Fear of flying persistent fear or anxiety when they consider flying, as well as during flying. They will avoid flying if they can, and the fear, anxiety, and avoidance cause significant distress and impair their ability to function. Take-off, bad weather, and turbulence appear to be the most anxiety provoking aspects of flying. The most extreme manifestations can include panic attacks or vomiting at the mere sight or mention of an aircraft or air travel. Around 60% of people with fear of flying report having some other anxiety disorder. The causes of flight phobia and the mechanisms by which it is maintained were
Proof that π is irrational omitting the inductive definition of the functions "A" and taking as a starting point their expression as an integral. This proof uses the characterization of as the smallest positive zero of the sine function. Suppose that is rational, i.e. for some integers "a" and , which may be taken without loss of generality to be positive. Given any positive integer "n", we define the polynomial function: and, for each "x" ∈ ℝ let Claim 1: is an integer. Proof: Expanding "f" as a sum of monomials, the coefficient of "x" is a number of the form where "c" is an