Irrational Man Irrational Man Irrational Man: A Study In Existential Philosophy is a 1958 book by the philosopher William Barrett, in which the author explains the philosophical background of existentialism and provides a discussion of several major existentialist thinkers, including Søren Kierkegaard, Friedrich Nietzsche, Martin Heidegger, and Jean-Paul Sartre. "Irrational Man" helped to introduce existentialism to the English-speaking world and has been identified as one of the most useful books that discuss the subject, but Barrett has also been criticized for endorsing irrationality and for giving a distorted and misleading account of Georg Wilhelm Friedrich Hegel. Barrett discusses existentialism and its background,
Proof that π is irrational 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 proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and Nicolas Bourbaki. Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich. In 1882, Ferdinand von Lindemann proved that is not just irrational, but transcendental as well.