Pythagorean Triples
1) The numbers 3, 4, and 5 are called Pythagorean triples since 3 2+ 4 2= 5 2. The numbers 5, 12, and 13 are also Pythagorean triples since 5 2 + 12 2= 13 2. Can you find any other Pythagorean triples? Actually, there is a set of formulas that will generate an infinite number of Pythagorean triples.
2) Select at least 5 more Pythagorean Triples. Show why your 5 sets of Pythagorean triples work in the Pythagorean Formula. They should all be different from each other, and should not be the multiple of another. All 5 different Pythagorean Triples should be done using the rule that allows you to find ALL the Pythagorean triples, show in detail using the rule how they were created.
In this solution I describe the series of formulas which can be used to generate Pythagorean triples. I explain these formulas in their historical context. I then go on to demonstrate how to derive any Pythagorean triple, step by step.
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