Oct 26, 2013 - -It is a triangle which has an angle that is 90 degrees. -The two sides that make up the right angle are called legs. -The side opposite the right.
The “Pythagorean theorem,” was inspired by the ancient Greek Mathematician Pythagoras who invented the theorem during 500 B.C. It has been argued that the “Ancient Babylonians” already understood the theorem long before the invention by Pythagoras. They knew the relationship between the sides of the triangle and while solving for the hypotenuse of an isosceles triangle, they came up with the approximate value of up to 5 decimal places. What is Pythagoras theorem? In a right-angled triangle, “The sum of squares of the lengths of the two sides is equal to the square of the length of the hypotenuse (or the longest side).”.
Pythagorean theorem, the well-known geometric that the sum of the squares on the legs of a right is equal to the on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a 2 + b 2 = c 2. Although the theorem has long been associated with Greek mathematician-philosopher ( c. 570–500/490 bce), it is actually far older.
Four Babylonian tablets from circa 1900–1600 bce indicate some knowledge of the theorem, or at least of special known as Pythagorean triples that satisfy it. The theorem is mentioned in the Baudhayana of, which was written between 800 and 400 bce. Nevertheless, the theorem came to be credited to Pythagoras. It is also proposition number 47 from Book I of. According to the Syrian historian ( c. 250–330 ce), Pythagoras was introduced to by and his pupil.
Microsoft customer support services website microsoft office. In any case, it is known that Pythagoras traveled to about 535 bce to further his study, was captured during an invasion in 525 bce by of Persia and taken to Babylon, and may possibly have visited India before returning to the Mediterranean. Pythagoras soon settled in Croton (now Crotone, Italy) and set up a school, or in modern terms a monastery ( see ), where all members took strict vows of secrecy, and all new mathematical results for several centuries were attributed to his name. Thus, not only is the first proof of the theorem not known, there is also some doubt that Pythagoras himself actually proved the theorem that bears his name. Some scholars suggest that the first proof was the one shown in the figure. It was probably independently discovered in several different. Book I of the Elements ends with Euclid’s famous “windmill” proof of the Pythagorean theorem.
( See.) Later in Book VI of the Elements, Euclid delivers an even easier demonstration using the proposition that the areas of similar triangles are proportionate to the squares of their corresponding sides. Apparently, Euclid invented the windmill proof so that he could place the Pythagorean theorem as the capstone to Book I. He had not yet demonstrated (as he would in Book V) that lengths can be manipulated in proportions as if they were commensurable numbers (integers or ratios of integers). The problem he faced is explained in the. A great many different proofs and extensions of the Pythagorean theorem have been invented.
Taking extensions first, Euclid himself showed in a theorem praised in antiquity that any symmetrical regular figures drawn on the sides of a right triangle satisfy the Pythagorean relationship: the figure drawn on the hypotenuse has an area equal to the sum of the areas of the figures drawn on the legs. The semicircles that define ’s lunes are examples of such an extension. ( See.) In the (or Nine Chapters), compiled in the 1st century ce in, several problems are given, along with their solutions, that involve finding the length of one of the sides of a right triangle when given the other two sides. In the, from the 3rd century, offered a proof of the Pythagorean theorem that called for cutting up the squares on the legs of the right triangle and rearranging them (“tangram style”) to correspond to the square on the hypotenuse.
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