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| | Mine Deputy Bud Eure from Rexton, has numerous hobbies including models, property developers [http://oewrecycling.com/?option=com_k2&view=itemlist&task=user&id=48484 new properties in singapore] singapore and reflexology. Would rather travel and was encouraged after visiting Cidade Velha. |
| [[File:Circle-withsegments.svg|thumb|200px|right|Circle illustration with circumference (C) in black, diameter (D) in cyan, radius (R) in red, and centre or origin (O) in magenta.]]
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| In classical [[geometry]], the '''radius''' of a [[circle]] or [[sphere]] is the length of a [[line segment]] from its [[Centre (geometry)|center]] to its [[perimeter]]. The name comes from [[Latin]] ''radius'', meaning "ray" but also the spoke of a chariot wheel.<ref name="radic">[http://dictionary.reference.com/browse/Radius Definition of Radius] at dictionary.reference.com. Accessed on 2009-08-08.
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| </ref> The plural of ''radius'' can be either ''radii'' (from the Latin plural) or the conventional English plural ''radiuses''.<ref>{{cite web|url=http://www.merriam-webster.com/dictionary/radius |title=Radius - Definition and More from the Free Merriam-Webster Dictionary |publisher=Merriam-webster.com |date= |accessdate=2012-05-22}}</ref> The typical abbreviation and [[variable (mathematics)|mathematic variable]] name for "radius" is '''r'''. By extension, the [[diameter]] '''d '''is defined as twice the radius:<ref name="mwd1">
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| [http://www.mathwords.com/r/radius_of_a_circle_or_sphere.htm Definition of radius] at mathwords.com. Accessed on 2009-08-08.</ref> | |
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| : <math>d \doteq 2r \quad \Rightarrow \quad r = \frac{d}{2}.</math>
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| 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. The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it. The inner radius of a ring, tube or other hollow object is the radius of its cavity.
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| For regular polygons, the radius is the same as its circumradius.<ref name="schaum">Barnett Rich, Christopher Thomas (2008), ''Schaum's Outline of Geometry'', 4th edition, 326 pages. McGraw-Hill Professional. ISBN 0-07-154412-7, ISBN 978-0-07-154412-2. [http://books.google.com.br/books?id=ab8lZG2yubcC Online version] accessed on 2009-08-08.</ref> The inradius of a regular polygon is also called [[apothem]]. 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.<ref name="yel">Jonathan L. Gross, Jay Yellen (2006), ''Graph theory and its applications''. 2nd edition, 779 pages; CRC Press. ISBN 1-58488-505-X, 9781584885054. [http://books.google.com.br/books?id=unEloQ_sYmkC Online version] accessed on 2009-08-08.</ref>
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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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| This formula uses the Sine Rule.
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| If the three points are given by their coordinates <math> (x_1,y_1) </math>,
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| <math> (x_2,y_2) </math> and <math> (x_3,y_3) </math>, one can also use the following formula :
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| : <math> r={\frac {\sqrt{ \left( \left( {\it x_2}-{\it x_1} \right) ^{2}+ \left( {\it y_2}-{\it y_1} \right) ^{2} \right) \left( \left( {\it x_2}-{\it x_3} \right) ^{2}+ \left( {\it y_2}-{\it y_3} \right) ^{2} \right) \left( \left( {\it x_3}-{\it x_1} \right) ^{2}+ \left( {\it y_3}-{\it y_1} \right) ^{2} \right)} }{ 2 \left| {\it x_1}\,{\it y_2}+{\it x_2}\,{\it y_3}+{\it x_3}\,{\it y_1}-{\it x_1}\,{\it y_3}-{\it x_2}\,{\it y_1}-{\it x_3}\,{\it y_2} \right| }}</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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| {{multicol}}
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| *[[Atomic radius]]
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| *[[Bend radius]]
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| *[[Bohr radius]]
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| *[[Filling radius]] in Riemannian geometry
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| * [[Minimum railway curve radius]]
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| *[[Radius (bone)]]
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| {{multicol-break}}
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| *[[Radius of convergence]]
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| *[[Radius of convexity]]
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| *[[Radius of curvature]]
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| *[[Radius of gyration]]
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| *[[Schwarzschild radius]]
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| {{multicol-end}}
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[[planetmath:2006|Radius (PlanetMath.org website)]]
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| [[Category:Spheres]]
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| [[Category:Circles]]
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| [[Category:Length]]
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Mine Deputy Bud Eure from Rexton, has numerous hobbies including models, property developers new properties in singapore singapore and reflexology. Would rather travel and was encouraged after visiting Cidade Velha.