Mathematical Treasure: Mesopotamian Square Root Table

A clay tablet containing on both sides a table of sexagesimal (base 60) integer square roots, written in cuneiform characters, is shown below. The southern Mesopotamian tablet dates from the period 1999-1800 BCE (University of Pennsylvania Library reference LJS 99).

To see a curator handle this tablet, watch the short video, "Manuscript Monday: LJS 99 - Table of integer square roots." The tablet is also featured in Penn in Hand: Selected Manuscripts (Penn Libraries website), where, however, the obverse (front) and reverse (back) of the tablet are misidentified as "Side 2" and "Side 1", respectively, and the obverse (identified as "Side 2") is shown upside down. Scholar of Mesopotamian mathematics Duncan Melville also recommends viewing the Mesopotamian multiplication table LJS 301, despite the fact that both its sides are shown upside down!

The images above were obtained through the courtesy of the University of Pennsylvania Libraries. The item resides 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 contributions to this article.

Index to Mathematical Treasures