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Pythagorean Triples Activities:
In mathematics education at the secondary level, we are familiar with the set of following Pythagorean Triples: (3,4,5) (5,12,13) etc. How many more are there?
Consider the set of following triples: (3,4,5) (5,12,13) (11,60,61). Can you see any pattern?
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| If you notice, the first numbers are odd and prime and the last two numbers in each triple differs by 1 |
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The investigation begins with this discovery of odd numbers, and differences of 1. Consider the general triple (a,b,c) and pythagoras' theorem (c² = a² + b²). There is a straight forward substiution using the difference of 1 to derive the general triple in terms of a² only. We can then easily convert the general triple into Excel® formulae and start to investigate pythagorean triples.
We first of all consider odd numbers between 1 and 20, then the even numbers, and finally double the even numbers (you will see why when you work through the activity)
Download
 Activity instructions (pdf - 131kb)
MS Excel® worksheet (16kb)
CSV worksheet (1kb - if you do not have a spreadsheet application that can open MS Excel® files)
 Adobe® Reader®
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