Talk:Hyperbolic motion

Weird and apparently rhetorical question
Is Lobachevski the greatest mathematician who ever got chalk on his coat? Baylink 07:21, 4 Dec 2004 (UTC)

H^3, Fermat metric, and Rindler
The so-called Fermat metric for the Rindler chart is H^3. (Hyperbolic three-space.) Someone else who has read the wonderful little book Gravitional Curvature by Frenkel should fix this article to clarify all this stuff. I'd do it, but I have my hands full with other stuff.---CH (talk) 04:55, 1 September 2005 (UTC)

Merger proposal
See book cited in previous note for explanation of merger proposal.---CH (talk) 04:59, 1 September 2005 (UTC)
 * This page is mostly 2D geometry and not about relativity. Vote against merger.Rgdboer 21:03, 1 September 2005 (UTC)

Simplification
I suggest adding info about the hyperbolic motion a spacecraft may undergo as it "slingshots" past the Sun, a planet, or moon. Such a spacecraft may also follow a parabolic path, depending on it's velocity and distance from the object. Since this would be the simplest definition of hyperbolic motion, I believe it should be placed first. Much of the info for this could be found under Planetary orbit.StuRat 19:01, 24 September 2005 (UTC)


 * Another suggestion is to make this a disambiguation page, pointing to the existing hyperbolic motion (relativity), a new hyperbolic motion (hyperbolic geometry) which would contain the body of this article, and a new hyperbolic motion (orbits) which would contain what I mentioned above. StuRat 19:08, 24 September 2005 (UTC)


 * A hatnote referring to hyperbolic orbit is okay, but calling that "hyperbolic motion" feels unnatural to me. —Tamfang (talk) 06:46, 27 May 2011 (UTC)

fundamentals
If inversion in a circle is not restricted to the unit circle, dilation can be represented as a composition of two inversions, reducing the number of fundamental half-plane motions. And what about reflection in a vertical line? —Tamfang (talk) 19:33, 22 May 2011 (UTC)

More generally, I'd prefer not to begin by tying the concepts to specific models: rather, say that all motions can be composed from no more than three hyperbolic reflections, and then give the expressions of reflection in the various models. —Tamfang (talk) 20:00, 22 May 2011 (UTC)


 * Yes, some astute observations on the inelegance of the quick introduction. For instance, reflection in a vertical line which is considered an isometry but reverses orientation of figures. The article was composed as a rapid entry to hyperbolic geometry of the upper-half plane; disk motions were tacked on when coquaternions were motivated. Your observations could be developed into constructive edits, which would naturally move the article more toward group theory. The trio of motions were what was wanted to construct the metric for a novice.Rgdboer (talk) 21:05, 22 May 2011 (UTC)


 * It has been a while since this article has been addressed. Small changes today do not meet your issues, which have me thinking about proper content. Note that Mario Pieri based his view of geometry on the notion of motion. Reconsidering the section developing the metric in HP took me to Introduction to special relativity since the objective originally was Introduction to hyperbolic geometry. Now nearly two centuries into the revolution of Bolyai & Lobachevski, there has been very little evidence of popularization of hyperbolic geometry. Defining the metric as a logarithm of a cross-ratio expects a lot from a student. The reference "Bonahon" follows a similar development to bring students in quickly.Rgdboer (talk) 00:49, 23 May 2011 (UTC)