Timeline for Why does inconstructibility of $\sqrt[3]{2}$ imply impossibility of cube doubling? [closed]
Current License: CC BY-SA 3.0
33 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2019 at 22:55 | review | Reopen votes | |||
| Aug 31, 2019 at 23:44 | |||||
| Feb 9, 2015 at 15:50 | comment | added | KConrad | @quid, thanks. I see that indeed my edit of the final question mark was a mistake. | |
| Feb 9, 2015 at 15:37 | comment | added | user9072 | @KConrad to see the revisions just click 'edited [SomeTimeAgo]' in the middle at the end of a post. (If this link does not exist there are no recorded edits.) | |
| Feb 9, 2015 at 15:21 | review | Reopen votes | |||
| Feb 9, 2015 at 15:37 | |||||
| Feb 9, 2015 at 14:02 | comment | added | KConrad | I was the one who changed the last question mark to a period, and that was because I thought it was a sentence. I am not sure how to view the edit history, but I think I saw it start with something like "The problem I see is perhaps the reason why...," hence not a question. If it really had been written as "Is the problem I see..." then certainly it should end in a question mark. | |
| Feb 9, 2015 at 13:57 | comment | added | KConrad | I am sorry that English spelling is so terrible (not "terrable"). | |
| Feb 9, 2015 at 13:48 | comment | added | KConrad | Because there is no such phrase as "field extension theory." You can say "using field extensions" if you want, but "field extension theory" does not exist, just like "number field theory" and "Galois group theory" do not exist. The spelling "constructable" looks as awkward to me as "invisable" does. They ought to end in "ible." | |
| Feb 9, 2015 at 10:54 | comment | added | Lutz Mattner | @KConrad: So "constructable" has again been changed, apparently by you, to "constructible", which may be an improvement and in any case does no harm. But why was my "basic field extension theory" changed to the less specific "basic field theory"? What is the point of such editing? | |
| Feb 9, 2015 at 7:28 | vote | accept | Lutz Mattner | ||
| Feb 9, 2015 at 0:18 | history | closed |
Qiaochu Yuan Michael Renardy Stefan Kohl♦ Anton Petrunin Andrés E. Caicedo |
Not suitable for this site | |
| Feb 9, 2015 at 0:14 | history | edited | KConrad | CC BY-SA 3.0 |
deleted 1 character in body; edited title
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| Feb 9, 2015 at 0:10 | answer | added | R.P. | timeline score: 14 | |
| Feb 8, 2015 at 23:52 | comment | added | Lutz Mattner | OK, my thought that "constructible" were wrong was wrong, but still "constructable" is not wrong, or is it? So why the edit? | |
| Feb 8, 2015 at 23:35 | comment | added | GH from MO | It was not me, but indeed "constructible" seems to be more widespread. See books.google.com/ngrams/… | |
| Feb 8, 2015 at 23:34 | comment | added | Andreas Blass | I agree with your wanting a question mark at the end of the question, but why do you object to the standard spelling "constructible"? | |
| Feb 8, 2015 at 23:25 | comment | added | Lutz Mattner | Someone, annoyingly, edited my question by changing the final question mark to a full stop (which I repaired a while ago), and changed "constructable" to "constructible", which I repaired just now. | |
| Feb 8, 2015 at 23:23 | history | edited | Lutz Mattner | CC BY-SA 3.0 |
Repaired a spelling edit by someone else.
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| Feb 8, 2015 at 22:41 | comment | added | Theo Johnson-Freyd | I would have thought a "compass and straight edge construction in $\mathbb R^3$" meant that you could draw a straight line between any two known points and you could draw a sphere with center any known point and passing through any other known point. Then you may intersect such drawings, and you "know" any isolated point of intersection. | |
| Feb 8, 2015 at 22:12 | comment | added | Aaron Meyerowitz | Think how much easier it would be to construct a regular pentagon if one only had to make five equilateral triangles. | |
| Feb 8, 2015 at 22:07 | history | edited | Lutz Mattner | CC BY-SA 3.0 |
edited body
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| Feb 8, 2015 at 22:03 | history | edited | KConrad | CC BY-SA 3.0 |
deleted 7 characters in body; edited title
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| Feb 8, 2015 at 21:39 | answer | added | David E Speyer | timeline score: 10 | |
| Feb 8, 2015 at 21:33 | review | Close votes | |||
| Feb 9, 2015 at 0:22 | |||||
| Feb 8, 2015 at 21:33 | comment | added | GH from MO | @LutzMattner: You can define the problem in the classroom as you wish (cf. my answer below). Then you can prove the theorem. | |
| Feb 8, 2015 at 21:33 | comment | added | Chris Wuthrich | No. But you can place your cube such that it appears as two unit squares and the cube of twice the volume appears as a larger square with sides $\sqrt[3]{2}$. So in the two planes of descriptive geometry you face the same problem of constructing that number, no ? | |
| Feb 8, 2015 at 21:32 | answer | added | GH from MO | timeline score: 3 | |
| Feb 8, 2015 at 21:31 | comment | added | Lutz Mattner | @Chris Wuthrich: Could you give a reference? | |
| Feb 8, 2015 at 21:30 | comment | added | Chris Wuthrich | In descriptive geometry it is quite clear that doubling the cube is the same as constructing $\sqrt[3]{2}$. But it may well be that your students did not see any descriptive geometry. | |
| Feb 8, 2015 at 21:29 | comment | added | Lutz Mattner | @Pietro Majer: Starting just in one coordinate plane, as the books do, does not allow you to get out of it. | |
| Feb 8, 2015 at 21:23 | comment | added | Simon Henry | I don't know how the proof you talk about works, but for the proof I know doing compass constructions in different planes won't change anything: At each step of the construction, either the field generated by the coordinate of the marked points is unchanged either it became a degree 2 extension of the previous one. SO if you start with point with rational coordinate you can only get point with coordinate in fields of degree 2^n, which excluded 2^(1/3) | |
| Feb 8, 2015 at 21:23 | comment | added | Lutz Mattner | @Simon Henry: Well, I don't have reasons to doubt this, but still I would have to somewho write it down to convince me and my students. And could not use complex numbers, as some texts prefer. | |
| Feb 8, 2015 at 21:15 | comment | added | Pietro Majer | I think that the classic problem refers in any case to compass-and-straightedge construction in the plane. Working in 3D does not seem to give more freedom, though (am I missing something?) | |
| Feb 8, 2015 at 21:01 | history | asked | Lutz Mattner | CC BY-SA 3.0 |