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): $7$