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Post by Admin on Feb 2, 2017 14:21:52 GMT
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Gary
GaryVasco
Posts: 3,352 
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Post by Gary on Feb 17, 2017 17:57:05 GMT
Vasco, Here is my answer. But after reading your excellent answer, I see that this one is hopelessly inadequate, so I withdraw it. I'll study your answer and then move on to chapter 7. Since writing the above, I decided to try writing my own version following your lead. nh.ch6.ex27.v2.pdf (88.23 KB) Gary |
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Post by Admin on Feb 17, 2017 19:23:41 GMT
Gary
The link doesn't seem to work.
Vasco
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Feb 17, 2017 19:27:18 GMT
Gary The link doesn't seem to work. Vasco Vasco, Perhaps that is all to the best (see my addition to the post). But I think it must be temporary, as it works now from here. Gary |
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Feb 17, 2017 22:33:41 GMT
Vasco,
The Pacific storms here have given me a bit more time to think about this problem. In our answers, we rotated the PD to contain points of interest: two points or h-lines, for example. We could just as well have rotated the interior of the sphere on two dimensions to bring points into the PD. It seems more natural to think about rotating the spherical volume as there are fewer objects to keep track of and one is normally more likely to rotate a spherical object in two dimensions than a disc, which one more often thinks of as rotating about a single axis. Then, an h-sphere would be created by rotating the sphere volume about the h-line diameter that bisects the arc of an h-line generator. The arc paints the new spherical surface within the volume of the unit sphere as the volume passes by it. A horosphere is created by rotating the sphere volume about the diameter that touches the horizon at the same point that the horosphere touches. Once an object is created by a rotation about a diameter on the PD, it can then be rotated to a new position inside the sphere by rotating the whole volume.
As I read a little further in your answer, I see you have also used rotations of the sphere (p. 2, para. 1).
The discussions of the Euclidean and h-radii on p. 2 are nice and potentially quite useful.
Gary
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