Timeline for Poincaré disk model: is this locus a known curve?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2012 at 10:33 | comment | added | j.c. | Google books pulled up the following page from Richter-Gebert's recent book "Perspectives on Projective Geometry", though I can't access most of the discussion: books.google.com/… | |
| Jan 25, 2012 at 4:34 | answer | added | Ian Agol | timeline score: 4 | |
| Aug 17, 2010 at 17:59 | answer | added | Grant Lakeland | timeline score: 3 | |
| Aug 1, 2010 at 1:31 | comment | added | Will Jagy | The next easiest, fixing $A = i$ and $B = \infty$ along the imaginary axis, forcing a right angle at $P = x + i y$ with $ x \geq 0$ gives the hyperbola $ y = \sqrt{1 + x^2}.$ So the answer to your question is at least slightly different from that of question 24307. If the answer with $ A = i$ and $ B = \lambda i$ with finite real $ \lambda > 0$ is a conic section other than a circular arc, well, I do not know the meaning of those in the upper half plane model, but I bet there are books that say. | |
| Jul 31, 2010 at 21:56 | comment | added | Will Jagy | Anyway, here is a link to the first page of the article that answers the other question (constant area instead of constant opposite angle) springerlink.com/content/h031vf8c7ydfaxrf | |
| Jul 31, 2010 at 18:27 | comment | added | Will Jagy | Found something. See this related question, perhaps strongly related. mathoverflow.net/questions/24307/… Note that, in the upper half plane model, if you take your points $A,B$ as being $0, \infty$ along the imaginary axis, you and they get the same answer: the locus is a slanted ray beginning at $0.$ | |
| Jul 31, 2010 at 4:48 | history | asked | Humberto José Bortolossi | CC BY-SA 2.5 |