Boundary of a torus or sphere?

Thread starter pivoxa15
Start date Nov 4, 2007
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Boundary Sphere Torus

In summary, a torus is a three-dimensional donut-shaped shape generated by revolving a circle around an axis. Its boundary is the outermost surface that separates the inside and outside, and it is a closed loop that wraps around the surface. This is different from a sphere, whose boundary is a single point at the center. These boundaries are used in various scientific fields, and while they cannot be changed, the size and dimensions of the shape can be altered.

Nov 4, 2007

pivoxa15

Homework Statement

What is the boundary of a torus?

What is the boundary of a sphere?

The Attempt at a Solution

Both 0?

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Nov 4, 2007

matt grime

Science Advisor

Homework Helper

Neither of them is 0. In both cases it is a symbol that looks like 0 I suppose. Why don't you start with the defintions, since many things are clearly implied by them?

Nov 4, 2007

pivoxa15

It is not the null set is it?

THe boundary must be a 1-manifold?

1. What is a torus?

A torus is a three-dimensional geometric shape that resembles a donut. It is a surface of revolution generated by revolving a circle in three-dimensional space around an axis that is coplanar with the circle. In simpler terms, it is a circular ring with a hole in the middle.

2. How is the boundary of a torus defined?

The boundary of a torus is the outermost surface of the shape. It is the edge or border that separates the inside and outside of the torus. In mathematical terms, it is a closed loop that wraps around the surface of the torus.

3. What is the difference between the boundary of a torus and a sphere?

The boundary of a torus is a closed loop that wraps around the surface of the shape, while the boundary of a sphere is a single point at the center of the shape. Additionally, the boundary of a torus is a two-dimensional surface, while the boundary of a sphere is a zero-dimensional point.

4. How is the boundary of a torus or sphere used in science?

The boundary of a torus and sphere are used in a variety of scientific fields, including physics, mathematics, and engineering. In physics, these shapes are used to model and understand the behavior of particles and waves. In mathematics, they are used to study topology and geometric properties. In engineering, they are used in the design and construction of various structures.

5. Can the boundary of a torus or sphere be changed?

No, the boundary of a torus or sphere is a fundamental property of the shape and cannot be altered. However, the size and dimensions of the shape can be changed, which will also affect the boundary. For example, stretching a torus into an oval shape will change the boundary, but it will still have a closed loop that wraps around the surface.