What is missing, for example, at square the circle, is the information that because the area of a circle is mathematically calculated using pi, which is irrational, there is no mathematical way of calculating the dimensions of a square with the same area as that of a given circle. But that does not mean that such a square cannot exist.
For example, at square the circle, the information is that because the area of a circle is mathematically calculated with pi, there is no way to calculate the dimensions of a square with same area as the given circle.