AskDefine | Define radii

Dictionary Definition

radius

Noun

1 the length of a line segment between the center and circumference of a circle or sphere [syn: r]
2 a straight line from the center to the perimeter of a circle (or from the center to the surface of a sphere)
3 a circular region whose area is indicated by the length of its radius; "they located it within a radius of 2 miles"
4 the outer and slightly shorter of the two bones of the human forearm
5 support consisting of a radial member of a wheel joining the hub to the rim [syn: spoke] [also: radii (pl)]radii See radius

User Contributed Dictionary

English

Pronunciation

  • US: /ˈɹeɪˌdi.aɪ/

Noun

radii
  1. Plural of radius

Esperanto

Verb

eo-verb radi

Latin

Noun

radii, radiorum ; second declension
  1. rays, plural of radius, ray

Extensive Definition

Circles

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 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, a polygon, a graph, or a mechanical part) is the distance from its 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 r=\frac.
To compute the radius of a circle going through three points P_1, P_2, P_3, the following formula can be used:
r=\frac
where \theta is the angle \angle P_1 P_2 P_3.
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.
radii in Arabic: شعاع
radii in Asturian: Radiu (xeometría)
radii in Min Nan: Poàⁿ-kèng
radii in Bosnian: Poluprečnik
radii in Bulgarian: Радиус
radii in Catalan: Radi (geometria)
radii in Chuvash: Радиус
radii in Czech: Poloměr
radii in Danish: Radius (cirkel)
radii in German: Radius
radii in Modern Greek (1453-): Ακτίνα (γεωμετρία)
radii in Spanish: Radio (geometría)
radii in Esperanto: Radiuso
radii in Basque: Erradio (geometria)
radii in French: Rayon (géométrie)
radii in Galician: Raio (xeometría)
radii in Korean: 반지름
radii in Indonesian: Radius
radii in Icelandic: Geisli (rúmfræði)
radii in Italian: Raggio (geometria)
radii in Hebrew: רדיוס
radii in Swahili (macrolanguage): Nusukipenyo
radii in Latvian: Rādiuss
radii in Luxembourgish: Radius
radii in Lithuanian: Spindulys
radii in Macedonian: Радиус
radii in Dutch: Straal (wiskunde)
radii in Japanese: 半径
radii in Norwegian: Radius
radii in Norwegian Nynorsk: Radius
radii in Polish: Promień
radii in Portuguese: Raio
radii in Romanian: Rază
radii in Quechua: Illwa
radii in Russian: Радиус
radii in Simple English: Radius
radii in Slovak: Polomer (kružnica)
radii in Slovenian: Polmer
radii in Serbian: Полупречник
radii in Finnish: Säde
radii in Swedish: Radie
radii in Tamil: ஆரம்
radii in Thai: รัศมี
radii in Vietnamese: Bán kính
radii in Turkish: Yarıçap
radii in Ukrainian: Радіус
radii in Chinese: 半径
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