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around 2000–1900 BCE

Babylonian Mud Wall Tablet

The mathematics of mud walls

Tablet MS 3052 dates from ancient Sumerian civilization around 2000–1900 BCE and probably originates from the city of Larsa. It contains eight mathematical exercises, including several drawings of subdivided trapezoids and triangles. Most problems are framed in terms of mud walls partitioned into two or more separate layers. Examples of problems include repairing a breach in a wall with mud from the top of the wall, measuring the thickness of a wall by drilling a hole through it and computing the dimensions of a rectangle comprised of two triangles, each corresponding to the (3, 4, 5) Pythagorean triple.

Babylonian Mud Wall Tablet

Problems about trapezoids or triangles divided into two or more smaller parts by transversals parallel to the base were popular in Old Babylonian mathematics. Such problems led to systems of linear or quadratic equations. One type of problem for divided trapezoids led to the equation + = 2 . Amazingly, old Babylonian mathematicians could find solutions in integers to both this equation and the similar equation + = (as seen in section 2 of this tablet) at least 1,200 years before Pythagoras.

Artifact dimensions

21.0 cm × 8.2 cm × 2.9 cm

Original artifact location

Larsa (historical name), Iraq (current name)

Current artifact location

Oslo, Norway

Catalog number

MS 3052

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

  • Friberg, J. "MS 3052. A Single-Column Mathematical Recombination Text." § 10.2 in A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection: Cuneiform Texts I. New York: Springer, pp. 254–274 and 493, 2007.