# Calculating e by Hand

**It’s become a bit of a tradition amongst math personalities on the internet to, on pi day (March 14th), go to ridiculous lengths to calculate pi by hand. Sometimes this means measuring the period of a pi-endulem, sometimes weighing a cardboard cutout of a circle. I’ve even see people do cartwheels. The rules are simple: calculate pi. No calculators allowed. Bonus points for originality and ridiculousness.**

**This is of course a riot of fun, and I always participate, but I can’t help but feel there’s another mathematical constant left out.**

**e, defined below, is a heavyweight math constant. Second only to pi, it is one of the most well-know and widely-used (amongst math people anyway).**

**Unfortunately, the world does not celebrate an e-day, so we don’t see too many people calculate e by hand. Let’s change that.**

**The standard ways to approximate e typically involve limits and/or infinite sums:**

**Unfortunately, preforming this is incredibly tedious and boring, so I put this project on the backburner.**

**One day, while surfing the /r/math subreddit, I discovered this interesting fact:**

**Pick a random number between 0 and 1. Repeat until the sum of the numbers picked is >1. On Average, this will take e picks.**

**This is perfect.**

**Of course, I could use a computer to generate the random numbers for me. However, that feels a little too close to using a calculator. I’m going to need dice.**

**The original plan was to get ahold of a d20 (a 20 sided die) then tally up the number of rolls it would take to get at least 21.**

**After explaining the situation to the man behind the counter at my local comic book store, he recommended something called “percentile dice.” Basically, it’s one d10 numbered 0-9, and another d10 numbered 00-90 (with increments of 10).**

**These dice are far better, because they gives a more even spread.**

**Now all that’s left is to sit down for ~2 hours and continually roll and add and roll and add.**

**Here are the results:**

**I decided at the beginning to stop once the 2 column reached the bottom of the page. This way, I can’t subconsciously bias the results (like stop after a run of 3s).**

**Now we calculate!**^{1}

**e ≈ 2.687**

**Only ~1% error too!**

^{1}This was the first time I’ve done long division in a long while

I initially gave the answer as 2.687!^{2}. The 2 was referencing a footnote, and the exclamation point was because math is exciting. Some people (intentionally) misunderstood this to mean 2.687 factorial (non-natural number factorials are a thing apparnetly), squared. This has now been fixed.

pedants.