Torus facts for kids

A Torus is a cool 3D shape that looks like a donut or a rubber ring! You can imagine making one by taking a simple circle and spinning it around in space.

To get this shape, the point you spin the circle around needs to be in the same flat area (called a plane) as the center of the circle. If the spinning point is outside the circle, you'll get a torus with a hole in the middle, which is often called a ring torus.

A ring torus, which looks like a donut!

What is a Torus?

A torus is a special kind of surface in geometry. It's like the surface of a donut, a bagel, or even an inner tube. It's a closed shape, meaning it has no edges or boundaries.

How a Torus is Formed

Imagine you have a circle. Now, pick a point outside that circle. If you spin the circle around that point, it will trace out the shape of a torus. Think of a tire: the rubber part is the torus, and the hole in the middle is where the axle goes.

Different Kinds of Tori

While the donut shape is the most common, there are other types of tori:

• Ring Torus: This is the classic donut shape with a hole in the middle. It's made when the spinning point is outside the circle.
• Horn Torus: If the spinning point is exactly on the edge of the circle, the hole shrinks to a single point.
• Spindle Torus: If the spinning point is inside the circle, the hole disappears completely, and the shape looks more like an apple.

Everyday Examples of Tori

You might not realize it, but tori are all around us!

• Donuts and Bagels: These tasty treats are perfect examples of a ring torus.
• Inner Tubes: When you float on water, you're often sitting in a torus-shaped tube.
• Lifebuoys: The rings used to rescue people in water are also tori.
• Tires: The shape of a car tire is a torus.

Torus in Math and Science

Tori are important in many areas of math and science.

• Topology: In a field called topology, a torus is a simple example of a "compact surface." It helps mathematicians study shapes and spaces.
• Physics: Tori are used to describe magnetic fields in some fusion reactors, like a tokamak, which are shaped like a torus to contain super-hot plasma.
• Computer Graphics: Artists and game designers use tori to create realistic 3D models of objects like rings, pipes, or even spaceship parts.

Images for kids

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  Poloidal direction (red arrow) and Toroidal direction (blue arrow) show how we can describe points on a torus.

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  This animation shows how a punctured torus can be turned inside-out!

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  A special kind of torus called a Clifford torus shown in a unique way.

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  This image shows how a torus is related to a Möbius strip, another cool shape!

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  You can imagine bending a rectangle to form a torus, but it often stretches the surface.

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  This is a toroidal polyhedron, a torus made from flat faces.

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  This shows how a torus can be divided into seven regions, where each region touches every other.

See also

In Spanish: Toro (geometría) para niños