Great Philosophers-Pythagoras: 5 Minute Philosophy No.7: Pythagoras Part 4: The Pythagorean Theorem


Great Philosophers-Pythagoras: 5 Minute Philosophy No.7: Pythagoras Part 4: The Pythagorean Theorem – ‘Possibly So Pythagoras’

The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students.

The Pythagorean Theorem is Pythagoras’ most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. The later discovery that the square root of 2 is irrational and therefore, cannot be expressed as a ratio of two integers, greatly troubled Pythagoras and his followers. They were devout in their belief that any two lengths were integral multiples of some unit length. Many attempts were made to suppress the knowledge that the square root of 2 is irrational. It is even said that the man who divulged the secret was drowned at sea.

In mathematics, the Pythagorean theorem, also known as Pythagoras’s theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the “Pythagorean equation”:[1]

a^2 + b^2 = c^2!, ,
where c represents the length of the hypotenuse and a and b the lengths of the triangle’s other two sides.

Although it is often argued that knowledge of the theorem predates him,[citation needed] the theorem is named after the ancient Greek mathematician Pythagoras (c. 570 – c. 495 BC) as it is he who, by tradition, is credited with its first recorded proof.[2][3] There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework.[4][5] Mesopotamian, Indian and Chinese mathematicians are all known to have discovered the theorem independently and, in some cases, provide proofs for special cases.

The theorem has been given numerous proofs – possibly the most for any mathematical theorem. They are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed, to objects that are not triangles at all, but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps and cartoons abound.

Credits:
This film includes film images of the educational film ‘Possibly So, Pythagoras”, originally produced by Bruce and Katharine Cornwell.” See – https://vimeo.com/channels/bkcfilms

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