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Mathematical Treasures: Old Babylonian Tablets

Frank J. Swetz (The Pennsylvania State University)

Above: A Babylonian tablet dated from the period 1990–1700 BCE supplies a listing of reciprocals for a selection of sexagesimal numbers. In Babylonian calculations the operation of division was performed by multiplication by the reciprocal of the divisor. The image above may be viewed in the University of Pennsylvania Digital Collection using reference number LJS 301. However, according to scholar of Mesopotamian mathematics Duncan Melville, the tablet is displayed upside down at the University of Pennsylvania website! The image shown above has been rotated 180 degrees.

The image above is of a Babylonian land survey record from ca 1750 BCE. Three adjacent fields are shown. The dimensions as well as the area of each field are recorded. All the fields border an irrigation canal depicted at the right of the tablet by double lines. Perhaps the calculations were intended for water use charges (University of Pennsylvania LJS 302).

The images above were obtained through the courtesy of the University of Pennsylvania Libraries. The items pictured above reside in the library's Lawrence J. Schoenberg Collection, Rare Book and Manuscript Library. We thank Duncan Melville, Professor of Mathematics at St. Lawrence University, for his contribution to this article.

Old Babylonian tablet YBC 07302 from Yale's Peabody Museum.

The Old Babylonian (ca 1900–1600 BCE) student tablet above requires the reader to compute the area of a circle. Eleanor Robson made a transliteration of the inscription (below) for her award-winning article, “Words and Pictures: New Light on Plimpton 322,” The American Mathematical Monthly 109 (2002): 105–120.

Drawing of YBC 07302 by Eleanor Robson for her landmark article on Plimpton 322.

This item is held by Yale University’s Peabody Museum (YBC 07302).

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasures: Old Babylonian Tablets," Convergence (January 2016)