radius

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

English

Pronunciation

• US: /ˈɹeɪˌdi.aɪ/

Noun

radii

1. Plural of radius

Esperanto

Verb

eo-verb radi

1. to radiate

Latin

Noun

radii, radiorum ; second declension

1. rays, plural of radius, ray

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

• Radius (bone)
• Radius of convergence