1. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 2. The theorem has been known for over 4000 years, though Pythagoras is credited with first proving it around 500 BC in Greece. 3. The theorem plays an important role in many fields of mathematics like trigonometry and connecting geometry and algebra.

1. Phytagorean THEOREM Submitted to: Ms. Gee yamat

2. He is a kid who loves Phytagorean He tried it once, twice And he became a Valedictorian. It is better than Science It is easy as Pi Find the appliance My oh My! Geeks correct wrong answers To avoid brain cancer Why giving us Math questions It only gives my stomach an indigestion. Phytagorean poem

4. A Brief History of Phytagorean More than 4000 years ago, the Babyloneans and the Chinese already knew that a triangle with the sides of 3, 4 and 5 must be a right triangle. They used this knowledge to construct right angles. By dividing a string into twelve equal pieces and then laying it into a triangle so that one side is three, the second side four and the last side five sections long, they could easily construct a right angle. A Greek scholar named Pythagoras, who lived around 500 BC, was also fascinated by triangles with these special side ratios. He studied them a bit closer and found that the two shorter sides of the triangles squared and then added together, equal exactly the square of the longest side. And he proved that this doesn't only work for the special triangles, but for any right triangle. Today we would write it somehow like this: a2 + b2= c2. In the time of Pythagoras they didn't use letters yet to replace variables. (They weren't introduced until the 16th century by Vieta.) Instead they wrote down everything in words, like this: if you have a right triangle, the squares of the two sides adjacent to the right angle will always be equal to the square of the longest side. We can't be sure if Pythagoras really was the first person to have found this relationship between the sides of right triangles, since no texts written by him were found. In fact, we can't even prove the guy lived. But the theorem a2 + b2= c2 got his name. Another Greek, Euclid, wrote about the theorem about 200 years later in his book called "Elements". There we also find the first known proof for the theorem. Now there are about 600 different proofs. Today the Pythagorean theorem plays an important part in many fields of mathematics. For example, it is the basis of Trigonometry, and in its arithmetic form it connects Geometry and Algebra.

5. The Tale of the Discovery of Phytagoras It was believed that Pythagoras discovered this theorem when waiting for the tyrannical ruler, Polycrates. While looking at the floor’s square tiling of the palace of Polycrates, Pythagoras thought of this interesting idea: A diagonal line may be used to cut or divide the square, and two right triangles would be produced from the cut sides. Examining it further, Pythagoras formulated the formula in mind.

6. A Story About Phytagoras Pythagoras lived in the 500s BC, and was one of the first Greek mathematical thinkers. He spent most of his life in the Greek colonies in Sicily and southern Italy. He had a group of followers (like the later disciples of Jesus) who followed him around and taught other people what he had taught them. The Pythagoreans were known for their pure lives (they didn't eat beans, for example, because they thought beans were not pure enough). They wore their hair long, and wore only simple clothing, and went barefoot. Both men and women were Pythagoreans. Pythagoreans were interested in philosophy, but especially in music and mathematics, two ways of making order out of chaos. Music is noise that makes sense, and mathematics is rules for how the world works. Pythagoras himself is best known for proving that the Pythagorean Theorem was true. The Sumerians, two thousand years earlier, already knew that it was generally true, and they used it in their measurements, but Pythagoras is said to have proved that it would always be true. We don't really know whether it was Pythagoras that proved it, because there's no evidence for it until the time of Euclid, but that's the tradition. Some people think that the proof must have been written around the time of Euclid, instead.

7. SUBMITTED By: Axel Robert O. David VI - St. Fidelis