A portrait of Leonhard Euler, who named the mathematical constant e, painted by Jakob Emanuel Handmann.
Tomorrow, February 7, is e Day! This year is the best year to celebrate the base of the natural logarithm because, like Pi Day 2015, the year lines up along with the month and day. Hurrah! People who prefer the day/month/year date convention can save these suggestions for July 2 or wait until January 27, 2082 and get one extra digit. (That seems like a long wait for one extra digit, but you do you.)
I wrote about the excellent number e for Slate and included some possible ways to observe e Day. In addition to putting some money in a checking account to take advantage of compound interest, I humbly suggest using a constant so tied up with change and growth to do some personal growth. Think of e Day as a second chance at my favorite holiday, New Year’s Day.
I have some other suggested e Day reads for you from around the math internet. In 2010, Math Goes Pop suggested January 27 for a yearly e Day observance that privileges the day/month convention countries the way Pi Day privileges month/day users. Wired and Mathnasium have shared e Day suggestions in the past. (For those keeping score, they posted those articles in February.)
Ben Orlin’s ABC book of e does not disappoint, with ebundant elliteration and a reminder that Euler was the wearer of one of the greatest hats in the history of mathematics.
For more on the number e itself, the MacTutor math history website has a nice overview of the history of the constant from its plucky days as the unrecognized base of the natural logarithm to the proof that it is not algebraic. John D. Cook has been making pretty pictures with sums involving complex exponential functions. You can find the exponential sum of the day here. He’s also written about why the natural logarithm is the most natural and how to live with exponential growth. (Hint: it might start slower than you think.)
An equation called Euler’s identity, eπi+1=0, has been called the “most beautiful equation.” I’m on the record as feeling kind of meh about Euler’s identity, and I’m not the only one. For one, just write eπi=-1 instead of obscuring it with a weird need to have a 0 in your formula. You can put a 0 into any formula you want! Beyond that, I love Euler’s formula eiθ=cosθ + i sinθ. Plugging in the number π for the angle θ doesn’t do much for me. But I must say I love 3Blue1Brown’s explanation of the identity in this video. (He has since expanded on the ideas in another video.)
Update, February 7: Imaginary.org has a page where you can find your birthday in e. Anthony Bonato wrote about e Day for his blog as well, describing e as the “Jan Brady of transcendental numbers.”
How will you celebrate e Day? Growth and reflection are well and good, and I’m all for busting out a little complex analysis, but after that, I’m going out for Ethiopian food.