square the circle

verb2

1. •
   To construct a square with the same area as a given circle by using only a finite number of steps with compass and straightedge, a task which is mathematically impossible.

   • The problem of squaring the circle is the problem of determining the ratio of the circumference of a circle to the diameter, which is called π. — 1946
2. •
   (figurative) To solve a famously difficult or impossible problem.