As a tree grows, the trunk enlarges year by year about its centre. Counting the rings tells us the age of the tree. We notice that each year the area of the cross section increases by an amount proportional to the perimeter (the length of the outside ring). We can express this mathematically. The area of a circle of radius r is 
r 2 and the perimeter is 2r. In calculus the derivative gives the rate of change, and here the derivative of the area is the perimeter.
