Musical instrument been used to play four notes of a diatonic scale. Researchers estimate the flute's age at between 43,400 and 67,000 years, making it the oldest known musical instrument and the only musical instrument associated with the Neanderthal culture. However, some archaeologists and ethnomusicologists dispute the flute's status as a musical instrument. German archaeologists have found mammoth bone and swan bone flutes dating back to 30,000 to 37,000 years old in the Swabian Alps. The flutes were made in the Upper Paleolithic age, and are more commonly accepted as being the oldest known musical instruments. Archaeological evidence of musical instruments was
Proof that π is irrational enough and that the sequence of all "g" converges to 0. But a sequence of numbers greater than or equal to |"y"| cannot converge to 0. Since "f"(/4) = cos(/2) = 0, it follows from claim 3 that /16 is irrational and therefore that is irrational. On the other hand, since another consequence of Claim 3 is that, if "x" ∈ Q \ {0}, then tan "x" is irrational. Laczkovich's proof is really about the hypergeometric function. In fact, "f"("x") = "F"(k; −"x") and Gauss found a continued fraction expansion of the hypergeometric function using its functional equation. This allowed