# Definition:Rational Diagonal

## 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 $5 \sqrt 2$.