square the circle

The phrase "square the circle" refers to a mathematical problem that was proven to be impossible by ancient Greek mathematicians. It relates to the challenge of constructing a square with the same area as a given circle using only a compass and straightedge - two basic tools of Euclidean geometry. Despite many attempts throughout history, no one has been able to solve this problem using these limitations. In a broader sense, "squaring the circle" has come to represent any attempt to achieve the impossible or reconcile conflicting or mutually exclusive concepts.