Post by Gary on Sept 8, 2016 6:03:08 GMT
Vasco,
I have written up some general notes on subsections pertaining to spherical geometry and quaternions with the object of emphasizing what for me were points of confusion. These had mainly to do with the frequent shifting between expressions belonging to $\Sigma$ and those belonging to $\mathbb{C}$ and to at least one hybrid expression, and to the relation of all of this to quaternions. I am putting it up for discussion. At points it may appear to be mere close paraphrasing of Needham, but I think the emphasis is different.
I have read over your reply to my question about $\tilde{\mathbb{P}} = \mathbb{R}^{\psi}_{\mathbf{v}} \mathbb{P} \mathbb{R}^{-\psi}_{\mathbf{v}}$. I'm afraid I still don't quite get it, but I am still working through Ex. 6, so maybe by the time I finish that, I will be able to derive it.
nh.ch6.notes.general.pdf (87.8 KB)
Gary
I have written up some general notes on subsections pertaining to spherical geometry and quaternions with the object of emphasizing what for me were points of confusion. These had mainly to do with the frequent shifting between expressions belonging to $\Sigma$ and those belonging to $\mathbb{C}$ and to at least one hybrid expression, and to the relation of all of this to quaternions. I am putting it up for discussion. At points it may appear to be mere close paraphrasing of Needham, but I think the emphasis is different.
I have read over your reply to my question about $\tilde{\mathbb{P}} = \mathbb{R}^{\psi}_{\mathbf{v}} \mathbb{P} \mathbb{R}^{-\psi}_{\mathbf{v}}$. I'm afraid I still don't quite get it, but I am still working through Ex. 6, so maybe by the time I finish that, I will be able to derive it.
nh.ch6.notes.general.pdf (87.8 KB)
Gary