- Cartesian equation:
DescriptionAfter Menaechmus constructed conic sections by cutting a cone by a plane, around 150 BC which was 200 years later, the Greek mathematician Perseus investigated the curves obtained by cutting a torus by a plane which is parallel to the line through the centre of the hole of the torus.
In the formula of the curve given above the torus is formed from a circle of radius whose centre is rotated along a circle of radius . The value of gives the distance of the cutting plane from the centre of the torus.
When the curve consists of two circles of radius whose centres are at and .
If the curve consists of one point, namely the origin, while if no point lies on the curve.