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Beyond Pythagoras
Member rating: No Rating | Words: | Submitted: Thu Sep 04 2003
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BEYOND PYTHAGORAS By: Megan Garibian 10A What this coursework has asked me to do is to investigate and find a generalisation, for a family of Pythagorean triples. This will include odd numbers and even numbers. I am going to investigate a family of right-angled triangles for which all the lengths are positive integers and the shortest is an odd number. I am going to check that the Pythagorean triples (5,12,13) and (7,24,25) cases work; and then spot a connection between the middle and longest sides. The first case of a Pythagorean triple I will look at is: The numbers 5, 12 and 13 satisfy the connection. 5² + 12² = 13² 25 + 144 = 169 169 = 13 The second case of a Pythagorean triple I will look at is: The numbers 7, 24 and 25 satisfy the connection. 7² + 24² = 25² 49 + 576 = 625 625 = 25 There is a connection between the middle and longest side....
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