The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change
of the curve's osculating plane. The torsion
is positive
for a right-handed curve, and negative for a left-handed
curve. A curve with curvature 
is planar iff 
.
The torsion can be defined by
 |
(1)
|
where 
is the unit normal
vector and 
is the unit binormal vector. Written explicitly
in terms of a parameterized vector function 
,
 |  |  |
(2)
|
 |  |  |
(3)
|
(Gray 1997, p. 192), where 
denotes a scalar triple
product and 
is the radius of curvature.
The quantity 
is called the radius of torsion and is denoted
or 
.
