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Pythagoras' Theorem Further Ideas
Pythagoras’ Theorem can be generalized to other sets of similar figures that surround a right-angled triangle, and students could investigate some of these. 
The Greeks used formulae to generate Pythagorean triples. Able students could explain how the following method works: - Choose two numbers m and n (m greater than n).
- To find the first number in the triple calculate m2 — n2.
- To find the second number in the triple calculate 2mn.
- To find the third number in the triple calculate m2 + n2.
Students can investigate what happens for different values of m and n, and try to distinguish ‘primitive’ triples, those that are not multiples of smaller triples. They could investigate what happens when consecutive whole numbers are chosen for m and n.
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