Timeline for cube + cube + cube = cube
Current License: CC BY-SA 3.0
23 events
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| S Nov 28, 2017 at 3:24 | history | suggested | jeq | CC BY-SA 3.0 |
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| Nov 28, 2017 at 2:12 | review | Suggested edits | |||
| S Nov 28, 2017 at 3:24 | |||||
| May 6, 2013 at 6:00 | history | edited | Denis Serre | CC BY-SA 3.0 |
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| May 6, 2013 at 5:24 | vote | accept | Denis Serre | ||
| May 5, 2013 at 18:39 | answer | added | Noam D. Elkies | timeline score: 53 | |
| Apr 17, 2013 at 0:43 | history | edited | Denis Serre | CC BY-SA 3.0 |
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| Apr 16, 2013 at 15:11 | answer | added | François Brunault | timeline score: 31 | |
| Mar 13, 2011 at 9:31 | comment | added | François Brunault | Here is an interesting link about the analogous problem for pythagorean triples : mathafou.free.fr/pbg/sol110d.html It turns out that for small pythagorean triples, a puzzle with only 4 pieces can be constructed. The smallest triples for which the minimal number of pieces doesn't appear to be known are (20,21,29) and (28,45,53). | |
| Jan 31, 2011 at 12:45 | vote | accept | Denis Serre | ||
| May 6, 2013 at 5:24 | |||||
| Jan 31, 2011 at 10:30 | history | edited | Denis Serre | CC BY-SA 2.5 |
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| Jan 30, 2011 at 17:43 | answer | added | JHI | timeline score: 90 | |
| Jan 29, 2011 at 23:32 | comment | added | fastforward | @Denis Where can one find the solution for N=8? Is it known if there are more then one solution for N=8 ? | |
| Jan 25, 2011 at 12:47 | comment | added | François Brunault | @John Bentin : such a puzzle was actually constructed. We used it last week during a mathematical exposition aimed at high school students. I found it already quite challenging. | |
| Jan 25, 2011 at 11:11 | comment | added | John Bentin | This would make a nice physical assembly puzzle. In the usual sort of puzzle, the symmetric assembly is easily dismantled into irregular pieces which are hard to reassemble. This one would be a satisfying puzzle in both directions (though perhaps easier in one direction than in the other). A lot more challenging would be $11^3+12^3+13^3+14^3=20^3$. | |
| Jan 25, 2011 at 6:50 | comment | added | Did | @Gerhard The solution to a version of the dissection problem is known: one cannot turn a cube into the regular simplex of the same volume through a finite number of cuts by hyperplanes, since these have different so called Dehn invariants. This holds in every dimension at least 3. In dimension 2, the area is a complete invariant, meaning that every polygons of the same area are equivalent, and the only nontrivial step of the proof is that any rectangle $L\times\ell$ can be turned into the square with side $\sqrt{L\ell}$. | |
| Jan 25, 2011 at 0:11 | comment | added | Gerry Myerson | Can you point us to the 8-piece solution? | |
| Jan 24, 2011 at 21:16 | comment | added | Gerhard Paseman | Also, suppose there is a proof that no two of the smaller cubes fit together inside the largest cube. That provides a proof that 5 is a lower bound for any such dissection. Gerhard "Ask Me About System Design" Paseman, 2011.01.24 | |
| Jan 24, 2011 at 21:09 | comment | added | Gerhard Paseman | How about the more general dissection problem (into continuous connected pieces, mind you) for solids? Are there results for turning a cude into a prism of the same volume with few cuts? Gerhard "Ask Me About System Design" Paseman, 2011.01.24 | |
| Jan 24, 2011 at 16:58 | history | edited | Denis Serre | CC BY-SA 2.5 |
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| Jan 24, 2011 at 13:35 | history | edited | Denis Serre | CC BY-SA 2.5 |
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| Jan 24, 2011 at 13:01 | comment | added | Did | A few years ago Raphaël Cerf played around similar problems for so-called polyominoes. This was in relation with the metastability of the 3D Ising model (no less), see combinatorics.org/Volume_3/Abstracts/v3i1r27.html. So he might know the answer. | |
| Jan 24, 2011 at 12:31 | comment | added | John Bentin | (+1) Regarding your definition of connectedness: Do you need the "arrows" to be of unit length? Otherwise, for example, two unit cubes along the same edge of $K_6$ but on opposite faces of it would be "connected" by an arrow of length 5. | |
| Jan 24, 2011 at 12:07 | history | asked | Denis Serre | CC BY-SA 2.5 |