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 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.