Timeline for On circles and ellipses drawn on an infinite planar square lattice
Current License: CC BY-SA 4.0
5 events
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| Jan 22, 2021 at 6:35 | comment | added | Nandakumar R | Thank you. I guess this gets n-1 of the 3D lattice points except the north pole on one plane. How could one possibly get a sphere to pass through n lattice points such that no 4 of them are coplanar? | |
| Jan 22, 2021 at 4:41 | comment | added | Noam D. Elkies | Yes, but the easiest way to do that is not very exciting: start with a Schinzel circle (or some variant such as the one I gave) with n-1 points, make it the intersection of R^2 with a large sphere in R^3 whose center has a positive z-coordinate, and use the lattice generated by Z^2 and the north pole . . . | |
| Jan 19, 2021 at 18:35 | comment | added | Nandakumar R | Thanks very much for those pointers! Just one further query: Kulikowski's proof (as given in Honsberger's 'Gems') shows how to construct a sphere such that exactly n points lie on it but those points are all coplanar. Is there a way to show the existence of a sphere in a 3D lattice such that it passes thru exactly n points, say, in general position, for any n? | |
| Jan 19, 2021 at 12:07 | history | edited | Alexey Ustinov | CC BY-SA 4.0 |
added 125 characters in body
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| Jan 19, 2021 at 11:57 | history | answered | Alexey Ustinov | CC BY-SA 4.0 |