## 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.

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