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

1. (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.

2. (figurative) To solve a famously difficult or impossible problem.

• morbus cyclometricus
• squircle
• square peg in a round hole (semantic overlap regarding a difficult problem)

• squaring the circle on Wikipedia.Wikipedia