Berlin Musical Instrument Museum Berlin Musical Instrument Museum The Berlin Musical Instrument Museum () is located at the Kulturforum on Tiergartenstraße in Berlin, Germany. The Museum holds over 3,500 musical instruments from the 16th century onward and is one of the largest and most representative musical instrument collections in Germany. Objects include a portable harpsichord once owned by Prussia’s Queen Sophie Charlotte, flutes from the collection of Frederick the Great, and Benjamin Franklin’s glass harmonica. The Museum was founded in 1888 at the Royal Academy of Music in Berlin from a collection assembled by Philipp Spitta and Joseph Joachim. Thirty-four instruments from the Museum
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