On the bifurcation behavior of a folded notebook page
Name
335_1_5.0097340.pdf
Size
2.26 MB
Format
Adobe PDF
Checksum (MD5)
c8248b3d3ae58512d2c5d3a34de11c61
Author(s)
Zhang, Chenguang
Date Issued
May 1, 2023
Publisher
American Association of Physics Teachers (AAPT)
Citation
Chenguang Zhang; On the bifurcation behavior of a folded notebook page. Am. J. Phys. 1 May 2023; 91 (5): 335–339.
Version
Final published version
Abstract
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.
Subjects
General Physics and Astronomy
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
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Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1119/5.0097340
