#1.3.9, 1.3.14, 1.5.10.
#1.3.11, 1.3.13, 1.3.17,
1.4.6, 1.5.2.
#1.5.14.
- 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.