Timeline for Proving that there are infinitely many points on the unit circle such that the distance between any two of them is a rational number.
Current License: CC BY-SA 4.0
12 events
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| Sep 11, 2023 at 20:07 | audit | Low quality posts | |||
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| Sep 6, 2023 at 23:33 | audit | Reopen votes | |||
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| Sep 2, 2023 at 17:48 | audit | Close votes | |||
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| Aug 13, 2023 at 7:08 | history | edited | Hammock | CC BY-SA 4.0 |
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| Aug 13, 2023 at 7:06 | comment | added | Hammock | I think I found the mistake. Nivne's theorem states that the only rational values of θ in the interval 0° ≤ θ ≤ 90° for which the cosine of θ degrees is also a rational number are 30 deg. The key is that theta is also rational. my bad. I missed that point | |
| Aug 13, 2023 at 6:25 | answer | added | orangeskid | timeline score: 5 | |
| Aug 13, 2023 at 5:56 | comment | added | Hammock | Are there infinitely many rational distances between two points on a unit circle? This question bugs me I don't know where I went wrong with both approaches, yielding opposite answers. | |
| Aug 13, 2023 at 5:21 | history | edited | Jyrki Lahtonen |
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| Aug 13, 2023 at 5:18 | comment | added | TheBestMagician | See Lulu's answer here: math.stackexchange.com/questions/1978452/… | |
| Aug 13, 2023 at 5:14 | comment | added | Jyrki Lahtonen | I don't know your source on Niven's theorem, but it feels likely that it is only about angles $\theta=\pi q$ with rational $q$. Or some such constraint on the angles. At least then we can relate to a question about real subfields of cyclotomic fields. | |
| Aug 13, 2023 at 5:06 | history | edited | Blue | CC BY-SA 4.0 |
More-informative title; edits for readability
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| Aug 13, 2023 at 4:45 | history | asked | Hammock | CC BY-SA 4.0 |