Timeline for On dissecting rectangles into rectangles
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Sep 8, 2020 at 8:31 | comment | added | Nandakumar R | Thanks very much! The paper linked above has a reference to Stillwell's 'Numbers and Geometry'. It has been established that say a sqrt(2) X 1/ sqrt(2) rectangle cannot be converted to a unit square without oblique cutting and pasting. And now, it is also clear that if two rectangles can be dissected into each other via rectilinear intermediate pieces, then they can be dissected into each other via rectangular pieces. So, in general, one can dissect rectangles to rectangles only by permitting oblique cuts - as for example Montucla does. | |
| Sep 8, 2020 at 0:20 | comment | added | user44143 | Thanks, I corrected this. | |
| Sep 8, 2020 at 0:20 | history | edited | user44143 | CC BY-SA 4.0 |
corrected as per comment
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| Sep 7, 2020 at 23:14 | comment | added | Pierre PC | It seems to me that the answer in the paper is that a decomposition with rectangle pieces exists if and only if the ratio of the lengths is the square of a rational ($w/h=r^2$). I don't see where rectilinear polygons are mentioned. | |
| Sep 7, 2020 at 20:13 | history | answered | user44143 | CC BY-SA 4.0 |