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 which in extreme cases of fear (horror and terror) can be a freeze response or paralysis. In humans and animals, fear is modulated by the process of cognition and learning. Thus fear is judged as rational or appropriate and irrational or inappropriate. An irrational fear is called a phobia. Psychologists such as John B. Watson, Robert Plutchik, and Paul Ekman have suggested that there is only a small set of basic or innate emotions and that fear is one of them. This hypothesized set includes such emotions as acute stress reaction, anger, angst, anxiety, fright, horror, joy, panic, and sadness.