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Beyond Pythagoras - I have been asked to investigate the relationships between different Pythagorean triples, and see if there is a mathematical pattern linking them.
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| Submitted: Fri Sep 19 2003
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Mathematics GCSE Coursework Year 10 January 2003 Beyond Pythagoras I have been asked to investigate the relationships between different Pythagorean triples, and see if there is a mathematical pattern linking them. In doing so I will at later date, be able to devise a formula which will enable me to work out any set of Pythagorean triples. I will only be able to construct this formula if there is a direct pattern within the Pythagorean triples. I have been given the first three Pythagorean triples: Term Number 'n' Shortest Side 'a' Middle Side 'b' Longest Side 'c' Perimeter 'P' Area 'A' 1 3 4 5 12 6 2 5 12 13 30 30 3 7 24 25 56 84 Pythagorean triples always satisfy the condition. The condition is a2+b2=c2 To check that the Pythagorean triples I have been given are correct I have decided to use Pythagoras Theorem. Pythagoras Theorem is c2 = a2 + b2. 'a' being the shortest side, 'b' being the middle side and 'c' being the longest side (hypotenuse) of a right angled triangle. The...
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