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 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