What is the Pythagorean theorem?
The Pythagorean theorem says that in a right triangle, the square of the longest side equals the sum of the squares of the other two sides: a² + b² = c².
In the formula, a and b are the two shorter sides, called legs, and c is the hypotenuse, the side opposite the right angle. For example, if the legs are 3 and 4 units long, then 3² + 4² = 9 + 16 = 25, and the hypotenuse is the square root of 25, which is 5.
The theorem is named after the Greek mathematician Pythagoras, who lived around 570 to 495 BC. However, the relationship was known much earlier. A Babylonian clay tablet called Plimpton 322, from about 1800 BC, lists sets of numbers that fit it, and it was also known in ancient India and China.
Why it is useful
The theorem lets you find distances that are hard to measure directly. Builders use it to check that corners are square, and it helps calculate distances on maps, the diagonal size of a TV screen and the length of a ladder needed to reach a window. It is also a foundation of trigonometry.
Did You Know?
There are hundreds of different proofs of the Pythagorean theorem. One was published in 1876 by James Garfield, who later became US president.