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Beyond Pythagoras This investigation is to study Pythagoras Theorem. I will try to find patterns and formulae to help predict Pythagorean Triples. About Pythagoras Pythagoras was a Greek Philosopher and Mathematician who is believed to have lived in the 6th century BC. He discovered many theorems but his most famous was: a2+b2= c2 What is a Pythagorean Triple? To answer this I first need to explain Pythagoras Theorem. Pythagoras States that in any right-angled triangle, a2+b2=c2. a is the shortest side, b the middle length side and c the hypotenuse (the longest side). A Pythagorean Triple is any set of integers that agrees this condition. For example 3, 4, 5 is a Pythagorean Triple because: 32+42=52 Because 32= 3x3= 9 42= 4x4= 16 52= 5x5= 25 9+16= 25 1. The numbers 5, 12, 13 satisfy the condition: 52+122=132 Because 52= 5x5= 25 122= 12x12= 144 132= 13x13= 169 25+144= 169 The numbers 7, 24, 25 72+242= 252 Because 72= 7x7= 49 242= 24x24= 576 252= 25x25= 625 44+576= 625 2. (a) I found...

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