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31:
1055:
607:
1575:
In a spherical coordinate system, the radius describes the distance of a point from a fixed origin. Its position if further defined by the polar angle measured between the radial direction and a fixed zenith direction, and the azimuth angle, the angle between the orthogonal projection of the radial
1050:{\displaystyle r={\frac {\sqrt {{\bigl (}(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}{\bigr )}{\bigl (}(x_{2}-x_{3})^{2}+(y_{2}-y_{3})^{2}{\bigr )}{\bigl (}(x_{3}-x_{1})^{2}+(y_{3}-y_{1})^{2}{\bigr )}}}{2{\bigl |}x_{1}y_{2}+x_{2}y_{3}+x_{3}y_{1}-x_{1}y_{3}-x_{2}y_{1}-x_{3}y_{2}{\bigr |}}}.}
512:
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215:
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.
1545:, as they correspond to a two-dimensional polar coordinate system in the plane through the point, parallel to the reference plane. The third coordinate may be called the
211:. 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
410:
1503:
of the system is the point where all three coordinates can be given as zero. This is the intersection between the reference plane and the axis.
1238:
1576:
direction on a reference plane that passes through the origin and is orthogonal to the zenith, and a fixed reference direction in that plane.
1803:
146:
1499:
In the cylindrical coordinate system, there is a chosen reference axis and a chosen reference plane perpendicular to that axis. The
1731:
1786:
1756:
1723:
1358:
335:
1494:
1880:
Groisman, Alexander; Steinberg, Victor (1997-02-24). "Solitary Vortex Pairs in
Viscoelastic Couette Flow".
306:
For many geometric figures, the radius has a well-defined relationship with other measures of the figure.
263:
1570:
1448:
1839:
1522:
that lies in the reference plane, starting at the origin and pointing in the reference direction.
1412:
24:
222:, the radius is the same as its circumradius. The inradius of a regular polygon is also called
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16:
Segment in a circle or sphere from its center to its perimeter or surface and its length
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1927:
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315:
121:, meaning ray but also the spoke of a chariot wheel. The typical abbreviation and
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1735:
219:
1911:
1690:
1193:
1959:
1591:
1456:
1953:
1919:
1835:
1777:
Advanced
Mathematics: Precalculus with Discrete Mathematics and Data Analysis
507:{\displaystyle r={\frac {|{\vec {OP_{1}}}-{\vec {OP_{3}}}|}{2\sin \theta }},}
250:
114:, and in more modern usage, it is also their length. The name comes from the
20:
1329:
then these values are also the radii of the corresponding regular polygons.
1622:
544:
227:
103:
1894:
1597:
1586:
1300:{\displaystyle R_{n}=1\left/\left(2\sin {\frac {\pi }{n}}\right)\right..}
1671:"Radius - Definition and More from the Free Merriam-Webster Dictionary"
1827:
30:
1422:
1345:
374:
246:
111:
1804:"Resonant electron beam interaction with several lower hybrid waves"
1437:
212:
189:{\displaystyle d\doteq 2r\quad \Rightarrow \quad r={\frac {d}{2}}.}
134:
75:
1481:
223:
1533:, while the angular coordinate is sometimes referred to as the
199:
If an object does not have a center, the term may refer to its
99:
95:
1944:
are cylindrical coordinates as a function of axial position"
1441:
115:
1646:(from the Latin plural) or the conventional English plural
1291:
1259:
373:
The radius of the circle that passes through the three non-
321:
19:
This article is about the line segment. For the bone, see
547:. If the three points are given by their coordinates
1541:. The radius and the azimuth are together called the
1361:
1241:
610:
413:
338:
266:
149:
1718:, 4th edition, 326 pages. McGraw-Hill Professional.
1693:
at dictionary.reference.com. Accessed on 2009-08-08.
1553:(if the reference plane is considered horizontal),
1773:Brown, Richard G. (1997). Andrew M. Gleason (ed.).
1774:
1390:
1299:
1049:
506:
362:
290:
188:
1888:(8). American Physical Society (APS): 1460–1463.
1879:
1951:
1802:Krafft, C.; Volokitin, A. S. (1 January 2002).
1801:
1447:The fixed point (analogous to the origin of a
1525:The distance from the axis may be called the
1036:
894:
882:
800:
793:
711:
704:
622:
1459:from the pole in the fixed direction is the
1401:
1391:{\displaystyle r={\frac {s}{2}}{\sqrt {d}}.}
363:{\displaystyle r={\sqrt {\frac {A}{\pi }}}.}
1463:. The distance from the pole is called the
1488:
1893:
1714:Barnett Rich, Christopher Thomas (2008),
1705:at mathwords.com. Accessed on 2009-08-08.
1781:. Evanston, Illinois: McDougal Littell.
1564:
1192:
29:
1952:
1747:Jonathan L. Gross, Jay Yellen (2006),
1772:
1751:. 2nd edition, 779 pages; CRC Press.
1708:
1766:
1684:
1406:
291:{\displaystyle r={\frac {C}{2\pi }}}
1696:
1642:The plural of radius can be either
1514:axis, to differentiate it from the
1060:
83:
13:
1741:
242:to any other vertex of the graph.
14:
1971:
1868:t is the longitudinal position...
1749:Graph theory and its applications
1506:The axis is variously called the
1417:The polar coordinate system is a
601:, the radius can be expressed as
234:is the minimum over all vertices
140:is defined as twice the radius:
1852:...in cylindrical coordinates (
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245:The radius of the circle with
163:
1:
1657:
1495:Cylindrical coordinate system
1335:
238:of the maximum distance from
1716:Schaum's Outline of Geometry
320:The radius of a circle with
7:
1912:10.1103/physrevlett.78.1460
1579:
1571:Spherical coordinate system
1322:are given in the table. If
10:
1976:
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1492:
1440:from a fixed point and an
1410:
1209:of a regular polygon with
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18:
1402:Use in coordinate systems
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1444:from a fixed direction.
543:. This formula uses the
1882:Physical Review Letters
1763:accessed on 2009-08-08.
1738:accessed on 2009-08-08.
1489:Cylindrical coordinates
1471:, and the angle is the
1413:Polar coordinate system
1197:A square, for example (
66: center or origin
25:Radius (disambiguation)
1594:in Riemannian geometry
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23:. For other uses, see
1673:. Merriam-webster.com
1603:Radius of convergence
1565:Spherical coordinates
1555:longitudinal position
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123:mathematical variable
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1703:Definition of radius
1691:Definition of Radius
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1318:for small values of
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1067:Circumscribed circle
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411:
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209:circumscribed sphere
205:circumscribed circle
203:, the radius of its
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133:. By extension, the
39: circumference
1904:1997PhRvL..78.1460G
1820:2002PhPl....9.2786K
1613:Radius of curvature
1608:Radius of convexity
1436:is determined by a
125:name for radius is
1808:Physics of Plasmas
1618:Radius of gyration
1473:angular coordinate
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1828:10.1063/1.1465420
1759:, 9781584885054.
1732:978-0-07-154412-2
1543:polar coordinates
1465:radial coordinate
1426:coordinate system
1407:Polar coordinates
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1842:on 14 April 2013
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1518:, which is the
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1569:Main article:
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1559:axial position
1493:Main article:
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1428:in which each
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1844:. Retrieved
1840:the original
1811:
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1587:Bend radius
1508:cylindrical
1477:polar angle
1423:dimensional
1205:The radius
1846:9 February
1677:2012-05-22
1658:References
1537:or as the
1516:polar axis
1461:polar axis
1455:, and the
1348:with side
1336:Hypercubes
1307:Values of
1065:See also:
314:See also:
1920:0031-9007
1836:1089-7674
1346:hypercube
1279:π
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375:collinear
352:π
283:π
247:perimeter
164:⇒
154:≐
112:perimeter
106:from its
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1928:54814721
1648:radiuses
1580:See also
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1438:distance
1235:, where
213:inradius
135:diameter
92:radiuses
76:geometry
1932:"where
1900:Bibcode
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377:points
310:Circles
302:Formula
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1170:1.461
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