Size of Circle
Radius of a circle can be measured. In what other ways can we describe "Size of a Circle"?
Circumference of a circle is directly proportional to its radius, i.e., there is a constant P such that Circumference = P * Radius
Area of a circle is directly proportional to the square of its radius, i.e., there is a constant Q such that Area = Q * Radius^2
How are P and Q related?
The region within a circle is partitioned into N equal-size sectors. Those sectors are rearranged into the figure on the right. The circle and the other figure have the same area. Drag the dot labeled N to change the number of sectors.
When N is (moderately) large, what is the (approximate) shape of the righthand figure?
Is there an easy way to compute area of a figure with that shape?
Scientists in several cultures, many years ago, used similar ideas to conclude that Q = P/2
Learn more about this by reading the article "Take It to the Limit" by Steven Strogatz.