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This was one of the three geometric problems of antiquity, and was perhaps first attempted by [[Anaxagoras]]. It was finally proved to be an impossible problem when pi was proven to be transcendental by Carl Louis Ferdinand von Lindemann in 1882.

This was one of the three geometric problems of antiquity, and was perhaps first attempted by [[Anaxagoras]]. It was finally proved to be an impossible problem when pi was proven to be transcendental by Carl Louis Ferdinand von Lindemann in 1882.

The other two problems from antiquity are "duplicating the cube" (constructing the length of the side of a cube that would have half the volume of a cube of a given side, effectively constructing the number cube root of 2) and "trisecting an angle".  These three problems were finally shown to be unsolvable by straightedge and compass with the algebraic tools of the 19^th century.

The other two problems from antiquity are: <br> "'''Duplicating the cube'''"  

:Construct the length of the side of a cube that would have half the volume of a cube of a given side, effectively constructing the number cube root of 2, and  

"'''Trisecting an angle'''"  

:Construct an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge, and a compass.   

 

These three problems were finally shown to be unsolvable by straightedge and compass with the algebraic tools of the 19^th century.

Squaring the circle is sometimes used as an idiom in common discourse to mean taking on an impossible task.

Squaring the circle is sometimes used as an idiom in common discourse to mean taking on an impossible task.