Squarring the Circle
Square of a Circle - Adjust X and Y values with X=Y to get area of Circle. ( The x and y values are the radius of the Circle ) See Green equation and Compare to Radius and Hypotenuse -- Check the Numbers -- It should work; even if you cube or change the exponents. X=4,Y=4, x^n=.5, y^n=.5 is an interesting setting. 1) Input Box x and y (Blue) input boxes are the radius of each circle ( please read the therom below which states the problem ) 2) Input Box Exponents (Red) x^n and y^n can be adjusted. ( Mostly, to see the squaring, you should probably leave the exponents at 2 ) 3) Scale - Leave Scale at value - .7071 4) The Hypotenuse (Green) is the actual Length of the Hypotenuse of the Triangle made from the x and y values - which are the radius of the Circles - which, their(radius) "square areas" are equal to the Areas of the Circles made from these radius
Square areas of Circle: Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. It had been known for some decades before then that the construction would be impossible if pi were transcendental, but pi was not proven transcendental until 1882. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π. The expression "squaring the circle" is sometimes used as a metaphor for trying to do the impossible.