Ancient Greeks: Pythagoras, Mathematics, and Music

Pythagoras of Samos was a Greek philosopher and mathematician who also founded a mystical relgious movement called Pythagoreanism. He is best known for his Pythagorean theorem which states:

In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse).
The truth is, though, Pythagoras may have picked up this proof on his travels to Asia, as this proof was well known among mathematicians there. For more on the Chinese proof, click here.

The Pythagorean School was a secretive society and so many details are not known, but some rules of the Pythagoreans included strict vegetarianism, prescriptions about silence, incense, picking up what had fallen, physical and moral purification, and a belief that "Everything that exists is a number." In around 400 B.C., the discovery of irrational numbers upset the Pythagoreans.

Pythagoras is also famous for his interest in the Music of the Spheres.

Using a stretched string on a movable bridge, Pythagoras discovered that there were certain intervals that pleased peoples' ears: an octave (1:2), fifth (2:3), and fourth (3:4).

To listen to what these different intervals sound like, check out Harmony and Proportion. More on musical intervals on the guitar and Pythagoras are here.

For younger kids, print out and read this excellent book chapter on Pythagoras and his followers.

More Resources
Listen to Samples of The Music of Ancient Greece
The History of Music
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