Fibonacci and Pythagoras

Fibonacci, your secrets are serene---
We can spend a lifetime studying you
As the Cat on the Mathologer's shirt
Bends to your hurricane of Phi.

Even Pythagoras, yes...
Bends to your will.
For, take four of your numbers in a square
Lined up in their sequence from the lowest on top
And the highest on the bottom,
Left to right,
And when cross multiplied completely,
Make legs and the hypotenuse of a right triangle;
Yes, one value even must be doubled, but how serene!
Know its inner circle, like a soul
Tangential to the Right Triangle's form.
And what's this?
Do you know the squares made
From the exterior of each line of the triangle?
That's how Pythagorean Theorem works?
So, the radii of exterior circles
Also, by cross multiplication,
Fit by three Euclidean Squares of Pi.

So also, counting by Fibonacci,
While working through Fibonacci
Creates Pythagorean Theorem's roots also;
Even when a number counted
Is not a Fibonacci number.