Timeline for Bézout's theorem for arcs in the plane
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2015 at 22:27 | vote | accept | Adam Sheffer | ||
| Jul 24, 2015 at 3:16 | comment | added | Will Sawin | @AdamSheffer We can do $a(x) = b(y)$ where $b'(y)$ has no real and $a(x)=z$ has $d$ roots for $z$ in some interval. Then perturbing $b$ by some polynomial with $d$ roots in that interval gives $d^2$, for $d$ odd, or $d(d-1)$, for $d$ even. | |
| Jul 23, 2015 at 23:45 | comment | added | Adam Sheffer | Very nice! Thank you. In general this symmetry trick gives $2d$ intersection points, which is still far from $d^2$. Do you think that it is possible to have more intersection points than that? | |
| Jul 23, 2015 at 23:40 | vote | accept | Adam Sheffer | ||
| Jul 23, 2015 at 23:42 | |||||
| Jul 23, 2015 at 23:10 | history | answered | Will Sawin | CC BY-SA 3.0 |