Math Bite: Proof of an Empirical Observation Made by Amos Oz’s Character

Doron ZEILBERGER^{1}

In Amos Oz’s latest novel Panther in the Basement (Hebrew, Keter, Jerusalem, 1995), Proffie, the book’s twelve-and-a-quarter-year-old precocious hero, makes the following observation regarding the ratio of his age to that of the age of his twenty-year-old neighbor, Yardena, on whom he has a crush (p. 127):

As the years will increase, the distance between me and her will decrease (in percentage), but the sad side is that this decreasing gap will decrease more and more slowly. Like a marathon-runner that got tired.

And indeed, the ratio of their ages, f(t) = t/(7.75 + t), is such that f′(t) = (7.75)/(7.75 + t)^{2} > 0, but f′′(t) = (−15.5)/(7.75 + t)^{3} < 0.

1 Department of Mathematics, Temple University, Philadelphia, PA 19122, USA. zeilberg@math.temple.edu

http://www.math.temple.edu/~zeilberg   . Supported in part by the NSF. Feb 8, 1996.