I have begun to construct a spiral of right-angles triangles thus:

The first triangle has legs both equal to 1.

Each subsequent triangle uses the hypotenuse of the previous triangle as one leg and a new line of length 1 as the other leg.

Every time the length of a spoke happens to be an exact whole number, I’ve marked it in red. I happened to notice that the angular distances between the red spokes are of a similar size.

My question is this: is it converging, and if so, to what?