MoMath + Wolfram

Funding for this project generously provided by Overdeck Family Foundation

around 1900–1600 BCE

Babylonian Circle Tablet

Babylonian approximation to π on annotated circle diagram

Babylonian tablet YBC 7302 from the Yale University collection contains a simple diagram of a circle together with three numbers written in cuneiform inside and around it. Simple inferences based on the location and values of the numbers suggest this tablet depicts a simple Babylonian approximation for π as 3.

Babylonian Circle Tablet

This Babylonian tablet from around 1900–1600 BCE contains a drawing of a circle with the numbers 3, 9 and 45 inscribed in cuneiform in various positions in and around it. Based on the position of the number 3 just overlapping the top the circle, it seems to indicate a circumference C = 3. Similarly, the location of 45 in the center of the circle suggests it may be the area. While there is no obvious interpretation of the number 9 based on its location to the right of the circle, the fact that it is the square of 3 suggests it could represent the circumference squared.

Artifact dimensions

8 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 021367


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Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Anderson, M.; Katz, V.; and Wilson, R. (Eds.). Sherlock Holmes in Babylon and Other Tales of Mathematical History. Providence, RI: American Mathematical Society, p. 19, 2004.
  • Neugebauer, O. and Sachs, A. (Ed.). Mathematical Cuneiform Texts. New Haven, CT: American Oriental Society and the American Schools of Oriental Research, p. 44, 1945.

Image Credits

Yale Peabody Museum of Natural History