Pythagorean Series

This is an illustration of the patterns in the infinite quantity of Pythagorean triangles - right triangles with sides like 3,4,5 and 5,12,13 and so on. They are commonly used by carpenters to establish a very accurate 90 degree angle over a long distance.

This chart was made by using a simple formula which uses the row and column number. Series of triangles are colored the same, in lines that extend away from the upper left. There are always 2 lines, because the formula forms 2 reciprocal partner series. One line is always vertical, and the other is always at 45 degrees, upperleft to lowerright.

Only "primitive" Pythagoreans are colored. No multiples. On the chart there is no distinction between multiples and non-Pythagoreans. They are all colored black.