Tarski's Circle-Square Problem

Tarski's Circle-Square Problem questions whether it's possible to dissect a circle into finitely many pieces that can be reassembled into a square of the same area, using only rigid motions (rotations and translations). It explores whether a circle and a square of equal area are "scissors congruent," meaning one can cut and rearrange one shape into the other without resizing. This problem touches on the deeper foundations of geometry and measure theory, highlighting questions about how shapes relate beyond just their area, with solutions involving advanced concepts like non-measurable sets and the axiom of choice.