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Pythagoras' theorem states that a²+b²=c² As you can see, a is the longest side, b is the middle side and c is the longest side (hypotenuse). The point of this coursework is to find b when a is an odd number and all of the sides are positive integers. Then after that I will go looking when a is a positive number. The numbers 3, 4 and 5 work in Pythagoras' theorem, 3²+4²=5² because 3²=3×3=9 4²=4×4=16 5²=5×5=25 and so 3²+4²=9+16=25=5² The numbers 5, 12 and 13 also work, 5²+12²=13² because 5²=5×5=25 12²=12×12=144 13²=13×13=169 and so 5²+12²=25+144=169=13² The numbers 7, 24 and 25 also work, 7²+24²=25² because 7²=7×7=49 24²=24×24=576 25²=25×25=625 and so 7²+24²=49+576=625=25² 3, 4 and 5 Perimeter= 3+4+5=12 Area= 1/2 ×3×4=6 5, 12 and 13 Perimeter= 5+12+13=30 Area= 1/2 ×5×12=30 7, 24 and 25 Perimeter= 7+24+25=56 Area= 1/2 ×7×24=84 From the first three terms I have realised that: - * a increases by 2 each time * a is equal to the formula ×2+1 from n * b is always even * c is always odd * c is always +1 of b * b=(a×n) + n I have also...

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