Symmetrically Designed Sifrei Torah: A Quantitative Analysis - Hakirah

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224 : Hạkirah, the Flatbush Journal of Jewish Law and Thought and the thickness of Rambam’s S”T was thus .024 etzbaos. 79 Since there are 4 etzbaos in a ‏,טפח and a tefach is between 3.3 inches (R’ Chayim Na’eh) and 4.2 inches (Chazon Ish), then an etzba is between .825 and 1.05 inches. Thus in terms of inches Rambam’s parchment was between .02 and .025 inches thick. H”M Chapter 9, footnote 4 writes: הנה אני עשיתי בספר תורה שכתבתי בכל המידות האלה ולא איתרמי לי וראיתי כי של גויל היה שהוא עב אבל בקלף שלנו א״א לכוין...‏ i.e. he was unable to duplicate Rambam’s results because his S”T parchment was thinner. This explains why it is so difficult now to reproduce Rambam’s results. For example, the thickness of parchment used in today’s S”T is about .012 inches or less. Using this thickness in equation 3, and holding all other values the same as those that Rambam used, yields a Circumference of approximately 18.9 etzbaos, i.e 5.1 etzbaos (21.2%) smaller than Rambam’s. 80 Thus ט׃ב שיעור הגיליון מלמטה,‏ ארבע אצבעות;‏ ולמעלה,‏ שלוש אצבעות;‏ ובין דף לדף,‏ שתי אצבעות.‏ לפיכך צריך שיניח בתחילת כל יריעה ובסופה,‏ רוחב אצבע אחת וכדי תפירה--‏ שנמצא כשתיתפר היריעה,‏ יהיה בין כל דף ודף בכל הספר כולו,‏ שתי אצבעות.‏ ויניח מן העור בתחילת הספר ובסופו,‏ כדי לגול עמוד.‏ (Note: H”M says that the 2 nd word in halacha 11 should be 4, not 6 etzbaos. This would change the radius of the etz but not alter the remaining numbers very much). If the circumference of an etz is 3 etzbaos then its radius must be 3/2π. 79 This is an upper bound on the thickness of Rambam’s parchment, since there are other sources of surface area that we have not included. As stated in halacha 2 (previous footnote), each parchment section has an extra etzba at each end to allow the parchment sections to be sewn together. There are between 3 and 8 columns of writing in each parchment section (halacha 12), and Rambam’s S”T had 226 columns. Thus, his S”T had at least 27 parchment sections and at least an additional 54 etzbaos of thickness. Finally, the end etzba of each parchment section sewn together protrudes slightly and does not allow an airtight rolling of the parchment. This too would increase the overall circumference of the S”T. 80 Expanding the size of the atzei chaim could also materially affect the circumference. We note that Aruch Hashulchan in Hilchos Sefer Torah does not mention the size of the atzei chaim.
Symmetrically Designed Sifrei Torah: A Quantitative Analysis : 225 anyone trying to replicate Rambam’s S”T without having similar parchment thickness will not succeed in equalizing circumference and height. Alternatively, using the formulae we have developed one can map out on paper a circumference-height equality by judiciously choosing the relevant variables.
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Symmetrically Designed Sifrei Torah
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Symmetrically Designed Sifrei Torah: A Quantitative Analysis - Hakirah

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