Radius: Difference between revisions
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{{otheruses}} |
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[[Image:CIRCLE 1.svg|thumb|right|Circle illustration]] |
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In classical [[geometry]], a '''radius''' of a [[circle]] or [[sphere]] its 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, which is half the [[diameter]]. |
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More generally — in [[geometry]], [[science]], [[engineering]], and many other contexts — the '''radius''' of something (e.g., a [[cylinder (geometry)|cylinder]], a [[polygon]], a mechanical part, or a [[galaxy]]) usually refers to the [[distance]] from its [[center (geometry)|center]] or [[axis of symmetry]] to its outermost points. If the object does not have an obvious center, the term may refer to its '''circumradius''', the radius of its [[circumscribed circle]] or [[circumscribed sphere]]. In either case, the radius may be more than half the diameter (which is usually defined as the maximum distance between any two points of the figure). |
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The '''radius''' of a regular polygon (or polyhedron) is the distance from its center to any of its vertices; which is also its circumradius. |
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In [[graph theory]], the [[radius (graph theory)|'''radius''' of a graph]] is the minimum over all vertices ''u'' of the maximum distance from ''u'' to any other vertex of the graph. |
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The name comes from [[Latin]] ''radius'', meaning "ray" but also the spoke of a chariot wheel. The plural in [[English language|English]] is '''radii''' (as in Latin), but '''radiuses''' is also occasionally used. |
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==Formulas for circles== |
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===Radius from circumference=== |
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The radius of the circle with [[perimeter]] ([[circumference]]) ''C'' is |
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: <math>r = \frac{C}{2\pi}.</math> |
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===Radius from area=== |
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The radius of a circle with [[area]] ''A'' is |
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: <math>r= \sqrt{\frac{A}{\pi}}.</math> |
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===Radius from three points=== |
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To compute the radius of a circle going through three points ''P''<sub>1</sub>, ''P''<sub>2</sub>, ''P''<sub>3</sub>, the following formula can be used: |
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: <math>r=\frac{|P_1-P_3|}{2\sin\theta}</math> |
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where ''θ'' is the angle <math> \angle P_1 P_2 P_3.</math> |
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==Formulas for regular polygons== |
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These formulas assume a regular polygon with ''n'' sides. |
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===Radius from side=== |
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The radius can be computed from the side ''s'' by: |
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: <math>r = R_n\, s</math> where <math> R_n = \frac{1}{2 \sin \frac{\pi}{n}} \quad\quad |
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\begin{array}{r|ccr|c} |
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n & R_n & & n & R_n\\ |
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\hline |
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2 & 0.50000000 & & 10 & 1.6180340- \\ |
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3 & 0.5773503- & & 11 & 1.7747328- \\ |
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4 & 0.7071068- & & 12 & 1.9318517- \\ |
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5 & 0.8506508+ & & 13 & 2.0892907+ \\ |
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6 & 1.00000000 & & 14 & 2.2469796+ \\ |
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7 & 1.1523824+ & & 15 & 2.4048672- \\ |
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8 & 1.3065630- & & 16 & 2.5629154+ \\ |
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9 & 1.4619022+ & & 17 & 2.7210956- |
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\end{array} |
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</math> |
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<!-- To add: radius from area, inradius from outradius, outradius from inradius --> |
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==Formulas for hypercubes== |
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===Radius from side=== |
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The radius of a ''d''-dimensional hypercube with side ''s'' is |
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:<math> r = \frac{s}{2}\sqrt{d}.</math> |
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== See also== |
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*[[Radius (bone)]] |
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*[[Radius of curvature]] |
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*[[Bend radius]] |
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*[[Radius of convexity]] |
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*[[Radius of convergence]] |
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*[[Radius of gyration]] |
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*[[Filling radius]] (Riemannian geometry) |
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[[Category:Geometry]] |
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[[Category:Length]] |
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[[ar:نصف قطر]] |
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[[ast:Radiu (xeometría)]] |
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[[zh-min-nan:Poàⁿ-kèng]] |
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[[be:Радыюс]] |
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[[be-x-old:Радыюс]] |
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[[bs:Poluprečnik]] |
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[[bg:Радиус]] |
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[[ca:Radi (geometria)]] |
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[[cv:Радиус]] |
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[[cs:Poloměr]] |
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[[da:Radius (cirkel)]] |
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[[de:Radius]] |
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[[el:Ακτίνα (γεωμετρία)]] |
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[[es:Radio (geometría)]] |
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[[eo:Radiuso]] |
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[[eu:Erradio (geometria)]] |
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[[fa:شعاع]] |
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[[fr:Rayon (géométrie)]] |
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[[gl:Raio (xeometría)]] |
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[[ko:반지름]] |
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[[id:Radius]] |
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[[is:Geisli (rúmfræði)]] |
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[[it:Raggio (geometria)]] |
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[[he:רדיוס]] |
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[[sw:Nusukipenyo]] |
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[[lv:Rādiuss]] |
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[[lb:Radius]] |
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[[lt:Spindulys]] |
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[[mk:Радиус]] |
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[[mr:त्रिज्या]] |
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[[ms:Jejari]] |
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[[mn:Радиус]] |
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[[nl:Straal (wiskunde)]] |
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[[ja:半径]] |
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[[no:Radius]] |
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[[nn:Radius]] |
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[[km:កាំ]] |
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[[pl:Promień (geometria)]] |
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[[pt:Raio]] |
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[[ro:Rază]] |
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[[qu:Illwa]] |
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[[ru:Радиус]] |
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[[simple:Radius]] |
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[[sk:Polomer (kružnica)]] |
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[[sl:Polmer]] |
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[[szl:Průmjyń]] |
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[[sr:Полупречник]] |
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[[fi:Säde]] |
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[[sv:Radie]] |
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[[ta:ஆரம்]] |
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[[th:รัศมี]] |
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[[tr:Yarıçap]] |
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[[uk:Радіус]] |
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[[ur:رداس]] |
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[[vi:Bán kính]] |
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[[zh:半径]] |