Area of a Circle vs. Square

Two Hundred Sixty Seventh Post: Area of a Circle vs. Square

Here at the math factory on Constructor’s Corner we are expanding our business and looking for more employees. Recently posted on the site was a parabola that explained the properties of a circle. We found the radius with only knowing the segment length. Now the work doesn’t stop there. If we find the area under the graph of the parabola we have the area of the circle and because we found the radius we know the area of the square. This square has a larger area than the circle, but from the data we should be able to find the square that has the same area as the circle. Some of the information I typed here could be wrong since I did not do any calculations on the area yet, but it is the idea that is important.

In the book “Old and New Unsolved Problems in Plane Geometry and Number Theory,” there is a problem called “Squaring the Circle.” It states “Can a circle be decomposed into finitely many sets that can be rearranged to form a square?” Although its hints on how to solve it do not relate directly to my solution of the parabola, I believe that there may be something there.

Something like, take the square that has the length and width of the radius of the circle and subtract its area by the area of the circle. Then take the left over area and solve the size... Ok so maybe there is more to it than I thought, but the idea is presented. We are looking not only looking for a solution, but need a solution that is simple enough to be useful when applied to common problems.

Also of note is the site: http://www.ngine.de/ is back up. This is the place to download “HAM” for the Game Boy programming. So until you program your Game Boy to cheat during your math exam... May the Creative Force be with You