How can I build a circle which must have the same area as a given square ?
The solution of the problem of squaring the circle by compass and straightedge demands construction of the number 
, and the impossibility of this undertaking follows from the fact that pi is a transcendental (non-algebraic and therefore non-constructible) number. If the problem of the quadrature of the circle is solved using only compass and straightedge, then an algebraic value of pi would be found, which is impossible. Johann Heinrich Lambert conjectured that pi was transcendental in 1768 in the same paper in which he proved its irrationality, even before the existence of transcendental numbers was proven. It was not until 1882 that Ferdinand von Lindemann proved its transcendence.
http://en.wikipedia.org/wiki/Squaring_the_circle
+118613 Let the side length of the sqare be x
The area of the square is x2
Area of circle is pi*r2
x2=pi*r2
radius=sqrt(x2/pi)
+128707 How can I build a circle which must have the same area as a given square ?
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"Squaring" the circle......a problem that the "ancients" were fascinated with!!!
I'm not an "expert" on this - some people on this site are probably far more knowledgeable about it - but it can't be done with standard "Euclidean" tools....i.e., compass and straightedge.
There HAVE been examples of people constructing various "curves" - a "lune," for instance -that equal the area of a given square.........(but they had to "cheat" to do it, as I understand)
I found something about this here.......it's quite interesting !!
http://en.wikipedia.org/wiki/Squaring_the_circle
The solution of the problem of squaring the circle by compass and straightedge demands construction of the number , and the impossibility of this undertaking follows from the fact that pi is a transcendental (non-algebraic and therefore non-constructible) number. If the problem of the quadrature of the circle is solved using only compass and straightedge, then an algebraic value of pi would be found, which is impossible. Johann Heinrich Lambert conjectured that pi was transcendental in 1768 in the same paper in which he proved its irrationality, even before the existence of transcendental numbers was proven. It was not until 1882 that Ferdinand von Lindemann proved its transcendence.
http://en.wikipedia.org/wiki/Squaring_the_circle
