Musical instrument first device considered a musical instrument is disputed. The oldest object that some scholars refer to as a musical instrument, a simple flute, dates back as far as 67,000 years. Some consensus dates early flutes to about 37,000 years ago. However, most historians believe that determining a specific time of musical instrument invention is impossible due to the subjectivity of the definition and the relative instability of materials used to make them. Many early musical instruments were made from animal skins, bone, wood, and other non-durable materials. Musical instruments developed independently in many populated regions of the world. However, contact
Proof that e is irrational a proof that "e" is not a root of a second degree polynomial with rational coefficients. This last fact implies that "e" is irrational. His proofs are similar to Fourier's proof of the irrationality of "e". In 1891, Hurwitz explained how it is possible to prove along the same line of ideas that "e" is not a root of a third degree polynomial with rational coefficients. In particular, "e" is irrational. More generally, "e" is irrational for any non-zero rational "q". Proof that e is irrational The number "e" was introduced by Jacob Bernoulli in 1683. More than half a