Fear of trains fear about rail travel was heightened after British surgeon John Eric Erichsen described a post-traumatic diagnosis known as railway spine or "Erichsen's disease". People diagnosed with this had no obvious injury and were rejected as fake. Nowadays it is known that traffic accidents may cause posttraumatic stress disorder. It has been variously called as "train phobia", "railroad phobia", "dread of railway travel", etc. The German term "Eisenbahnangst" used, e.g., by Sigmund Freud was literally converted into Greek as "siderodromophobia" (Eisen = sideron = iron, Bahn = dromos = way, Angst = phobos = fear). In cases when this anxiety exceeds
Proof that π is irrational Proof that π is irrational In the 1760's, Johann Heinrich Lambert proved that the number (pi) is irrational: that is, it cannot be expressed as a fraction "a"/"b", where "a" is an integer and "b" is a non-zero integer. In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and Nicolas Bourbaki. Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich. In 1882, Ferdinand von Lindemann proved that is not just irrational, but transcendental as well.