1 May 2018

Torus


In geometry, in popular language, the torus is an object whose shape is a donut. More precisely, the torus is a surface of revolution generated by revolving a circle of radius \(r\) in three-dimensional space about an axis coplanar at a distance \(R\) from its center.

The shape of the torus depends on the sign of the expression \(R-r\):
  • \(R=0\): The torus is a sphere, because the rotation axis is one of the diameters of the circle;
  • \(R<r\): The torus is said to be a "spindle torus" and takes the form of a pumpkin;
  • \(R=r\): The torus is said to be a "horn torus", with no "hole";
  • \(R>r\): The torus is said to be "open" and resembles to a donut.

\(\left(x^2+y^2+z^2+0.57^2-0.52^2\right)^2=0.57^2\left(x^2+y^2\right)\)

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