Timeline for Why does inconstructibility of $\sqrt[3]{2}$ imply impossibility of cube doubling?
Current License: CC BY-SA 3.0
12 events
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| Feb 9, 2015 at 0:28 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Feb 8, 2015 at 23:52 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Feb 8, 2015 at 23:48 | comment | added | GH from MO | You are right, let me fix this. | |
| Feb 8, 2015 at 23:43 | comment | added | R.P. | Wait, shouldn't $K$ be the union of all Galois extensions of $2$-power degree over $\mathbb{Q}$? I don't think the set of all algebraic numbers of $2$-power degree forms a field (e.g. any two degree-$4$ subextensions of an $S_4$-extension give rise to a degree-$12$ compositum...). | |
| Feb 8, 2015 at 22:10 | comment | added | GH from MO | @LutzMattner: I don't think you will find a reference for the claim in my added section, but the proof should be a straightforward adaptation or consequence of what is written. | |
| Feb 8, 2015 at 21:58 | comment | added | GH from MO | @LutzMattner: See my added section. | |
| Feb 8, 2015 at 21:58 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Feb 8, 2015 at 21:46 | comment | added | Lutz Mattner | I dont' think so. From points just in the $x$-$y$-plane you can not construct any point not belonging to it. | |
| Feb 8, 2015 at 21:42 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Feb 8, 2015 at 21:37 | comment | added | GH from MO | @LutzMattner: A physically given cube determines three distances between their vertices: each of these is constructible from the edge length, so the problem told by the oracle of Delos is equivalent to the one I described. Note that a compass is designed for plane drawings. | |
| Feb 8, 2015 at 21:34 | comment | added | Lutz Mattner | Well, but this does not fit well to the story of the oracle of Delos asking for the doubling of a certain physically given cube. | |
| Feb 8, 2015 at 21:32 | history | answered | GH from MO | CC BY-SA 3.0 |