Timeline for continuous R^2xR^2xR^2/E^+(2) -> R^3 injection?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 6, 2013 at 12:41 | vote | accept | Leon Avery | ||
| Jan 5, 2013 at 21:33 | comment | added | Leon Avery | So, following algori's last comment above, if I decide to yank out the speed, which is the scale factor, I'm left with $S^2$, which by Borsuk-Ulam explains why I was always left with 1 bit of missing info when I tried to map the remaining two degrees of freedom to $\mathbb{R}^2$. | |
| Jan 5, 2013 at 21:14 | comment | added | Leon Avery | Hmm. I already see the practical problem with this: the information about speed of movement ends up spread out over x, y, and z, and I really want it in a single number. Ah, well. That's biology, which is my problem. You answered my question. | |
| Jan 5, 2013 at 21:01 | comment | added | Leon Avery | OK, right. Here's what I have. Not exactly what you propose for some practical reasons having to do with the application, but the same idea: $v_1 = z_2 - z_1$, $v_2 = z_3 - z_2$, $(\rho,\phi) = (|v_1/v_2|, arg(v_1/v_2))$, $r = |v_1| + |v_2|$, $\theta = \pi - 2 tan^-1(\rho)$, Convert $(r,\phi,\theta)$ to (x,y,z) in the usual way. Great! I'll give this a try. Muchas gracias. Umm... dumb question: How the Hell do I create a line break in a comment? | |
| Jan 5, 2013 at 20:48 | vote | accept | Leon Avery | ||
| Jan 6, 2013 at 12:41 | |||||
| Jan 5, 2013 at 20:13 | comment | added | Todd Trimble | This seems to work. Good! | |
| Jan 5, 2013 at 19:54 | history | answered | Eric Wofsey | CC BY-SA 3.0 |