torusshaped

Torus-shaped describes objects or forms that resemble a torus, a doughnut-like shape with a central hole. In geometry, a standard torus is formed by revolving a circle of radius r around an axis in the same plane at distance R from the circle’s center, with R greater than r. The resulting surface has a major radius R and a minor radius r.

There are two related senses of torus-shaped. A torus can be viewed as a hollow surface—the 2D boundary of a solid torus—or as a solid body itself, a filled-in donut. Topologically, the hollow torus is equivalent to the product of two circles, denoted S1 × S1, and it has genus 1. By contrast, the solid torus is the 3D volume bounded by that surface and is homeomorphic to S1 × D2.

In practical terms, torus-shaped objects are common in everyday life and engineering. Examples include doughnuts and bagels, lifebuoys and inner tubes, and various ring-shaped magnets and seals. In technology, toroidal designs are used for components such as toroidal transformers and inductors, where the doughnut-like core helps confine magnetic flux and reduce electromagnetic interference. In physics and engineering, torus-shaped configurations are also studied for plasma confinement in fusion devices and for certain kinds of aerospace and mechanical components.

Overall, torus-shaped forms are defined by a ring-like geometry that combines a circular cross-section with a central hole, and they occupy important roles across mathematics, science, and industry.