Musical instrument classification and some other woodwinds, such as the flute and bagpipe), other wind instruments such as the organ, and the stick-struck santur (a board zither). The distinction between fretted and open was in classic Persian fashion. Musical instrument classification Throughout history, various methods of musical instrument classification have been used. The most commonly used system divides instruments into string instruments, woodwind instruments, brass instruments and percussion instruments; however, other schemes have been devised. The oldest known scheme of classifying instruments is Chinese and dates from the 3rd millennium BC. It grouped instruments according to the materials they are made of. Instruments
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.