Torus

Torus

A Torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a ring torus or simply torus if the ring shape is implicit.

Description

A torus should not be confused with a solid torus, which is formed by rotating a disk, rather than a circle, around an axis. A solid torus is a torus plus the volume inside the torus. Real-world examples of toroidal objects include inner tubes.

A circle rotated about a coplanar axis that does not intersect the circle produces a torus. This is intuitively clear for a ring torus, which is more commonly known as a "doughnut" or "bagel".

Mathematics

In topology, a ring torus is homeomorphic to the Cartesian product of two circles: S1 × S1, and the latter is often used to describe the former.

In differential geometry of surfaces, a torus is a standard example of a surface of revolution. A torus can also be described as a quotient of the Euclidean plane by a lattice of two periods. More generally, a torus is a compact Riemann surface.

In popular culture

Torus shapes are commonly used in 3D computer graphics, computer gaming and generative art, being very easy to generate from a mesh grid.

See also

• Villarceau circles
• Clifford torus
• Dupin cyclide
• Torus knot
• Torus mandibularis
• Torus palatinus

References

Torus Resources
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