  We give a completely constructive solution to Tarski's circle squaring
problem. More generally, we prove a Borel version of an equidecomposition
theorem due to Laczkovich. If $k \geq 1$ and $A, B \subseteq \mathbb{R}^k$ are
bounded Borel sets with the same positive Lebesgue measure whose boundaries
have upper Minkowski dimension less than $k$, then $A$ and $B$ are
equidecomposable by translations using Borel pieces. This answers a question of
Wagon. Our proof uses ideas from the study of flows in graphs, and a recent
result of Gao, Jackson, Krohne, and Seward on special types of witnesses to the
hyperfiniteness of free Borel actions of $\mathbb{Z}^d$.
