# 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- Plural of radius

## Esperanto

### Verb

eo-verb radi- to radiate

## Latin

### Noun

radii, radiorum ; second declension# 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.## See also

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