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Funding for this project generously provided by Overdeck Family Foundation

around 1900–1600 BCE

Babylonian Square Root of 2 Tablet

Computing the square root of 2 in base 60

Circular tablet YPM BC 021354 contains a drawing of a square and its diagonals together with the sexagesimal representation of the diagonal length written in cuneiform numerals.

Babylonian Square Root of 2 Tablet

This famous tablet is one of few Babylonian tablets that consists entirely of a geometrical diagram (plus numbers). It demonstrates that Babylonian scribes both knew the Pythagorean theorem and were able to accurately calculate square roots. The diagram depicts a square with its diagonals together with an accurate approximation of the square root of 2. In addition, the number 30 is written above the upper-left side and the length of a diagonal corresponding to a square of this edge length is written beneath the horizontal diagonal.

Artifact dimensions

7 cm diam.

Original artifact location

Babylonia (historical name), Iraq (current name)

Current artifact location

Peabody Museum of Natural History, New Haven

Catalog number

YPM BC 021354 (current), YBC 07289 (historical)


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Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Maor, E. The Pythagorean Theorem: A 4000-Year History. Princeton, NJ: Princeton University Press, pp. 4–7, 2007.
  • Neugebauer, O. and Sachs, A. (Ed.). Mathematical Cuneiform Texts. New Haven, CT: American Oriental Society and the American Schools of Oriental Research, pp. 42–43, 1945.

Image Credits

Yale Peabody Museum of Natural History