Pythagoras’ Theorem a 2 + b 2 = c 2 The fundamental theorem every child is forced to learn!

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Presentation transcript:

Pythagoras’ Theorem a 2 + b 2 = c 2 The fundamental theorem every child is forced to learn!

History of the theorem Pythagoras of Samos was a Greek philosopher responsible for many important developments in mathematics! But rumour has it Pythagoras’ Theorem was known to the Babylonians some 1000 years before Pythagoras. However we all believe he was the first person to prove the theorem and that is why the theorem takes his name.

Proofs! Most Proofs Of Pythagoras' Theorem Eleftherios Argryopoulos of Greece, has discovered 520 different proofs of the Pythagorean theorem over a period of 11 years from 1986 to GUINNESS WORLD RECORD Proof without words! If only all proofs were as simple.

The theorem in 3-D Usually denoted a 2 + b 2 + c 2 = d 2, but here d 2 = h 2 You just can’t get the pictures these days! The application of Pythagoras’ Theorem in three dimensions involves the relationship between the perpendicular edges of a rectangular block and the solid diagonal of the same block.

Pythagorean Triples There is a simple formula that gives all the Pythagorean triples. Suppose m and n are two positive integers with m < n. Then the triple can be found: a = n 2 – m 2, b = 2mn, c = n 2 + m 2 This formula gives all the Pythagorean triples! Here are the first few: m = 1, n = 2 gives (3,4,5) m = 1, n = 3 gives (8,6,10) m = 2, n = 3 gives (5,12,13) m = 2, n = 4 gives (12,16,20) and so on… m = 6, n = 10 gives (64,120,136)

Applications On a lighter note, does the theorem have any applications?? It’s main use is in architecture and any form of structural planning By using Pythagoras’ theorem to work out the hypotenuse of a drill you can work out the size of the hole created! You can use the theorem to work out the height of a house or awkward object. Slightly more interesting: a musical harps strings are all angled. When building a harp, if you take each string as a hypotenuse you can work out the correct spacing between each string using the theorem!