Two of the earliest known documented approximations of the value of $\pi$ are $\pi_B=\frac{25}{8}=3.125$ and $\pi_E=\left(\frac{16}{9}\right)^2$, from Babylonian and Egyptian sources respectively. I've read that the Egyptian figure at least could be justified through some geometrical diagram which made the approximation a visually obvious statement about the areas of circles and squares. As far as I know, the Babylonian value on the other hand could have simply been obtained empirically through direct measurement of circle diameters and circumferences; I really have no idea. My question is simply can anyone provide simple visual proofs of these approximations? It doesn't matter to me if the proofs happen to be the historically used ones or not, as long as they get the job done.
Side-note: The Egyptian value pertains to the area-$\pi$, whereas the Babylonian one is about the circumference-$\pi$. As far as anyone knew back in the day, the two constants were not necessarily equal a priori. Bonus points go to answers that can demonstrate both approximations for both pi's.
Here we have a visual proof of the egyptian $\pi$:
And here one of the babylonian $\pi$: