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Maths GCSE coursework: Beyond Pythagoras Within this investigation I will look at the relationships between the lengths, perimeters and areas of right-angled triangles. This looks at Pythagorean Triples, three numbers that satisfy the condition of: (smallest number)2 + (middle number)2 = (largest number)2 This can also be expressed as: a2 + b2 = c2 I will look first at an odd number as the 'smallest number' then continue to even numbers. The objective of this investigation is to be able to: Make predictions about Pythagorean triples. Make generalisations about the lengths of sides. Make generalisations about the perimeter and area of the corresponding triangles. To prove a Pythagorean triple you must check that the three numbers satisfy the condition. So... 5, 12, 13 52 + 122 = 25 + 144 = 169 = 132 It is a Pythagorean triple because 5² + 12² = 13². To try a second one: 7, 24, 25 7² + 24² = 49 + 576 = 625 =...

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