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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
This is an application of the Pythagorean theorem, = +, and the result agrees with the given value, c = 1.25. [ 11 ] [ 16 ] That the area is also correct is verified by computing the product, ab . [ 11 ]
The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras, [216] [214] [217] [218] but he may have been the first to introduce it to the Greeks. [219] [217] Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof. [220]
Thales of Miletus (c. 624/623 – c. 548/545 BC) is the first known individual to use deductive reasoning applied to geometry, by deriving four corollaries to Thales' theorem. [1] Pythagoras (c. 570 – c. 495 BC) was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five ...
The Baudhāyana Śulvasūtra states the rule referred to today in most of the world as the Pythagorean Theorem. The rule was known to a number of ancient civilizations, including also the Greek and the Chinese, and was recorded in Mesopotamia as far back as 1800 BCE. [7]
Bhaskaracharya proof of the pythagorean Theorem. Some of Bhaskara's contributions to mathematics include the following: A proof of the Pythagorean theorem by calculating the same area in two different ways and then cancelling out terms to get a 2 + b 2 = c 2. [21] In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations ...
The five-piece dissections used in the proofs by Al-Nayrizi and Thābit ibn Qurra (left) and by Henry Perigal (right). This tiling is called the Pythagorean tiling because it has been used as the basis of proofs of the Pythagorean theorem by the ninth-century Islamic mathematicians Al-Nayrizi and Thābit ibn Qurra, and by the 19th-century British amateur mathematician Henry Perigal.
[7] According to one statement, Hippasus left no writings, [7] according to another he was the author of the Mystic Discourse, written to bring Pythagoras into disrepute. [ 19 ] A scholium on Plato 's Phaedo notes him as an early experimenter in music theory , claiming that he made use of bronze disks to discover the fundamental musical ratios ...