The hardest part of problem 1.3.9 is understanding what is meant
by "a rigid body moves along a curve." I think the picture to have in
mind is a cube with three adjacent sides labeled T, N and B. The box
moves in such a way that each of the vectors T, N, B point
(perpendicularly) through the side of the box with the corresponding
letter. To complete the problem, you just only need to use the properties
they give you to prove the desired result. Having this picture in
mind will help with some of the following problems, though.
In problem 1.3.13 there is an error in the definition of the
linking number. To get the linking number you must add up all the
+1's and -1's and divide by 2 (according to Charles
Livingston's "Knot Theory").
UPDATE: The author of our text is actually correct in what he has
written. He instructs us to count only the intersections where alpha
passes under beta, rather than the more usual method of
counting every crossing.