Timeline for Lattice-point-free buffers around circles
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 30, 2013 at 17:20 | comment | added | Joseph O'Rourke | Great---Thanks, Abhinav! This resolves my other question as well. | |
| Oct 30, 2013 at 16:50 | vote | accept | Joseph O'Rourke | ||
| Oct 30, 2013 at 16:39 | comment | added | Vít Tuček | I see. Much obliged. | |
| Oct 30, 2013 at 16:13 | comment | added | Abhinav Kumar | You apply it with $x = r^2$. It gives a lattice point $(a,b)$ with $n = a^2 + b^2$, where $n$ is between $r$ and $\sqrt{r^2 + C\sqrt{r}}$. Therefore the distance to the circle is $\sqrt{n} - r$, but $r = \sqrt{r^2} \leq \sqrt{n} \leq \sqrt{r^2 + Cr^{1/2}} = r(1 + r^{-3/2}/2 ) = r + r^{-1/2}/2$. | |
| Oct 30, 2013 at 15:53 | comment | added | Vít Tuček | I don't understand. Doesn't this give only a bound $\beta(r) \leq Cr^{\frac{1}{4}}$? | |
| Oct 30, 2013 at 15:32 | history | answered | Abhinav Kumar | CC BY-SA 3.0 |