Fear of needles Fear of needles Fear of needles, known in medical literature as needle phobia, is the extreme fear of medical procedures involving injections or hypodermic needles. It is occasionally referred to as "aichmophobia" or "belonephobia", although these terms may also refer to a more general fear of sharply pointed objects. It has also been referred to as "trypanophobia", although the origin and proper usage of that term is highly controversial. The condition was officially recognized in 1994 in the DSM-IV (Diagnostic and Statistical Manual, 4th edition) as a specific phobia of blood/injection/injury type. Phobic level responses to injections cause sufferers to
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