Pythagorean triples

This lesson is one in a series of lessons on Pythagoras theorem. The purpose of this lesson is to have students undertake a mathematical exploration to find Pythagorean triples, that is, sets of positive integers {a, b, c} such that a2 + b2 = c2. Students apply trial and error to identify sets of positive integers {a, b, c} that are Pythagorean triples using a spreadsheet. They apply scaling to develop new triples from a known triple, and use a formula (Euclid’s formula) to generate Pythagorean triples. They then take a systematic approach to explore if there are any emerging patterns. This lesson is an example of an exploration within mathematics itself rather than an application of mathematics to contexts involving practical problems or other learning areas.