Pythagoreans noticed that strings produce different notes
when they vibrate. If the ratios of the length of two strings are
whole numbers, the notes make different pitches. They also knew
that any triangle with side ratios of 3:4:5 was a right triangle.
The Pythagoreans were the first to prove that the Pythagorean
Theorem was correct, even though Pythagoras learned it from the
Babylonians in his travels. During the 6th century BC, a square
with a side of n was shown as the area of a square with a side of
n. The Pythagorean Theorem stated that in a right triangle, the
square of side a added to the square of side b will be equal to the
square of side c (the hypotenuse).
Irrational numbers are numbers with decimals that do not
terminate, or repeat. The most widely known irrational number is
p (pi). Pi can be calculated to billions
of digits that go on forever. The number pi is related to curves,
ellipses (ovals) and circles.