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A Remarkable Collection of Babylonian Mathematical TextsOld Babylonian Hand Tablets with Practical Mathematics

A Remarkable Collection of Babylonian Mathematical Texts: Old Babylonian Hand Tablets with... Old Babylonian Hand Tablets with Practical Mathematics 7.1. MS 2317. Division of a Funny Number by a Non-Regular Factor 7.1 a. Interpretation of the Three Numbers in the Text MS 2317 (Fig. 7.1.1) is a quite small square hand tablet, inscribed on the obverse with three lines of num- bers. At first sight, the text looks unpromising. The meaning of the four wedges in line 1 is not immediately clear, and the numbers 13 and 4 41 37 in lines 2 and 3 are, quite obviously, non-regular sexagesimal numbers. obv. 1 1 rev. blank 3 cm Fig. 7.1.1. MS 2317. A division exercise for a funny number. A renewed look at the text reveals that it is unexpectedly interesting. The key to understanding what is going on here is to work in sexagesimal arithmetic. Indeed, a moment’s reflection leads to the insight that the 3-place sexagesimal number in line 3 can be factorized as 4 41 37 = 4 37 · 1 01. For verification, note that 4 37 · 1 01 = 4 37 00 + 4 37 = 4 41 37. Hence, 4 41 37 is the product of two non- regular prime numbers, 4 37 (= http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Remarkable Collection of Babylonian Mathematical TextsOld Babylonian Hand Tablets with Practical Mathematics

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Publisher
Springer New York
Copyright
© Springer Science+Business Media, LLC 2007
ISBN
978-0-387-34543-7
Pages
155 –187
DOI
10.1007/978-0-387-48977-3_7
Publisher site
See Chapter on Publisher Site

Abstract

Old Babylonian Hand Tablets with Practical Mathematics 7.1. MS 2317. Division of a Funny Number by a Non-Regular Factor 7.1 a. Interpretation of the Three Numbers in the Text MS 2317 (Fig. 7.1.1) is a quite small square hand tablet, inscribed on the obverse with three lines of num- bers. At first sight, the text looks unpromising. The meaning of the four wedges in line 1 is not immediately clear, and the numbers 13 and 4 41 37 in lines 2 and 3 are, quite obviously, non-regular sexagesimal numbers. obv. 1 1 rev. blank 3 cm Fig. 7.1.1. MS 2317. A division exercise for a funny number. A renewed look at the text reveals that it is unexpectedly interesting. The key to understanding what is going on here is to work in sexagesimal arithmetic. Indeed, a moment’s reflection leads to the insight that the 3-place sexagesimal number in line 3 can be factorized as 4 41 37 = 4 37 · 1 01. For verification, note that 4 37 · 1 01 = 4 37 00 + 4 37 = 4 41 37. Hence, 4 41 37 is the product of two non- regular prime numbers, 4 37 (=

Published: Jan 1, 2007

Keywords: Work Norm; Market Rate; Geometric Progression; Tabular Array; Division Problem

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