Book:Tablet/YBC 7289

Tablet YBC $7289$

Tablet YBC $7289$ is one of the clay tablets from the Old Babylonian period.

Contents

A square with two diagonals.

The sides of the square are marked with the cuneiform numerals for $30$.

Above one of the diagonals is:

$1; 24, 51, 10$

which is the length of the diagonal of a square of side length $1$.

Below it is:

$42; 25, 35$

which is its product with $30$.

Thus $42; 25, 35$ is the length of the diagonal of a square of side length $30$.

From Pythagoras's Theorem, the length of the diagonal of a square of side length $1$ is $\sqrt 2$.

The approximation $1; 24, 51, 10$ is correct to $6$ decimal places.

Sources

• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: The beginnings of geometry