Irrational number number to ratios of continuous magnitude. In his commentary on Book 10 of the "Elements", the Persian mathematician Al-Mahani (d. 874/884) examined and classified quadratic irrationals and cubic irrationals. He provided definitions for rational and irrational magnitudes, which he treated as irrational numbers. He dealt with them freely but explains them in geometric terms as follows: In contrast to Euclid's concept of magnitudes as lines, Al-Mahani considered integers and fractions as rational magnitudes, and square roots and cube roots as irrational magnitudes. He also introduced an arithmetical approach to the concept of irrationality, as he attributes the following to irrational
Irrational exuberance Irrational exuberance "Irrational exuberance" is a phrase used by the then-Federal Reserve Board chairman, Alan Greenspan, in a speech given at the American Enterprise Institute during the dot-com bubble of the 1990s. The phrase was interpreted as a warning that the market might be overvalued. Greenspan's comment was made during a televised speech on December 5, 1996 (emphasis added in excerpt): The Tokyo market was open during the speech and immediately moved down sharply after this comment, closing off 3%. Markets around the world followed. The prescience of the short comment within a rather dry and complex speech would not