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Primary sourceArtifactc. 1800-1600 BC

YBC 7289

c. 1800-1600 BC

A Babylonian clay tablet computing the diagonal of a square, showing mathematical knowledge related to the Pythagorean theorem long before Pythagoras.

This Babylonian tablet shows the mathematical idea behind the 'Pythagorean' theorem was known well before Pythagoras's lifetime.

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Black and white photograph of a clay tablet, roughly circular with a broken edge, showing cuneiform wedge marks and labeled numbers 30, 1, 24, 51, 10, 35, 25, 42 inscribed in a diagonal and square diagram.
A black and white rendition of my own photograph of the Yale Babylonian Collection 's Tablet YBC 7289 (c. 1800–1600 BCE), showing a Babylonian approximation to the square root of 2 (1 24 51 10 w: sexagesimal ) in the context of Pythagoras' Theorem for an isosceles triangle . The tablet also gives an example where one side of the square is 30, and the resulting diagonal is 42 25 35 or 42.4263888...(30 x square root of 2). All use should attribute both me (mentioning http://www.math.ubc.ca/~cass/E

About this source

What it is

This small round clay tablet, known as YBC 7289, was made by a student in southern Mesopotamia sometime between 1800 and 1600 BC. It shows a square with its diagonals and a highly accurate numerical approximation of the square root of 2. It is held at the Yale Babylonian Collection.

Why it matters

The tablet proves that the mathematical relationship later named the Pythagorean theorem was known and used over a thousand years before Pythagoras was born. It is a reminder that many ideas credited to famous Greek names were already known in other, older civilizations.

Look closer

  • What does this tablet suggest about who really deserves credit for the 'Pythagorean' theorem?
  • Why might Pythagoras's name have become attached to an idea with such a long earlier history?
  • What kind of person made this tablet, and what does that tell you about ancient education?

This artifact is part of the curated material that grounds the AI version of Pythagoras on Humy.ai — when students ask about related events, the AI can quote it and cite it.

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