Recorder (musical instrument) a performance by its billed inventor, Anton Heberle ( 1806–16). Tarasov has contested Heberle's status as the inventor of the instrument, and has argued that the csakan grew out of a Hungarian war hammer of the same name, which was converted into a recorder, perhaps for playing military music. Around 1800, it was highly fashionable for make walking sticks with additional functions (e.g., umbrellas, swords, flutes, oboes, clarinets, horns) although the csakan was the most popular of these, and the only one that became a musical instrument in its own right. The earliest instruments were shaped like a walking stick
Proof that e is irrational Proof that e is irrational The number "e" was introduced by Jacob Bernoulli in 1683. More than half a century later, Euler, who had been a student of Jacob's younger brother Johann, proved that "e" is irrational; that is, that it cannot be expressed as the quotient of two integers. Euler wrote the first proof of the fact that "e" is irrational in 1737 (but the text was only published seven years later). He computed the representation of "e" as a simple continued fraction, which is Since this continued fraction is infinite and every rational number has a terminating continued