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Ali Dickson 17th November 2002 Investigating Pythagorean Triples Introduction Pythagoras was probably the most famous mathematician ever to live. He came up with the concept that to find the length of the hypotenuse of a right-angled triangle, you could apply this formula: a²+b²=c² If you square the lengths of the two shorter sides (a and b), then add them together, the get the length of the hypotenuse squared (c). This is Pythagoras' theorem. Hypotenuse (The side opposite the right angle) a=3 c=5 b=4 a²= 9 b²= 16 a² (9) + b² (16) = c² (25) Perimeter = 3 + 4 + 5 = 12 units Area = 1/2 × 3 × 4 = 6 square units Three numbers that fit this formula, such as 3,4,5, are called Pythagorean triples. There are many other combinations of numbers that also fit the pattern such as 5,12,13, or 7,24,25. Below is another example of how this rule works. a=5 c=13 b=12 a² = 25 b² = 144 c² = 169 a² (25)...

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