A curve with Cartesian equation

Around 150 BC, Menaechmus constructed Conic Sections by cutting a Cone by a Plane. Two hundred 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 center of the Hole of the Torus (MacTutor).

In the Formula of the curve given above, the Torus is formed from a Circle of Radius whose center is rotated along a Circle of Radius . The value of gives the distance of the cutting Plane from the center of the Torus.

When , the curve consists of two Circles of Radius whose centers are at and . If , the curve consists of one point (the origin), while if , no point lies on the curve. The above curves have , (3, 1, 2) (3, 0.8, 2), (3, 1, 4), (3, 1, 4.5), and (3, 0, 4.5).

**References**

MacTutor History of Mathematics Archive. ``Spiric Sections.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Spiric.html.

© 1996-9

1999-05-26