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Saneeta Mandil 10R Maths Coursework Beyond Pythagoras Pythagoras Theorem is a2 + b2 = c2. 'a' being the shortest side, 'b' being the middle side and 'c' being the longest side (hypotenuse) of a right angled triangle. Pythagorean triples are a family of right-angled triangles for which all the positive integers and the shortest side is an odd number. The first part of my investigation is to study the family of Pythagorean triples where the shortest side is an odd number and all three sides are positive integers. The numbers 3, 4 and 5 satisfy the condition 32 + 42 = 52 (Smallest number) 2 + (middle number) 2 = (largest number) 2 The numbers 3, 4 and 5 can be the lengths - in appropriate sides units - of the sides of a right-angled triangle. 5 3 4 32 = 3 x 3 = 9 42 = 4 x 4 =16 52 = 5 x 5 =25 and so 32+...

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