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Counting Tritangent Planes of Space Curves

by Thomas F. Banchoff, Terence Gaffney, and Clint McCrory

If a plane is tangent to a smooth simple closed space curve, C, the
plane is said to be a *tritangent* plane. A *stall**
of C is a point of zero torsion, and a stall is said
to be **transverse* if the curvature is non-zero, the derivative
of the torsion is non-zero, and the osculating plane is transverse to
C away from the stall. So if *x* is a transverse stall
of C, then an interval of C lies on one side of the osculating
plane, and so the plane intersects C at an even number of points
(other than x), say *2n*. The number *n* is said to
be the *index* of x.

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This paper presents a formula for the number of tritangent planes
of a curve in terms of the index the stalls of the curve.
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