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Funding for this project generously provided by Overdeck Family Foundation

around 2000–1900 BCE

Babylonian Nested Triangle Tablet

Triangular band divided into trapezoids

This Babylonian tablet gives a figure of two nested equilateral triangles divided into three congruent trapezoids, with numbers annotated along various edges and the number 35 prominently written in cuneiform in the lower right. It is likely this tablet was an unfinished student exercise to compute the area of the band.

Babylonian Nested Triangle Tablet

The annotations in the figure indicate various lengths. In particular, the inner triangle side length is indicated with the cuneiform glyph for 1 (which actually stands for the number 10—an interpretation that must be inferred due to the lack of a positional zero in Babylonian number notation), the trapezoid side lengths as the glyphs 1 6 4 (meaning 16 + 40/60 = 50/3), and the length of the long trapezoid base as the glyphs 4 3 2 (meaning 43 + 20/60 = 130/3). The number 35 written at the bottom is the central median length of the trapezoid, which gives the trapezoid's area when multiplied by its height.

Artifact dimensions

7.1 cm diam. × 2.5 cm thick

Original artifact location

Babylonia (historical name), Iraq (current name)

Current artifact location

Oslo, Norway

Catalog number

MS 2192


Geometry timeline Babylonian Nested Triangle Tablet Babylonian Geometrical Problem Tablet Babylonian Sippar Recombination Text Moscow Mathematical Papyrus Euclid's Elements Euclid Diagram Papyrus Moche Net Balance Scale Al-Tusi's Commentary on the Elements

Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Friberg, J. A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection: Cuneiform Texts I. New York: Springer, pp. 202–205, 2007.
  • Friberg, J. "Matematiska kilskriftstexter i den norska Schøyensamlingen." Nordisk Matematisk Tidskrift, Vol. 52, pp. 150–151, 2004.