Timeline for Integer lattice points on a hypersphere
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 7, 2022 at 1:03 | comment | added | Daniel Asimov | Joel Reyes Noche: For each pair of lattice points there is a midpoint. Now choose a center c for the sphere that is not one of these (countably many) midpoints. As the radius is slowly increased from 0, the sphere will contain only one additional lattice point at a time. So any number of points is achieved with a certain range of radii. | |
| May 23, 2013 at 1:20 | comment | added | JRN | Not directly related to the question, but is it true that the problem is open if the $k$ lattice points are inside the hypersphere? | |
| May 23, 2013 at 0:29 | vote | accept | Liu Jin Tsai | ||
| May 22, 2013 at 23:44 | answer | added | Laila Podlesny | timeline score: 17 | |
| May 22, 2013 at 22:42 | comment | added | Gerhard Paseman | Note that if it is true for n=2, then it is true for all n, by using a hypersphere of well chosen irrational radius with all the lattice points sitting in a two dimensional subspace. Gerhard "Irrational Solutions To Rational Problems" Paseman, 2013.05.21 | |
| May 22, 2013 at 22:32 | answer | added | J.C. Ottem | timeline score: 7 | |
| May 22, 2013 at 22:29 | comment | added | Gerhard Paseman | Ryan, not if the sphere is not centered at the origin. Gerhard "Ask Me About System Design" Paseman, 2013.05.21 | |
| May 22, 2013 at 22:29 | comment | added | J.C. Ottem | @Ryan, the sphere need not have its center in the origin.. | |
| May 22, 2013 at 22:23 | comment | added | Ryan Budney | $k$ has to be even, since if $x$ is an integer point on the sphere, $-x$ is as well. | |
| May 22, 2013 at 22:20 | history | asked | Liu Jin Tsai | CC BY-SA 3.0 |