Spiric Section
A curve with Cartesian equation
Around 150 BC,
Menaechmus constructed Conic Sections by cutting a Cone by aPlane. Two hundred years later, the Greek mathematician Perseus investigated the curves obtained by cutting aTorus 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 
whosecenter is rotated along a Circle of Radius 
. The value of 
gives the distance of the cutting Planefrom 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. Theabove 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.
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