Area of a Circle

I am putting together a chapter about area for my new geometry book and I wanted to share about this really cool way to find the area. The way that is traditionally done (which is still awesome) is to break the circle into sectors (triangle-like pieces) and arrange them into a rectangle. But another way is to make the circle out of concentric rings made of string.  We could then lay these strings out straight, forming a “staircase” or right triangle with the longest string equal to the circumference, 2πr, and the height would be the radius, r.  Thus the area of the “right triangle” formed would be 1/2 * 2πr * r = πr^2! That is what the picture for the post today represents. So cool.

Michael Waski