Chapter 6 exercise 6

Vasco,

It was instructive to read your answers to Ch 6, Ex. 6, especially the shorter alterative to (i), the answer to (ii), and the answer to (vii). I find your answer to (v) a little hard to follow.

My answer to (vii) is deficient. I find the question difficult to follow, even after a rereading of the last section of Ch 1. But it's not hard to follow your answer and it appears to be what the question was aiming at. I will probably put your answer aside and see if I can reproduce it. I think I need to plot these transformations to see if I can reproduce plausible movements.

Gary

Gary

I have rewritten the proof of part (v). I hope it is now easier to follow.
I found that struggling with this exercise, especially part (vii), helped me to a closer understanding of (29). I still do not feel completely at ease with it, but enough to be able to move on I think. I am quite happy to engage in more discussion of these topics if you wish. My impression at this point is that Needham decided to introduce quaternions in order to make the mathematical manipulations simpler and to avoid getting bogged down in lots of algebraic manipulations which would risk obscuring the essential ideas. If I am right then I think it worked quite well, but it still requires some mental gymnastics to deal with the concept of the quaternions themselves.
I notice that Needham does not use them anywhere else in the book, except for exercises 7 and 8 in chapter 6, which I will now have a go at - he writes with trepidation!

Vasco