Happy Lévy Day

Illustration: Randi Klett; Images: iStockphoto; Konrad Jacobs

Every child asks why there's a mother's day and a father's day but no children's day and gets the same answer: "Every day is a children's day." (Actually, there's a Universal Children's Day on 20 November, but parents keep that a secret.)

An eerie parallel suggests itself: every day is surely some sort of constant day, but only one gets any respect. That would be Pi day, which was marked with great fanfare nearly two weeks ago: 3.1415..., don't you know.

So today, the 27th day of the 3rd month, we at IEEE Spectrum raise a toast to Pi Day's forgotten cousin, Lévy Day, named for the Lévy constant, 3.27582291872....

It was found in 1936 by the French mathematician Paul Lévy, some time after the necessity of its existence had been demonstrated by the Soviet mathematician Aleksandr Khinchin. It is defined as e (a constant itself) raised to the power (π squared divided by (12 natural log 2)). That looks awful as a sentence, so let me draw you a picture instead. 

Yes, it's hard to grasp, and that's one big reason why it hasn't got as much media coverage as pi.

Other reasons: on Pi Day you get to eat pie, pi is easy to pronounce, and it's uncannily useful in physics, engineering, and mathematics itself. Lévy's constant is of interest mainly to those interested in numbers; it helps to describe the behavior of the continued fraction expansion of most real numbers. 

Also, people love the Greek letter π. And that suggests a way to build up Levy Day: Rename it for γ, the Greek letter that represents the constant. It's all part of a classicizing nomenclature that was popularized in the 18th century by the great Swiss mathematician Leonard Euler. True, the letter is already used to represent a host of constants in engineering, physics, math, and even finance. Perhaps the weightiest of them all includes the Swiss giant's name: the Euler-Mascheroni constant.

But so what? How many of those other gamma constants spell out a calendar date?

So, Happy Gamma Day!

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