Guo Musical Instrument Company New Design. Guo Musical Instrument Company Guo Musical Instrument Company (GMIC) is a Taiwan-based musical instrument manufacturer, specializing in flutes, piccolos, flute head joints, and saxophone necks and head joints. Founded by Geoffrey Guo in 1988, GMIC offers its products for sale online and through various retailers all over the world. Some of its instruments include a tenor flute, a G soprano flute, grenaditte flutes and a new C flute design called a Tocco flute. Many of these models of flutes and piccolos come in many different colors. In 2004, Geoffrey Guo and flute professor Mark Dannenbring developed the grenaditte
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.