Musical instrument material composition, their size, etc. However, the most common academic method, Hornbostel-Sachs, uses the means by which they produce sound. The academic study of musical instruments is called organology. A musical instrument makes sounds. Once humans moved from making sounds with their bodies—for example, by clapping—to using objects to create music from sounds, musical instruments were born. Primitive instruments were probably designed to emulate natural sounds, and their purpose was ritual rather than entertainment. The concept of melody and the artistic pursuit of musical composition were unknown to early players of musical instruments. A player sounding a flute to signal
Proof that π is irrational Proof that π is irrational In the 1760's, Johann Heinrich Lambert proved that the number (pi) is irrational: that is, it cannot be expressed as a fraction "a"/"b", where "a" is an integer and "b" is a non-zero integer. In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and Nicolas Bourbaki. Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich. In 1882, Ferdinand von Lindemann proved that is not just irrational, but transcendental as well.