Why is the area of a circle proportional to the square of its radius? And why is that ratio the same as the ratio of the circumference to the diameter?

In which I talk about linear approximations and the shape of home plate.

Approximation Theory and Operators in Functional Spaces Publication Trend The graph below shows the total number of publications each year in Approximation Theory and Operators in Functional Spaces.

Stein's Method And Probability Approximations Publication Trend The graph below shows the total number of publications each year in Stein's Method And Probability Approximations.