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
Irrational number to show that π is irrational, whence it follows immediately that π is irrational also. The existence of transcendental numbers was first established by Liouville (1844, 1851). Later, Georg Cantor (1873) proved their existence by a different method, which showed that every interval in the reals contains transcendental numbers. Charles Hermite (1873) first proved "e" transcendental, and Ferdinand von Lindemann (1882), starting from Hermite's conclusions, showed the same for π. Lindemann's proof was much simplified by Weierstrass (1885), still further by David Hilbert (1893), and was finally made elementary by Adolf Hurwitz and Paul Gordan. The square root of 2