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Pythagoras Theorem is the formula for working out the hypotenuse of a right-angled triangle when the other two sides of the triangle are given. The formula for Pythagoras Theorem is: a²+b²=c². In this formula, a is the shortest side, b is the middle side, and c is the shortest side. Pythagorean Triples are when the three sides of the right-angled triangle are all whole numbers. The first five Pythagorean Triples are: 3, 4, 5-because 9(3²) +16(4²) =25(5²) 5, 12, 13-because 25(5²) +144(12²) =169(13²) 7, 24, 25-because 49(7²) +576(24²) =625(25²) 9, 40, 41-because 81(9²) +1600(40²) =1681(41²) 11, 60, 61-because 121(11²) +3600(60²) =3721(61²) As you may have noticed, the last two numbers (b and c) have a difference of 1. You may have also noticed that the first and last numbers (a and c) are odd numbers and the middle numbers (b) are even. This investigation is about finding a formula for various different purposes including finding the nth Pythagorean Triple, the...

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