Astraphobia immediately identified as a phobia because children naturally go through many fears as they mature. Their fear of thunder and lightning cannot be considered a fully developed phobia unless it persists for more than six months. In this case, the child's phobia should be addressed, for it may become a serious problem in adulthood. To lessen a child's fear during thunderstorms, the child can be distracted by games and activities. A bolder approach is to treat the storm as an entertainment; a fearless adult is an excellent role model for children. The most widely used and possibly the most effective
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