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
Fear but allowed in a parent's presence if required. Developing a sense of equanimity to handle various situations is often advocated as an antidote to irrational fear and as an essential skill by a number of ancient philosophies. Often laboratory studies with rats are conducted to examine the acquisition and extinction of conditioned fear responses. In 2004, researchers conditioned rats ("Rattus norvegicus") to fear a certain stimulus, through electric shock. The researchers were able to then cause an extinction of this conditioned fear, to a point that no medications or drugs were able to further aid in the extinction process. However