# Definition:Rational Diagonal

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## Definition

The number $7$ (seven) was referred to by the ancient Greeks as the **rational diagonal** of the $5 \times 5$ square.

This was on account of the fact that:

- $5^2 + 5^2 = 50 \approx 7^2 = 49$

## Historical Note

The concept of the **rational diagonal** was raised by Plato in his * Republic* of c. $380$ BCE.

Plato was aware that the actual length of the diagonal of the $5 \times 5$ square is the irrational number $5 \sqrt 2$.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $7$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $7$