A question on Pythagorean stretches

[Baltorigamist]

I just wanted to know if Pythagorean triples (3/4/5; 5/12/13) applied to the axial/axial+1 Pythagorean stretches. I don't have my copy of ODS on me at the moment.
I still have to memorize the formulas for these, but I've used Pythagorean stretches in several of my previous designs. However, this is the first time I've ever used one that goes between different elevations. A Pythagorean triple happens to apply, but the vertices luie at axial, axial, and axial+1 respectively.
Any help would be appreciated.

Note that I've only taken geometry and a bit of algebra 2.

[jsu718]

Geometry teacher to the rescue.

EVERY odd number has a pair that follows

3 has 4 and 5
5 has 12 and 13
7 has 24 and 25
9 has 40 and 41
11 has 60 and 61
13 has 84 and 85

And they grow from there. There is a similar pattern for even numbers starting from 4 (with 3 and 5), but with the other two numbers separated by two.

The formula for that comes from Euclid. For odd numbers like the ones you want...
b = a^2/2 − 1/2 and c = b + 1

For the even numbers, just as a reference
b = a^2/4 - 1 and c = b+2