Timeline for Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height [closed]
Current License: CC BY-SA 3.0
18 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Jun 27, 2015 at 3:03 | review | Reopen votes | |||
| Jun 27, 2015 at 13:20 | |||||
| Jun 20, 2015 at 16:53 | review | Reopen votes | |||
| Jun 20, 2015 at 19:41 | |||||
| Jun 20, 2015 at 16:37 | history | edited | Sergei Akbarov | CC BY-SA 3.0 |
added 62 characters in body
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| Jun 20, 2015 at 15:54 | history | closed |
Eric Wofsey Chris Godsil Joonas Ilmavirta Peter Michor Stefan Kohl♦ |
Not suitable for this site | |
| Jun 20, 2015 at 15:52 | comment | added | Sergei Akbarov | Even for the dimension $n=3$ this trick becomes bulky. To say nothing about $n>3$. Or I don't know something? Anyway this looks like a new invention of bicycle. It's difficult to believe that nobody did this before. | |
| Jun 20, 2015 at 15:23 | review | Close votes | |||
| Jun 20, 2015 at 15:54 | |||||
| Jun 20, 2015 at 14:59 | comment | added | Eric Wofsey | Alternatively (and probably more along the lines you were looking for), you can just imitate the elementary school proof that the area of a parallelogram is its base times its height (by chopping off a triangle and gluing it back on to get a rectangle). | |
| Jun 20, 2015 at 9:28 | answer | added | Liviu Nicolaescu | timeline score: 1 | |
| Jun 20, 2015 at 8:26 | comment | added | Sergei Akbarov | Is it possible that this wasn't proved in textbooks? | |
| Jun 20, 2015 at 8:15 | comment | added | Eric Wofsey | You don't need the entire machinery of Jordan measure; for parallelopipeds, it is easy to directly estimate how many cubes of side length $\epsilon$ you can fit inside it. By induction, you can approximately tile the base, and now just stack translated copies of that tiling vertically. | |
| Jun 20, 2015 at 7:55 | comment | added | Sergei Akbarov | Eric, I don't understand. Do you mean that for proving this it is nesessary to extend $V_n$ to the Jordan (or Lebesgue) measure (and only after that this becomes evident)? I believe there is a simple trick that allows to prove this without going to Jordan. | |
| Jun 20, 2015 at 7:43 | comment | added | Eric Wofsey | It seems like this should be straightforward by breaking the parallelopipeds into tiny congruent pieces and then using these pieces to approximately tile each other. | |
| Jun 20, 2015 at 7:43 | comment | added | Sergei Akbarov | I meant, disappeared from the list of the questions on the main page. I thought, this means that nobody is interested. | |
| Jun 20, 2015 at 7:38 | comment | added | Zev Chonoles | Well, that's indeed what I thought you meant, but my confusion is that your math.SE question is still visible to me. (If you felt it didn't get enough attention on math.SE, editing-to-bump or a bounty are the standard approaches.) | |
| Jun 20, 2015 at 7:34 | comment | added | Sergei Akbarov | Perhaps, this is my bad English. What is it called when something appears and disappears immediately? | |
| Jun 20, 2015 at 7:31 | comment | added | Zev Chonoles |
What does flashed and disappeared mean... ?
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| Jun 20, 2015 at 6:47 | history | asked | Sergei Akbarov | CC BY-SA 3.0 |