How did Pythagoras find the pythagorean theorem? - Answers

Pythagoras went to Babylon and studied with the Chaldean stargazers. He went to Egypt and studied the lore of the priests at Memphis and Diospolis. In Egypt he studied with the people known as the "rope-stretchers". These were the engineers who built the pyramids. They held a very special secret in the form of a rope tied in a circle with 12 evenly spaced knots. It turns out that if the rope was pegged to the ground in the dimensions of 3-4-5, a right triangle would emerge instantly. This enabled them to lay the foundations for their buildings accurately. He traveled to all the known parts of the Mediterranean world. During his travels he came to the conclusion that the earth must be round. In history, he is given credit as the first person to spread this idea. Pythagoras spent many years learning by traveling. Some say he made it the whole way to India and was deeply influenced, for he took up Oriental dress, including a turban. Many of his mystical ideas like number magic and reincarnation were typical of the East. Finally he returned home. He was probably the single most educated man on the face of the earth at that point. He wanted to share what he knew, but the people of his home town Samos were less than enthusiastic. Tired of finding no one who would listen to his learning, he decided to "buy" a student. He found a homeless child and offered him a bribe. Pythagoras would pay him three obli for every lesson the boy mastered. Now the boy thought this was great. He could sit all day in the shade of a large tree and listen to this old man and could make better wages than in a whole day's work in the hot sun. Naturally, he concentrated hard while Pythagoras introduced him to mathematical disciplines. From the simple calculations of the Egyptian rope-stretchers, to the methods of the Phoenician navigators, to abstract rules and reasoning, Pythagoras led his pupil on. Soon the subject became so interesting that the boy begged for more and more lessons. At this point, Pythagoras explained that he could not afford to pay someone to just listen to him anymore. So they reached a bargain. The boy had saved enough to pay Pythagoras for his lessons. This was probably the start of organized education. Eventually Pythagoras left the island of Samos and settled on the Isle of Croton. This is where he formed his Secret Brotherhood. The Secret Brotherhood was a religious order with initiation rites and purifications and Pythagoras was its supreme unquestioned leader. He taught them that KNOWLEDGE WAS THE GREATEST PURIFICATION, and for them knowledge meant mathematics. The most famous discovery that Pythagoras made came from his fascination with the Egyptian 3-4-5 rope-stretchers triangle. He had spent years thinking about it and what magic it might hold. Lo and behold,..........it DID hold a great deal of mathematics and for Pythagoras that was the same thing as magical power. One day while drawing in the sand he found that if a square is drawn from each side of the 3-4-5 triangle, the area of the two small squares added together equals the area of the large square. 3^2+4^2=5^2 9 + 16 = 25 He examined other right triangles and found it was true with them also: 6^2 + 8^2 = 10^2 36 + 64 = 100 9^2 + 12^2 = 15^2 81 + 144 = 225 So he decided to announce it as a revelation from the god Apollo, who many claimed to be his father. When he revealed this finding to his followers, he used the general terms of a & b for the shorter legs and c for the longer side which he gave the name "hypotenuse". Thus we have the famous PYTHAGOREAN THEOREM! a^2 + b^2 = c^2