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 Laczkovich to find a new and simpler proof of the fact that the tangent function has the continued fraction expansion that Lambert had discovered. Laczkovich's result can also be expressed in . In fact, Γ("k")"J"(2"x") = "x""f"("x"). So Laczkovich's result is equivalent to: If "x" ≠ 0 and if "x" is rational, then 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