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 fraction, "e" is irrational. A short proof of the previous equality is known. Since the simple continued fraction of "e" is not periodic, this also proves that "e" is not a root of second degree polynomial with rational coefficients; in particular, "e" is irrational. The most well-known proof is Joseph Fourier's proof by contradiction, which is based upon the equality Initially "e" is assumed to be a rational number of the form ⁄. Note that "b" could not be equal to 1 as "e" is not an integer. It can be shown using the above equality that "e" is strictly