Irrational Man (1883-1891) Nietzsche's "most lyrical book" and "the expression of the loneliest Nietzsche." Finally, Barrett applies existentialist thought to the world of the late 1950s, during the Cold War. "Irrational Man" includes two appendices, "Negation, Finitude, and the Nature of Man", which reprints a 1957 paper by Barrett, and "Existence and Analytic Philosophers", a highly technical discussion of existentialism in relation to analytic philosophy. "Irrational Man" was first published in 1958 by Doubleday & Company, Inc. Later editions include those published by Greenwood Press, Inc. in 1977 and Anchor Books in 1990. "Irrational Man" received a positive review from Robert Jordan
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