Pythagoras's Constant

The number

$$\sqrt{2}=1.4142135623\dots,$$

which the Pythagoreans proved to be Irrational. The Babylonians gave the impressive approximation

$$\sqrt{2}\approx 1+{24\over 60}+{51\over 60^2}+{10\over 60^3}=1.41421296296296\dots$$

(Guy 1990, Conway and Guy 1996, pp. 181-182).

See also Irrational Number, Octagon, Pythagoras's Theorem, Square

References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 25 and 181-182, 1996.

Guy, R. K. ``Review: The Mathematics of Plato's Academy.'' Amer. Math. Monthly 97, 440-443, 1990.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 126, 1993.