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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)

Timeline

PythagoreanTheorem timeline Babylonian Mud Wall Tablet Babylonian Inner Diagonal Tablet Babylonian Square Root of 2 Tablet Berlin Pythagorean Theorem Papyrus Plimpton 322 Vedic Fire Altar Rectangle Diagonal Vedic Fire Altar Square Diagonal Euclid's Elements Ptolemy's Quadrilateral Theorem Zhoubi Suanjing Pythagorean Theorem Proof Ibn Qurra's Pythagorean Theorem Proofs Lilāvatī of Bhāskara II

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