• $A = A_0 = \lbrace x^2 + y^2 \le 1 \rbrace$ ← unit circle
• $B = B_0 = \lbrace \max(|x|,|y|) \le 1 \rbrace$ ← unit square
• $f(x,y) = (x,y)/\sqrt2$ ← injection from $A$ to $B$ (shrinking by $1/\sqrt2$)
• $g(x,y) = (x,y)/\varphi$ ← injection from $B$ to $A$ (shrinking by $1/\varphi$, where $\varphi$ is the golden ratio)

This gives a decreasing sequence of subsets of $A$ and $B$

• $A_n = g(B_{n-1})$ is
• a circle with radius $(\sqrt2)^{-k} \varphi^{-k}$ if $n = 2k$