance from the center to a vertex. This is the same as the radius of a circumscribed circle with the same center. This latter formulation is sometimes used to define the radius of an arbitrary polygon and is called the circumradius.
== See also==
*[[Radius (bone)]]
*[[Radius of convergence]]
[[Category:Geometry]]
[[ar:نصف قطر]]
[[ast:Radiu (xeometría)]]
[[zh-min-nan:Poàⁿ-kèng]]
[[bs:Poluprečnik]]
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[[ca:Radi (geometria)]]
[[cv:Радиус]]
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[[da:Radius (cirkel)]]
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[[el:Ακτίνα (γεωμετρία)]]
[[es:Radio (geometría)]]
[[eo:Radiuso]]
[[eu:Erradio (geometria)]]
[[fr:Rayon (géométrie)]]
[[gl:Raio (xeometría)]]
[[ko:반지름]]
[[id:Radius]]
[[is:Geisli (rúmfræði)]]
[[it:Raggio (geometria)]]
[[he:רדיוס]]
[[sw:Nusukipenyo]]
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[[mk:Радиус]]
[[nl:Straal (wiskunde)]]
[[ja:半径]]
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[[ro:Rază]]
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[[sk:Polomer (kružnica)]]
[[sl:Polmer]]
[[sr:Полупречник]]
[[fi:Säde]]
[[sv:Radie]]
[[ta:ஆரம்]]
[[th:รัศมี]]
[[vi:Bán kính]]
[[tr:Yarıçap]]
[[uk:Радіус]]
[[zh:半径]]