# Radius

## Etymology

- Date: circa 1611

## Definitions

- 1 : a line segment extending from the center of a circle or sphere to the circumference or bounding surface
- 2 a : the bone on the thumb side of the human forearm; also : a corresponding part of vertebrates above fishes

- b : the third and usually largest vein of an insect's wing

- 3 a : the length of a radius <a truck with a short turning radius>

- b : the circular area defined by a stated radius
- c : a bounded or circumscribed area

## Description

In classical geometry, a **radius** 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, which is half the diameter.

More generally — in geometry, science, engineering, and many other contexts — the radius of something (e.g., a cylinder, a polygon, a mechanical part, a hole, or a galaxy) usually refers to the distance from its center or axis of symmetry to a point in the periphery: usually the point farthest from the center or axis (the outermost or maximum radius), or, sometimes, the closest point (the short or minimum radius). 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.

The radius of a regular polygon (or polyhedron) is the distance from its center to any of its vertices; which is also its circumradius. The inradius of a regular polygon is also called apothem.

In graph theory, the radius of a graph is the minimum over all vertices u of the maximum distance from u to any other vertex of the graph.

The name comes from Latin radius, meaning "ray" but also the spoke of a chariot wheel. The plural in English is radii (as in Latin), but radiuses can be used, though it rarely is.[1]