"I illustrate the importance of growing the size of the pie to one’s share of pie to my entrepreneurship students at the Stanford Graduate School of Business by reminding them of the formula for a circle’s circumference versus its area. The formula for circumference (a proxy for share of pie) is linear (2 πr) vs. the formula for area, which is exponential (πr²)."
It seems to me that the value of growing the size of the pie as well as one's share of the pie is pretty easily understood and not in need of an analogy. But yet, this guy has decided to use one, and it is terrible.
Not only is it quadratic, not exponential (a relatively minor detail), but what on earth, exactly, is the radius meant to represent in this analogy?