Torsion (Differential Geometry)
The rate of change of the Osculating Plane of a Space Curve. The torsion 
is Positive for aright-handed curve, and Negative for a left-handed curve. A curve with Curvature 
is planarIff 
.
The torsion can be defined by
where
is the unit Normal Vector and 
is the unit Binormal Vector. Written explicitly in terms of aparameterized Vector Function 
,
where
denotes a Scalar Triple Product and 
is the Radius ofCurvature. The quantity 
is called the Radius of Torsion and is denoted 
or 
.See also Curvature, Radius of Curvature, Radius of Torsion
References
Gray, A. ``Drawing Space Curves with Assigned Curvature.'' §7.8 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 145-147, 1993. Kreyszig, E. ``Torsion.'' §14 in Differential Geometry. New York: Dover, pp. 37-40, 1991.
- Pearson System
- Pearson Type III Distribution
- Peaucellier Cell
- Peaucellier Inversor
- Peaucellier's Linkage
- Pedal
- Pedal Circle
- Pedal Coordinates
- Pedal Curve
- Pedal Line
- Pedal Point
- Pedal Triangle
- Peg Knot
- Peg Solitaire
- Peg Top
- Peirce's Theorem
- p-Element
- Pell Equation
- Pell-Lucas Number
- Pell-Lucas Polynomial
- Pell Number
- Pell Polynomial
- Pell Sequence
- Pencil
- Penrose Stairway