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 e is irrational Proof that e is irrational The number "e" was introduced by Jacob Bernoulli in 1683. More than half a century later, Euler, who had been a student of Jacob's younger brother Johann, proved that "e" is irrational; that is, that it cannot be expressed as the quotient of two integers. Euler wrote the first proof of the fact that "e" is irrational in 1737 (but the text was only published seven years later). He computed the representation of "e" as a simple continued fraction, which is Since this continued fraction is infinite and every rational number has a terminating continued