The Gaussian-School of Higher-Arithmetic (1831, updated 2022); tutorial #21 page 6a.

The Arithmetic of Clocks, page 6a.

Here I add the quarter circles. Every circle in the quarter series is just 0.7788... (e^-0.25) times smaller than the one outside it. We need to imagine that we are looking down an infinite hole or well with a continuous surface. We can call this bottomless well or bottomless number pit the exponential-polar-manifold. It is worth noting here that every single member (including an infinite extent of rational fractions between every whole number) of the entire trebly infinite geometric series (except for zero) is equivalent to a flat (finger counting) number that our mathematicians refer to as an irrational number; but the nature of space-time is very rational indeed. The only irrationality here comes from fallible thinking that in reality is nothing more than neo-Pythagorean flat-plane-arithmetic, unreasonably applied within the exponential Universe of time and space.