Guo Musical Instrument Company 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 flute. This
Proof that π is irrational In 1761, Lambert proved that is irrational by first showing that this continued fraction expansion holds: Then Lambert proved that if "x" is non-zero and rational then this expression must be irrational. Since tan(/4) = 1, it follows that /4 is irrational and therefore that is irrational. A simplification of Lambert's proof is given below. This proof uses the characterization of as the smallest positive number whose half is a zero of the cosine function and it actually proves that is irrational. As in many proofs of irrationality, the argument proceeds by reductio ad absurdum. Consider the sequences ("A") and