Ochlophobia Ochlophobia Ochlophobia ("Fear of Crowds") and demophobia ("Fear of Unruly Mobs") are terms for types of social phobia or social anxiety disorder whose sufferers have a fear of crowds. Sufferers may offer various rationalizations of the phobia, such as the fear being trampled in a crowd, getting a deadly disease from people within the crowd, getting lost in the crowd, or feeling insignificant when surrounded by a crowd. People who are shy and introverted are most likely to experience ochlophobia, but not all introverts have anxiety problems. Ochlophobic people are often unable to handle situations involving parties, going to theaters,
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.