Q0. Can all rationals in $(0,1)$ be realized at $x$-coordinates of tangent circles in the arrangement below?
I think the answer to Q0 is Yes.
Rationals up to depth $16$.
Q1. What is the ratio of the area covered by the disks touching the $x$-axis in $(0,1)$, and the triangular region between the $x=0$ and $x=1$ circles and the $x$-axis?
Far-fetched:
Q2. Is there any way to use this example to show intuitively that the cardinality of the reals exceeds the cardinality of the rationals.
I think the answer to Q2 is No.