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
The Story of the Youth Who Went Forth to Learn What Fear Was their wedding, the boy's continuing complaints annoyed his wife to no end. Reaching her wits' end, she sent for a bucketful of stream water, complete with gudgeons. She tossed the freezing water onto her husband while he was asleep. As he awoke, shuddering, he exclaimed that while he had finally learned to shudder, he still did not know what true fear was. The fairy tale is based on a tale from the German state of Mecklenburg and one from Zwehrn in Hesse, probably from Dorothea Viehmann, as told by Ferdinand Siebert from the area of the Schwalm. In the first