... values: a b c 3 4 5 5 12 13 7 24 25 I will now predict the next two values in the table so I can work out a general formula for this pythagorean family. By using the differencing method I can see that 'a' has a difference of 2 between each pythagorean triplet I predict the next two 'a' values to be 9 and 11 From the table I can also see that there is a quadratic sequence for the 'b' value so I predict the next two values to be 40 and 60 Also from my table, I can see the 'c' value is b+1 so my two next predictions I'm going to prove are: a b c 9 40 41 11 60 61 a² = 9² =81 b² = 40² =1600 c² = 41² =1681 a²+b² =81+1600 =1681 a²+b²=c² so Pythagoras's theory holds for (9,40,41) because they satisfy the condition of a²+b²=c² in a right angled triangle. a² = 11² =121 b² = 60² =3600 c² = 61² =3721 a²+b² =121+3600 =3721 a²+b²=c² so Pythagoras's theory holds for (11,60,61) ...

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