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 e is irrational numbers. Still another proof can be obtained from the fact that Define formula_11 as follows: Then: which implies: for any integer formula_15 Note that formula_16 is always an integer. Assume formula_17 is rational, so, formula_18 where formula_19 are co-prime and formula_20 It's possible to appropriately choose formula_21 so that formula_22 is an integer i.e. formula_23 Hence, for this choice, the difference between formula_22 and formula_16 would be an integer. But from the above inequality, that's impossible.So, formula_17 is irrational. This means that formula_27 is irrational. In 1840, Liouville published a proof of the fact that "e" is irrational followed by