# Book:Tablet/YBC 7289

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## Tablet YBC $7289$

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

### Contents

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