a wave of primitive pythagorean bombers

graphing the pythagorean triples

understanding the patterns; how the graph was constructed

(great) pictures: Adam Cunningham and John Ringland (from Wikipedia)

a ppt is here

what dimensions would the next triangles have?
why are there gaps in the rows?

these are primitive pythagorean triples: no common factors in all three numbers

there are many patterns to explore, mainly involving the number 4 as a factor

the 'lines': families of triples, are connected by a constant relationship ('horizontally' or rows)
as are the 'vertical' values

students will need to be able to find 'm' and 'n' for each triple from one of the pythagorean triple generator formulae (sometimes called Euclid's formula):