It was also announced that the Maple component of assignment 3 is to be optional. See the assignments on the web for more info.
The subject of today's lecture was arc length and curvature, which is described in section 11.8 of the textbook.
The arc length of a space curve was examined by sectioning the curve into a polygonal path and summing over the lengths of the sections. In the limit of an infinite number of infinitesimally small sections, this becomes an integral.
It is sometimes useful to re-paramaterize a curve in terms of its arc length.
Curvature was defined in terms of the derivative of the unit tangent vector. It was shown that this curvature is the same as the inverse of the radius of the osculating (tangent) circle.
The Normal Vector and the Binormal Vector of a spacecurve were defined.