Astraphobia Astraphobia Astraphobia, also known as astrapophobia, brontophobia, keraunophobia, or tonitrophobia is an abnormal fear of thunder and lightning, a type of specific phobia. It is a treatable phobia that both humans and animals can develop. The term astraphobia is composed of the words ἀστραπή (astrape; lightning) and φόβος (phobos; fear). A person with astraphobia will often feel anxious during a thunderstorm even when they understand that the threat to them is minimal. Some symptoms are those accompanied with many phobias, such as trembling, crying, sweating, panicked reactions, the sudden feeling of using the bathroom, nausea, the feeling of dread, insertion
Quadratic irrational number expressed as for integers ; with , and non-zero, and with square-free. When is positive, we get real quadratic irrational numbers, while a negative gives complex quadratic irrational numbers which are not real numbers. This implies that the quadratic irrationals have the same cardinality as ordered quadruples of integers, and are therefore countable. Quadratic irrationals are used in field theory to construct field extensions of the rational field . Given the square-free integer , the augmentation of by quadratic irrationals using produces a quadratic field ). For example, the inverses of elements of ) are of the same form as