Timeline for Covering a Cube with a Square
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Mar 29, 2017 at 17:22 | comment | added | Gerhard Paseman | Also, if you are clever about folding and stacking, this involves only two straightedge cuts and one fold, whereas the dissection above needs at least two folds to reduce the number of straightedge cuts to two. Gerhard "Time Is Money Is Product" Paseman, 2017.03.29. | |
| Mar 29, 2017 at 17:14 | comment | added | Gerhard Paseman | As I discovered after posting mathoverflow.net/a/263267, one can cut down the vertical middle of the 2x3 rectangle (forming two 1x3's) for another 5 piece cover, with pieces whose shapes are easier to manage in practice, with the same small triangle piece as being the smallest bit of paper to handle. Gerhard "Thinking In Mass Production Terms" Paseman, 2017.03.29. | |
| Mar 29, 2017 at 11:38 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image links broken; now fixed.
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| Feb 26, 2015 at 1:55 | history | edited | Yoav Kallus | CC BY-SA 3.0 |
updated urls for some pictures
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| May 6, 2012 at 20:11 | vote | accept | Joseph O'Rourke | ||
| Apr 1, 2017 at 11:52 | |||||
| May 4, 2012 at 16:07 | comment | added | Gerhard Paseman | Hmm. Maybe the above L shaped suggestion involves 6 pieces. Gerhard "Let Me Count Them Again" Paseman, 2012.05.04 | |
| May 4, 2012 at 16:05 | comment | added | Gerhard Paseman | If I haven't messed up, another five piece construction starts with cutting a 2 by sqrt(6) rectangle from the square, cutting an L shape out of the corner, and use the remaining pieces to form another L shape. This covers four faces of the cube with the cut lines being on cube edges and not on the faces. Gerhard "Pretty Is In Beholder's Eye" Paseman, 2012.05.04 | |
| May 4, 2012 at 12:19 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Added photos.
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| May 4, 2012 at 10:18 | comment | added | Joseph O'Rourke | Wow! $\mbox{}$ | |
| May 4, 2012 at 4:21 | comment | added | Yoav Kallus | OK. Posted to soon earlier. The change from the T tetromino to the S tetromino actually allows going down to five pieces instead of six. | |
| May 4, 2012 at 4:19 | history | edited | Yoav Kallus | CC BY-SA 3.0 |
added 13 characters in body
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| May 4, 2012 at 3:56 | comment | added | Yoav Kallus | Changed answer to CW. | |
| May 4, 2012 at 3:54 | history | made wiki | Post Made Community Wiki by Yoav Kallus | ||
| May 4, 2012 at 3:48 | comment | added | Yoav Kallus | Fedja, that's a great improvement on my extremely lazy effort! I like your construction, but I made an illustration of a slightly more symmetrical version of it, which I find a little more pleasing. | |
| May 4, 2012 at 3:44 | history | edited | Yoav Kallus | CC BY-SA 3.0 |
added 556 characters in body
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| May 4, 2012 at 0:34 | comment | added | fedja | Assuming that "pieces" mean "connected polygonal pieces", we can take a 3 by 2 rectangle, cut it into a T-shape and two unit squares and then use the standard "sliding cut" to turn it into a square, giving the total of 6 pieces to cover the unit cube. Can we do better? | |
| May 4, 2012 at 0:15 | comment | added | fedja | Actually, any two polygons of the same area are equidecomposable and the surface of the cube can be unfolded into a polygon, so the result is nice but not terribly surprising. Of course, the question about the minimal number of pieces remains. | |
| May 3, 2012 at 23:54 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 282 characters in body; added 1 characters in body
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| May 3, 2012 at 23:51 | comment | added | Joseph O'Rourke | Brilliant!! :-) | |
| May 3, 2012 at 21:10 | history | answered | Yoav Kallus | CC BY-SA 3.0 |