Rotating torus

A torus is a geometric shape that resembles a doughnut or a tire. It is a three-dimensional shape that can be created by rotating a circle around an axis that is in the same plane as the circle but does not intersect it. A torus has two radii: a smaller radius (r) that measures the distance from the center of the tube to the center of the torus, and a larger radius (R) that measures the distance from the center of the torus to the center of the rotating circle.

The implicit equation of a torus in Cartesian coordinates can be written as:

This equation describes a torus as a level surface of a function of three variables. It is implicit because it does not explicitly give the coordinates of the points on the torus, but rather describes the relationship between the coordinates that satisfy the equation.

Tori are found in many areas of mathematics, science, and engineering, including topology, geometry, physics, and computer graphics. They are also commonly used in architecture and design due to their aesthetic appeal and structural properties.

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