Let be a sequence of independent and identically distributed random variables, and let be the number of “record highs” upon to and including event . For example, each can represent the amount of rainfall in a year, where is amount of rainfall recorded the first time that records were kept. As shown in *Gamma* (page 125), the expected number of record highs is

.

As noted in *Gamma*,

Two arbitrary chosen examples are revealing. The Radcliffe Meteorological Station in Oxford has data for rainfall in Oxford between 1767 and 2000 and there are five record years; this is a span of 234 recorded years and . For Central Park, New York City, between 1835 and 1994 there are six record years over the 160-year period and , providing good evidence that English weather is that bit more unpredictable.

When I researching for my series of posts on conditional convergence, especially examples related to the constant , the reference *Gamma: Exploring Euler’s Constant* by Julian Havil kept popping up. Finally, I decided to splurge for the book, expecting a decent popular account of this number. After all, I’m a professional mathematician, and I took a graduate level class in analytic number theory. In short, I don’t expect to learn a whole lot when reading a popular science book other than perhaps some new pedagogical insights.

Boy, was I wrong. As I turned every page, it seemed I hit a new factoid that I had not known before.

In this series, I’d like to compile some of my favorites — while giving the book a very high recommendation.

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