Primitive Pythagorean Triples

Scott Farrar | @farrarscott |

Primitive Pythagorean Triples {x,y,z} can be generated by two positive integers a and b.

x = 2ab
y = a^2 - b^2
z = a^2 + b^2

as long as ...
(1) b < a
(2) a and b have opposite parity
(3) a and b are relatively prime (GCD=1)

Drag the slider at the bottom to progress through a. The y-axis will show possible b values.

Then check the box for Scale Triples using Principle Complex SqRt and drag a back and forth.

1. Which Pythagorean Triple would fill in the first "hole" in the blue grid? Why is it not there?

2. 6^2 + 8^2 = 10^2. Is this triple plotted?