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

Timeline

Pi timeline Susa Mathematical Tablets Babylonian Circle Tablet Liu Hui's Exhaustion Method π Tombstone of Ludolph van Ceulen Jones's Use of the Symbol π Indiana Pi Bill

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