Today is e day, named after the number 2.718… Each year, e days falls on February 7. This year is particularly “e-like” or “e-ey”, as 18 occurs after 2.7 in its digits.

Named Euler’s number or Napier’s constant, the number e is transcendental, meaning that it is not the root of any polynomial equation with integer coefficients. The number e is the second most famous transcendental number behind π. Think of e as the Jan Brady of transcendentals numbers.

What is e and why would anyone care about it?

In honor of e day, I’ve collected together some random facts about it.

The first 50 digits of e are: 2.71828182845904523536028747135266249775724709369995

Google raised $2,718,281,828 for its IPO, which is the product of e and one billion dollars.

If you form the infinite sum of the reciprocals of the factorials of all the non-negative integers, you obtain e = 1/0! + 1/1! + 1/2! + 1/3! + … (here 0! = 1).

The derivative of the exponential function y = e^{x} is itself. No other exponential function y = a^{x }has that property when a ≠ e.

If you put $1 in the bank and compound interest continuously for one year, then at the end of the year you will have $e dollars in your account.

If we take the limit of the sequence (1+1/n)e^{n} as n tends to infinity, then we obtain e.

Ron Watkins computed 5 trillion digits of e in 2016. The 5 trillionth digit of e is 8.

The number e features in the famous Euler’s equation: e^{iπ} + 1 = 0. This equation is often touted as the most beautiful in all of mathematics. We also have the lovely Euler’s formula: e^{ix} = cos x + i sin x.

John Napier was the first to reference e in 1816, but its discovery is usually accredited to Jacob Bernoulli in 1683.

No one knows whether the number e^{e} is either transcendental. We can’t even prove its irrational.

Daniel Wedge wrote the catchy “e song” about Euler’s number in 2010. I can’t think of anything to top this so I’ll stop here.

[…] via Happy e day! — The Intrepid Mathematician […]

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