## Squaring the Circle

Among the many mathematical problems put forward by the ancient Greeks was the problem of squaring the circle - that is, constructing a square with the same area as a given circle, using only a straight edge and compass.
$r$
and area
$\pi r^2$
this means constructing a square of side x such that
$x^2 = \pi r^2 \rightarrow x= r \sqrt{\pi}$
.
This was later shown to be impossible as a consequence of the fact that
$\pi$
is not the solution of any polynomial equation with rational coefficients (coefficients that can be written as fractions), hence the circle cannot be squared.