On the bifurcation behavior of a folded notebook page
We study how a bound notebook page can be folded once so that the page is visible when the notebook is closed and becomes a bookmark. An additional practical requirement is that the folded page stays within the same side of the bind, so that it does not get creased further when one closes the notebo...
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| Format: | Article |
| Language: | en_US |
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American Association of Physics Teachers (AAPT)
2023
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| Online Access: | https://hdl.handle.net/1721.1/153226 |
| _version_ | 1811084118408036352 |
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| author | Zhang, Chenguang |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Zhang, Chenguang |
| author_sort | Zhang, Chenguang |
| collection | MIT |
| description | We study how a bound notebook page can be folded once so that the page is visible when the notebook is closed and becomes a bookmark. An additional practical requirement is that the folded page stays within the same side of the bind, so that it does not get creased further when one closes the notebook. This simple problem displays a remarkably rich bifurcation behavior, which can be analyzed using undergraduate calculus. The main finding is that the optimal way of folding the page depends on the page's aspect ratio and changes abruptly when the latter exceeds the critical value of 1.207 11. This behavior also resembles a first-order phase transition in thermodynamics despite its geometric origin. |
| first_indexed | 2024-09-23T12:45:06Z |
| format | Article |
| id | mit-1721.1/153226 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:45:06Z |
| publishDate | 2023 |
| publisher | American Association of Physics Teachers (AAPT) |
| record_format | dspace |
| spelling | mit-1721.1/1532262024-01-05T16:10:43Z On the bifurcation behavior of a folded notebook page Zhang, Chenguang Massachusetts Institute of Technology. Department of Mathematics General Physics and Astronomy We study how a bound notebook page can be folded once so that the page is visible when the notebook is closed and becomes a bookmark. An additional practical requirement is that the folded page stays within the same side of the bind, so that it does not get creased further when one closes the notebook. This simple problem displays a remarkably rich bifurcation behavior, which can be analyzed using undergraduate calculus. The main finding is that the optimal way of folding the page depends on the page's aspect ratio and changes abruptly when the latter exceeds the critical value of 1.207 11. This behavior also resembles a first-order phase transition in thermodynamics despite its geometric origin. 2023-12-21T17:57:51Z 2023-12-21T17:57:51Z 2023-05-01 Article http://purl.org/eprint/type/JournalArticle 0002-9505 1943-2909 https://hdl.handle.net/1721.1/153226 Chenguang Zhang; On the bifurcation behavior of a folded notebook page. Am. J. Phys. 1 May 2023; 91 (5): 335–339. en_US 10.1119/5.0097340 Creative Commons Attribution An error occurred on the license name. https://creativecommons.org/licenses/by/4.0/ application/pdf American Association of Physics Teachers (AAPT) AIP Publishing |
| spellingShingle | General Physics and Astronomy Zhang, Chenguang On the bifurcation behavior of a folded notebook page |
| title | On the bifurcation behavior of a folded notebook page |
| title_full | On the bifurcation behavior of a folded notebook page |
| title_fullStr | On the bifurcation behavior of a folded notebook page |
| title_full_unstemmed | On the bifurcation behavior of a folded notebook page |
| title_short | On the bifurcation behavior of a folded notebook page |
| title_sort | on the bifurcation behavior of a folded notebook page |
| topic | General Physics and Astronomy |
| url | https://hdl.handle.net/1721.1/153226 |
| work_keys_str_mv | AT zhangchenguang onthebifurcationbehaviorofafoldednotebookpage |