torus
Sign in to savethumb|A ring torus with a selection of circles on its surface thumb|As the distance from the axis of revolution decreases, the ring torus becomes a horn torus, then a spindle torus, and finally degeneracy (mathematics)|degenerates into a double-covered [[sphere.]] thumb|A ring torus with aspect ratio 3, the ratio between the diameters of the larger (blue) circle and the smaller (red) circle. The two radii coordinates are shown as well. The radius denoted by capital, R, is the distance from the geometric center of the outer ring lying outside the volume, to the center of the inner ring. The rad
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A torus is a doughnut-shaped geometric surface created by rotating a circle around an axis, and it can take different forms depending on how far the circle is from that axis. Mathematicians study tori because they are fundamental shapes that appear in geometry and can transform into other shapes, such as spheres, by changing their dimensions.
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Article
19 sectionsContents
- Etymology
- Geometry
- Differential geometry for the ring torus
- Topology
- Two-sheeted cover
- ''n''-dimensional torus
- Configuration space
- Flat torus
- Conformal classification of flat tori
- Genus ''g'' surface
- Toroidal polyhedra
- Automorphisms
- Coloring a torus
- de Bruijn torus
- Cutting a torus
- See also
- Notes
- References
- External links
thumb|A ring torus with a selection of circles on its surface thumb|As the distance from the axis of revolution decreases, the ring torus becomes a horn torus, then a spindle torus, and finally degeneracy (mathematics)|degenerates into a double-covered [[sphere.]] thumb|A ring torus with aspect ratio 3, the ratio between the diameters of the larger (blue) circle and the smaller (red) circle. The two radii coordinates are shown as well. The radius denoted by capital, R, is the distance from the geometric center of the outer ring lying outside the volume, to the center of the inner ring. The radius denoted by lower case, r, is the distance from the inner ring's center to the surface of the torus. In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially referred to as a doughnut.
If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution, also known as a ring torus. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus (or self-crossing torus or self-intersecting torus). If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a toroid, as in a square toroid.