# How to memorize the value of e to 15 decimal places

I learned the following trick for memorizing the value of e from my colleague, Gene White. It never fails to impress calculus students (given a wide enough definition of “impress”).

Start by carefully looking at this picture:

That’s a 20 dollar bill, so memorize “2” and put down the decimal point.

The picture on the bill is of Andrew Jackson. He was our seventh President, so put a “7” after the decimal point to get 2.7.

Jackson was elected in 1828, so put down “1828” next. Since there’s a 2 in front of the decimal place, put “1828” a second time. We’re now up to 2.718281828.

Now look at the red square over Jackson’s face. The diagonal creates two congruent right triangles with angle measures 45, 90, and 45. So, add on 459045 to get 2.718281828459045. And that’s e to 15 places.

I’m open to suggestions on how to memorize more of the digits.

Filed under Calculus, Geekhood, Math, Teaching

### 13 responses to “How to memorize the value of e to 15 decimal places”

1. If it works for you, it works. But I had most of that part of E memorized already, while, after I finish this comment, I will likely continue to be ignorant of Jackson’s election year (and even Presidential sequence, sorry).

I once had over 100 digits of pi memorized (without practice, I’m now down to maybe 50 or so), and I wrote down how I memorized them. My technique seems more arbitrary (lots of it is based purely on patterns, as well as a mild dose of synesthesia), but I think it’s no less arbitrary than yours, really.

But, like I said, if it works, it works.

2. I’ve study some mnemonic systems, so I’m of more than one mind on this sort of thing. First, anything that works for one’s purposes is, of course, valid. I’m not sure your method would work well for a lot of folks, but motivation is certainly a big issue regardless. If you need the first 15 digits of e, this is surely one way that could work for some people.

Coincidentally, I KNOW that Jackson was the 7th president, because I used the president list to test the mnemonic system I learned from Harry Lorayne and Jerry Lucas’ book, THE MEMORY BOOK, and from Bruno H. Furst’s earlier STOP FORGETTING! system back around 1980 or so. That’s one ordered list that was small enough to be manageable but long enough to be challenging and semi-useful. Of course, I knew the number for some presidents already (e.g., Washington, Adams, Jefferson, Lincoln) and the ones from McKinley on I knew in order (but not necessarily by number). Similarly, most folks who need to know a few digits of pi or e already know them without much effort: just repetition suffices for a few places.

To do an extended memorization of an irrational number, however, you need more of a system. The method you propose isn’t too bad, but it requires memorizing things like Jackson being the 7th president who was elected in 1828 (something I could memorize with the system I use if I cared to, just as I used it to memorize some important dates surrounding the English Revolution and Restoration when teaching the method to some high school kids who needed those numbers for a test), and when to use that “2” to mean “repeat the last group of digits you added. That last thing seems particularly arbitrary, but repetition would eventually make it somewhat trivial, I suppose.

That raises the issue of refreshing memorized facts like this (things that are arbitrary and can’t be gotten by deduction, unlike, say, the fact that the ratio of the sides of a 30, 60, 90 triangle is 1: sqr(3) : 2, which can be gotten from the Pythagorean Theorem.). Without occasional refreshing/review, generally I find that there’s a certain amount of deterioration over time. I once knew all the chemical elements by atomic number (and vice versa), ironic in that I was a horrid chemistry student, though maybe knowing some mnemonics at the time would have helped a bit. But I don’t use chemistry at all, and I probably lost about 50% of what I memorized back in 1981 or so through disuse. That which we use more frequently is either learned by repetition or reinforced and solidified through use.

The method Lorayne/Lucas and Furst propose is flexible and would work well with the digits of pi or e, just as well-practiced mnemonists like Lorayne have used it very quickly and facilely to memorize pages of the phone book chosen at random. Not quite THAT slick myself, I’m afraid, but their methods are definitely easy to learn and master with a little practice.

I haven’t applied the methods to memorizing strings of completely arbitrary digits, but it’s really easy to do so. The best part is that as you do in the method you show, you can “chunk” digits any way you find convenient. We have loads of research that suggests our limit with short-term memory/immediate recall (which I’m not sure are quite the same thing) is 7 plus or minus two “bits” of info, where an arbitrary digit (no way to anticipate it logically) is one bit. Chunking reduces multiple bits to one, so that we might take the (not so arbitrary) sequence “149219185744995551212” and chunk it into 1492, 1918, 57, 4499, and 5551212, then note that these might be Columbus’ landing in the New World, the end of WW I, Heinz 57 varieties, the “purity of Ivory Soap” (99 and 44/100% pure!) and of course, the old number for long distance information sans specific area code). Then, we can imagine Columbus landing in “America,” encountering some WW I soldiers celebrating the end of the war with a ‘feast’ of Heinz beans, then using Ivory Soap to wash up so they can call information to get an important phone number of someone they want to share the good news with.

The system I’d use for pi or e is less dependent upon finding “happy coincidences” (or pre-selecting for them) in groups of arbitrary digits, however. It would take a while to explain it here, however, and I suspect the information is available on-line, and definitely can be found in the books I mentioned (probably elsewhere, too).

Of course, to return to the big question: why? ;^)

3. Geez everybody, I just meant this as a fun party trick. 🙂

4. Of course, it can be just that. Doesn’t mean it can’t be some other things, too.

5. Try learning the Peg system, it’s not that difficult. My MathCounts team can do pi to 100 the first week. Check it out: http://dvsd.schoolwires.net/1860201027145649457/Blog/browse.asp?A=398&BMDRN=2000&BCOB=0&C=56844

6. Not knowing much about MathCounts, I’m puzzled as to why knowing pi to 100 places would be a necessary thing for that competition. Or why anyone would in fact learn it other than as an exercise in memorizing.

• Michael, the main reason people memorize pi to a million places, or what-have-you, is to solidify their geek street cred. Plain and simple. See also: http://www.youtube.com/watch?v=N9qYF9DZPdw

• That link dosn’t work where I live, sadly.

“This video contains content from Vevo, who has blocked it in your country on copyright grounds.”

😦

7. It’s not necessary for the competition. But other things are, like knowing the primes less that 100, the root and square of some common numbers and such.

8. Neat trick.

So basically it boils down to 2.7 – 1828 – 1828 – 45 – 90 -45.

9. bob

I remember hearing “Jackson, Jackson wore a pair of 45’s” can’t remember where I heard it tho’.

http://www.bautforum.com/archive/index.php/t-102307.html

10. raj

Simply amazing…