In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, a torus (pl. tori) is a surface of revolution

Surface of revolution

A surface of revolution is a surface in Euclidean space created by rotating a curve around a straight line in its plane ....

 generated by revolving a circle

Circle

A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....

 in three dimensional space about an axis coplanar with the circle. In most contexts it is assumed that the axis does not touch the circle - in this case the surface has a ring shape and is called a ring torus or simply torus if the ring shape is implicit.

Other types of torus include the horn torus, which is generated when the axis is tangent to the circle, and the spindle torus, which is generated when the axis is a chord of the circle.