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Post by Admin on Sept 19, 2016 18:07:26 GMT
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Gary
GaryVasco
Posts: 3,352 
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Post by Gary on Sept 19, 2016 19:11:13 GMT
Good to know. I'm still looking over Ex. 7.
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Sept 21, 2016 0:50:21 GMT
Vasco,
I started reading Ch 6, Ex 8. Would I be correct to assume that $\tilde{p}$ refers to inversion of $p$ in the unit circle in $\mathbb{C}$ so that $\mathbf{V}$ would be an axis perpendicular to the plane of $0-p-\hat{p}$?
Gary
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Post by Admin on Sept 21, 2016 7:17:41 GMT
Vasco, I started reading Ch 6, Ex 8. Would I be correct to assume that $\tilde{p}$ refers to inversion of $p$ in the unit circle in $\mathbb{C}$ so that $\mathbf{V}$ would be an axis perpendicular to the plane of $0-p-\hat{p}$? Gary Gary This is the way I see it: the sphere is rotated about some axis $\textbf{V}$. The point $p$ is any point in the complex plane and $\widetilde{p}$ is what $p$ is mapped to by the Mobius transformation $\mathbb{R}^{\psi}_{\textbf{v}}$, induced on the complex plane by rotation of the sphere. I would recommend re-reading subsection 4 on pages 286-290 - I find I need to re-read it after every meal at the moment! Vasco |
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Sept 21, 2016 15:42:34 GMT
Vasco,
Thanks. I'll take another look at those passages.
Gary
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Sept 24, 2016 5:40:32 GMT
Vasco, Here is my answer set for Exercise 8. I haven't looked at yours yet, but the exercise didn't seem problematic, except perhaps for how one is to know beforehand that $\mathbb{P}$ in (iii) is a pure quaternion. nh.ch6.ex8.pdf (317.61 KB) Gary |
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Post by Admin on Oct 2, 2016 15:55:06 GMT
Vasco, Here is my answer set for Exercise 8. I haven't looked at yours yet, but the exercise didn't seem problematic, except perhaps for how one is to know beforehand that $\mathbb{P}$ in (iii) is a pure quaternion. View AttachmentGary Gary Since we are trying to prove (29) on page 292 where $\mathbb{P}$ is defined as a pure quaternion just above (29), then I don't think it's a problem. Vasco |
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Oct 3, 2016 17:58:58 GMT
Vasco, Here is my answer set for Exercise 8. I haven't looked at yours yet, but the exercise didn't seem problematic, except perhaps for how one is to know beforehand that $\mathbb{P}$ in (iii) is a pure quaternion. Gary Gary Since we are trying to prove (29) on page 292 where $\mathbb{P}$ is defined as a pure quaternion just above (29), then I don't think it's a problem. Vasco Vasco, yes, agreed. Gary |
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