radii

Radii is the plural form of radius. In geometry, radius refers to the fixed distance from the center of a circle or sphere to any point on its boundary. In anatomy, radii (plural) denotes the forearm bone known as the radius.

In planar geometry, the radius of a circle with radius r determines key measures: the circumference is 2πr and the area is πr^2. The concept extends to spheres, where the radius r yields surface area 4πr^2 and volume 4/3 π r^3. Radii also appear in three-dimensional contexts as lines from the center of a sphere to its surface, and the idea of radial symmetry describes objects that look the same after rotation about the center.

In polar coordinates, r is the radial distance from the origin, while the angle specifies direction. This framework underpins many problems and diagrams that use radii to describe circular or spherical shapes, sectors, and arcs.

Radii in anatomy refer to the radius bone of the forearm. In the standard anatomical position, the radius lies on the lateral (thumb) side of the forearm and runs parallel to the ulna. The proximal end forms part of the elbow joint through the radioulnar articulations, while the distal end interacts with the carpal bones at the wrist. The interosseous membrane connects the radius and ulna along their lengths, enabling forearm rotation. Common injuries involve distal radius fractures, which are especially prevalent after falls onto an outstretched hand.

Etymologically, radii is formed from the Latin plural of radius and is used across disciplines to denote multiple distances or objects sharing the same radial relationship.