Squaring the circle
![Squaring the circle: the areas of this square and this circle are both equal to π. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized compass and straightedge.Some apparent partial solutions gave false hope for a long time. In this figure, the shaded figure is the Lune of Hippocrates. Its area is equal to the area of the triangle ABC (found by Hippocrates of Chios).](/Images/godic/202502/05/Squaring_the_circle.svg3629.png")
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![A partial history by Florian Cajori of attempts at the problem.[4]](/Images/godic/202502/05/Quadrature_of_Circle_Cajori_19193629.png")
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Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.