Given a circle with radius [math]r[/math], we would like to know whether we can obtain a square whose area is the same as the area of the circle by Euclidean construction. It is easy to see that the length of each side of such square is [math]r\sqrt{\pi}[/math]. In other words, the problem reduce to determining whether [math]\sqrt{\pi}[/math] is a constructible number. To simplify the problem further, since we can take square and square root by Euclidean construction, then it is equivalent to see whether [math]\pi[/math] is constructible or not.[br][br]The problem of squaring a circle has been of great interest to mathematicians in the history of mathematics. One of them is Hippocrates, who had a very interesting strategy to tackle the problem. However, his method was doomed to failure because in 1880, a German mathematician called [b]Ferdinard von Lindemann[/b], completely settled the problem by showing that [math]\pi[/math] is not a constructible number!