Timeline for Differential equation with some constraints
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 29, 2011 at 18:21 | comment | added | Michael Hardy | .....but I am willing to use $\wp$ and things like Jacobi's elliptic functions. If we momentarily adopt Euler's willingness to say that if $\alpha$ is an infinitely small positive number then $\sin\alpha=\alpha$, then when $c$ is an infinitely small positive number, the curve can be parametrized using the ordinary sine and cosine functions. So if $c$ is merely very small, then one should get periodic functions that are approximately those. | |
| Aug 29, 2011 at 18:07 | comment | added | Michael Hardy | It's more a case of my not having decided what I should be willing to do........ | |
| Aug 29, 2011 at 12:57 | comment | added | Noam D. Elkies | Thanks, Robert! Yes, the original curve, to say nothing of the $dt$ double cover, looks much more complicated, but M.Hardy seems willing to extract square roots of a function of one variable for free in his setting $-$ in any case he'll have to take some inverse trig function to recover his original variables $\alpha,\beta,\gamma$. | |
| Aug 29, 2011 at 11:54 | comment | added | Robert Bryant | Very nice, Noam! I especially like the relation with the K3 surface. I knew that the curve on $x^2$, $y^2$, $z^2$ was an elliptic curve with some symmetries, but I didn't figure out the properties of the ($8$-fold) branched cover that represents the original $xyz$-curve or the branched cover of that on which $dt$ is actually a meromorphic differential. | |
| Aug 29, 2011 at 5:48 | comment | added | Noam D. Elkies | I tried to include this link to the Miranda-Persson paper, which however does not seem to work in the above answer: springerlink.com/content/u30268141h636x04/fulltext.pdf | |
| Aug 29, 2011 at 5:47 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |