square the circle

English

square the circle (third-person singular simple present squares the circle, present participle squaring the circle, simple past and past participle squared the circle)

(geometry) 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.
- 1946, Bertrand Russell, History of Western Philosophy, I.24:
  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.
(figurative) To solve a famously difficult or impossible problem.

to construct a square with the same area as a circle

to solve a difficult problem