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 In 1761, Lambert proved that is irrational by first showing that this continued fraction expansion holds: Then Lambert proved that if "x" is non-zero and rational then this expression must be irrational. Since tan(/4) = 1, it follows that /4 is irrational and therefore that is irrational. A simplification of Lambert's proof is given below. This proof uses the characterization of as the smallest positive number whose half is a zero of the cosine function and it actually proves that is irrational. As in many proofs of irrationality, the argument proceeds by reductio ad absurdum. Consider the sequences ("A") and