Curves in space
If point
in space moves according to 
, the position vector of 
is expressed as
and the tangent vector is expressed as
If
is the arc length from point 
to point 
along 
,
The inverse function satisfying
exists.
is expressed as
.The 2nd derivative is expressed as
.
is expressed as 
.The 2nd derivative is expressed as
.
Curvature
Radius of curvature
Principal normal vector
Principal normal vector
Torsion
Let us denote the angle formed by
and 
as 
.
Frenet-Serret formulas
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