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A curve with Cartesian equation
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.