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Beyond Pythagoras Maths Pure Coursework 1 By: Ben Ingram 10R Beyond Pythagoras Pythagoras Theorem: Pythagoras states that in any right angled triangle of sides 'a', 'b' and 'c' (a being the shortest side, c the hypotenuse): a2 + b2 = c2 E.g. 1. 32 + 42 = 52 9 + 16 = 25 52 = 25 2. 52 + 122 = 132 3. 72 + 242 = 252 25 + 144 = 169 49 + 576 = 625 132 = 169 252 = 625 All the above examples are using an odd number for 'a'. It can however, work with an even number. E.g. 1. 102 + 242 = 262 100 + 576 = 676 262 = 676 N.B. Neither 'a' nor 'b' can ever be 1. If either where then the difference between the two totals would only be 1. There are no 2 square numbers with a difference of 1. 32 9 42 16 52 25 62...

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