torus

The two-dimensional surface of a doughnut or inner-tube shape; the word comes from the Latin for "bulge" and was first used to describe the molding around the base of a column. One way to think of a torus is as a surface of revolution obtained by rotating a circle around an axis that lies in the plane of the circle but doesn't intersect the circle. The volume of a torus is π²r²d and its surface area is 4π²rd, where r is the radius of the circle and d the distance of its center from the line.

In the general case, where the shape being so rotated is any closed plane curve, the resulting surface is called a toroid. Although, as said above, the usual torus in three-dimensional space is shaped like a doughnut, the concept of the torus is extremely useful in higher dimensional space as well.

Related category

• SOLIDS AND SURFACES

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