Gary
GaryVasco
Posts: 3,352 
|
Post by Gary on Jan 2, 2017 21:54:35 GMT
Vasco,
I was looking at your answer to Ex 14 (iii) trying to figure out why I couldn't solve what seemed to be a pretty straightforward problem. I see that you determined that the two shaded triangles are similar, but in general they can't be because when you make $ds$ perpendicular to $z_p$ the line for $ds$ does not form a right angle with the line from the origin to $z_p + dr$. But I think we might argue that as $dr$ tends to zero, the similarity is approximated. What do you think?
Gary
|
|
|
|
Post by Admin on Jan 2, 2017 22:43:06 GMT
Gary
Yes, I agree with you. In the limit the triangles are similar.
Vasco
|
|
Gary
GaryVasco
Posts: 3,352
|
Post by Gary on Jan 3, 2017 2:13:09 GMT
Gary As a result of our discussions about exercise 14, I realised I had not compared my result in part (i) of exercise 14 with the result of exercise 9 as required by the exercise. I have now amended my solution to include this comparison and replaced the original version with the new one. I have also amended my solution to part (ii) slightly, to make it clearer (I hope). Vasco Vasco, I will look at it. I have also added my solutions to (ii) - (vi) to the original posting of (i). Gary |
|
|
|
Post by Admin on Jan 3, 2017 8:30:09 GMT
Gary
In your document you refer to elliptic circles/curves. I have not come across this term before. Does it just mean circles on the sphere which are not great circles? If the answer is yes do you know the origin of the term?
Vasco
|
|
Gary
GaryVasco
Posts: 3,352
|
Post by Gary on Jan 3, 2017 15:05:56 GMT
Gary In your document you refer to elliptic circles/curves. I have not come across this term before. Does it just mean circles on the sphere which are not great circles? If the answer is yes do you know the origin of the term? Vasco Vasco, It should more properly refer to elliptic transformations, from Figure 26, p. 153, but it's something that struck me when I started the exercise and I should have returned to it to see if it expressed my meaning. I think one could define it as a family of circles on $\Sigma$ with planes orthogonal to an axis of $\Sigma$, so that seems to me to work. For the problem, it would be a family of circles on $\Sigma$ with parallel planes orthogonal to the standard N/S axis. They are projected from N to a parallel complex plane that touches S. I have rewritten the exercise to this effect and will repost. Gary |
|
