Torus

A torus, in geometry, is a doughnut-shaped, three-dimensional figure formed when a circle is rotated through 360° about a line in its plane, but not passing through the circle itself. The word torus is derived from a Latin word meaning bulge. The plural of torus is tori. Another common example of a torus is the inner tube of a tire. Imagine, for example, that the circle lies in space such that its diameter is parallel to a straight line. The figure that is formed is a hollow, circular tube, a torus. A torus is sometimes referred to as an anchor ring.

The surface area and volume of a torus can be calculated if one knows the radius of the circle and the radius of the torus itself; that is, the distance from the furthest part of the circle from the line about which it is rotated. If the former dimension is represented by the letter r, and the latter dimension by R, then the surface area of the torus is given by 4π² Rr, and the volume is given by 2π² Rr₂, where π (pi) is the constant approximately equal to 3.14.

Problems involving the torus were well known to and studied by the ancient Greeks. For example, the formula for determining the surface area and volume of the torus came about as the result of the work of Greek mathematician Pappus of Alexandria, who lived around the third century AD. The Pappus’ theorem for surfaces of revolution is stated: area equals the circumference of the path taken by the center of mass of the figure as it revolves, multiplied by its outer perimeter. The Pappus’ theorem for solids of revolution is stated: volume equals the circumference of the path taken by the center of mass of the figure as it revolves, multiplied by its area. Today, problems involving the torus are of special interest to topologists; that is, mathematicians with special interests in topology, the study of the properties of geometric figures and solids that remain constant when stretched or bent.

See also Topology.

to·rus / ˈtôrəs/ • n. (pl. to·ri / ˈtôrī/ or to·rus·es) 1. Geom. a surface or solid formed by rotating a closed curve, esp. a circle, around a line that lies in the same plane but does not intersect it (e.g., like a ring-shaped doughnut). ∎  a thing of this shape, esp. a large ring-shaped chamber used in physical research.2. Archit. a large convex molding, typically semicircular in cross section, esp. as the lowest part of the base of a column.3. Anat. a ridge of bone or muscle: the maxillary torus.4. Bot. the receptacle of a flower.

Torus

A torus is a doughnut-shaped, three-dimensional figure formed when a circle is rotated through 360° about a line in its plane , but not passing through the circle itself. Imagine, for example, that the circle lies in space such that its diameter is parallel to a straight line. The figure that is formed is a hollow, circular tube, a torus. A torus is sometimes referred to as an anchor ring.

The surface area and volume of a torus can be calculated if one knows the radius of the circle and the radius of the torus itself, that is, the distance from the furthest part of the circle from the line about which it is rotated. If the former dimension is represented by the letter r, and the latter dimension by R, then the surface area of the torus is given by 4π2Rr, and the volume is given by 2π2Rr2.

Problems involving the torus were well known to and studied by the ancient Greeks. For example, the formula for determining the surface area and volume of the torus came about as the result of the work of the Greek mathematician Pappus of Alexandria, who lived around the third century a.d. Today, problems involving the torus are of special interest to topologists.

See also Topology.

torus (pl. tori). Bold projecting convex moulding of semicircular section, e.g. on either side of the scotia in an Attic base. Larger tori, e.g. on the base of a triumphal column, are often enriched with bay-leaf garlands.

torus The shape of a doughnut; a geometrical surface formed by rotating a circle (or other closed curve) about a circle in its plane without intersecting it.