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.
For a circle of radius  
  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  
  is not the solution of any polynomial equation with rational coefficients (coefficients that can be written as fractions), hence the circle cannot be squared.

Add comment

Security code