Can a torus be a sphere?

If the axis of revolution passes twice through the circle, the surface is a spindle 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 a related shape, a toroid.

Can a torus be turned inside out?

A punctured torus can be turned inside out like a glove. During such a topological procedure areas are allowed to be stretched or squeezed, but not ripped or joined.

Is a torus topologically equivalent to a sphere?

On the other hand, a closed surface such as a torus (doughnut) is not equivalent to a sphere, since no amount of bending or stretching will make it into a sphere, nor is a surface with a boundary equivalent to a sphere, e.g., a cylinder with an open top, which may be stretched into a disk (a circle plus its interior).

What is a 2D torus?

1D torus is a simple circle, and 2D torus has the shape of a doughnut. At one dimension, a torus topology is equivalent to a ring interconnect network, of a shape of a circle. At 2D, it is equivalent to a 2D mesh, but with extra connection at the edge nodes, which is the definition of 2D torus.

Is a torus hollow?

The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced. If the revolved figure is a circle, then the object is called a torus.

Is torus A 3D shape?

A torus is a 3D shape formed by a small circle that rotates around a bigger circle. It usually looks like a circular ring, or a donut.

Is space a torus?

Inside ordinary three-dimensional space, there’s no way to build an actual, smooth physical torus from flat material without distorting the flat geometry. Imagine you’re a two-dimensional creature whose universe is a flat torus.

What’s the difference between a torus and a sphere leash?

On a sphere, the leash can always be pulled in; on a torus, sometimes it can’t be. (See homotopy.) Share Cite Follow edited Jul 2 ’14 at 18:16 answered Jul 2 ’14 at 15:06 user21467user21467 $\\endgroup$ 22 97 $\\begingroup$This seems cruel to two-dimensional dogs$\\endgroup$ – Ben Grossmann Jul 2 ’14 at 15:07 28

What is the integral of a torus and a sphere?

A sphere has genus zero and so χ(S2) = 2, while a torus has genus one and so χ(T) = 0. You could, as the ordinance survey people do, choose triangulation points on your surface, measure the Gaussian Curvature at those points and then use this to approximate the above integral. Travel a lot and depict a map of the world.

How do you know if you are on a torus?

If your second path crosses your first line once, you are on a sphere. If it doesn’t cross or it crosses more than once, you are on a torus. Otherwise you are on a sphere. EDIT: This assumes that “torus” means “perfectly symmetrical donut”, in the general case of torus = sphere+handles, it will not work.

What is the difference between a torus and a solid torus?

A torus should not be confused with a solid torus, which is formed by rotating a disc, rather than a circle, around an axis. A solid torus is a torus plus the volume inside the torus. Real-world approximations include doughnuts, many lifebuoys, and O-rings.