Toroid (geometry) facts for kids

Toroid

Torus

A toroid is a special three-dimensional (3D) shape that looks a bit like a donut or a lifebuoy. You make a toroid by spinning another shape, like a circle or a square, around a straight line. This line is called an axis, and it must be outside the shape you are spinning.

For example, if you spin a simple circle around an axis that doesn't touch the circle, the shape you get is called a torus. A torus is a type of toroid.

What is a Toroid?

A toroid is a solid shape that has a hole in the middle, just like a donut. The word "toroid" comes from "torus," which is the most common example of this kind of shape.

How Toroids Are Made

Imagine you have a flat shape, like a square, a triangle, or even an irregular blob. Now, imagine a straight line (the axis) somewhere next to this shape, not touching it. If you spin the flat shape all the way around this axis, it creates a 3D toroid.

The shape you spin is called the "generating curve" or "generating polygon." The path it takes as it spins forms the toroid.

Examples of Toroids

• Torus: This is the most famous toroid. It's made by spinning a circle around an axis. Think of a donut, a car tire, or a swimming tube.
• Toroidal Polyhedron: This is a toroid made from flat faces, like a polyhedron (a 3D shape with flat sides). It still has a hole in the middle.

Where You Might See Toroids

Toroids are not just cool shapes in math class! They show up in many places:

• Electronics: Many electronic parts, like inductors and transformers, use toroid shapes. This is because the shape helps them work more efficiently.
• Physics: In plasma physics, scientists study toroid-shaped devices called tokamaks. These are used in experiments to create energy, similar to how the sun makes energy.
• Everyday Objects: Besides donuts and tires, you can see toroid shapes in some types of bagels, rings, and even some types of gaskets.

Images for kids

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  Poloidal direction (red arrow) and Toroidal direction (blue arrow)

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  Turning a punctured torus inside-out

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  A stereographic projection of a Clifford torus in four dimensions performing a simple rotation through the xz-plane

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  The configuration space of 2 not necessarily distinct points on the circle is the orbifold quotient of the 2-torus, T2/S2, which is the Möbius strip.

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  In three dimensions, one can bend a rectangle into a torus, but doing this typically stretches the surface, as seen by the distortion of the checkered pattern.

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  A toroidal polyhedron with 6 × 4 = 24 quadrilateral faces

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  This construction shows the torus divided into seven regions, every one of which touches every other, meaning each must be assigned a unique color.

See also

In Spanish: Toroide para niños