Timeline for A rational distance problem with (possibly) multiple solutions
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 22, 2023 at 21:01 | comment | added | Noam D. Elkies | You're welcome. On further thought, if Q is symmetrical about a diagonal D of rational length then there are infinitely many "P points" on D $-$ this again comes down to the infinitude of primitive Pythagorean triples. So we get points in the interior and also arbitrarily far. If D has rational length but is not a symmetry axis then we usually stll get infinitely many "P points" on D because they're parametrized by an elliptic curve with a few rational points. Alas a unit square is symmetrical about its diagonals but they do not have rational length so this simple approach fails. | |
| Dec 22, 2023 at 18:55 | history | edited | Daniel Asimov | CC BY-SA 4.0 |
Fixed typo; added "primitive"
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| Dec 22, 2023 at 18:36 | comment | added | Nandakumar R | Nice! From the last remark, I understand you think that there should be quads for which there are indeed infinitely many 'P points' that lie in the interior. And pushing the envelope, one could wonder if there are quads for which there are P points that are farther than any finite distance d! Thanks. | |
| Dec 22, 2023 at 18:32 | vote | accept | Nandakumar R | ||
| Dec 22, 2023 at 18:19 | history | answered | Noam D. Elkies | CC BY-SA 4.0 |