Find Your Name In Pi

By Michael Hartley

This website has a page where you can search for your name in the digits of pi. Besides some general notes, I've also provided teacher's notes right here. If you're a teacher looking for ideas on how to use this "pi search engine" in a classroom setting, read on.

First though, the whole idea of finding words in pi depends on few mathematical concepts that many lower school kids will not be familiar with. Kids first meet pi in grade 4 or 5 or so, since it's related to areas or circumferences of circles. They may pick up that pi is a rather special number beyond just circles, but won't really know why. The reason pi is special is that it turns up all over mathematics, in many places that have nothing (apparenltly) to do with circles at all.

For example, if you add up \(1 + rac14 + rac19 + rac1{16} + \dots\) (all the multiplicative inverses of the square numbers), and multiply by 6, you get \(\pi^2\), the square of pi. Or, if you work out \(1 - rac13 + rac15 - rac17 + rac19 - \dots\), the sum very very very slowly - but surely - approaches \(rac\pi4\), a quarter of pi. The link between circles and these sums is not at all obvious.

Then, there are probablity problems whose solutions involve pi (eg, the chance that two random numbers have a common factor). There are a bazillion calculus problems where pi appears. It's useful in the formulae for a swinging pendulum and for Einstein's General Relativity. It's even related to the famous Mandelbrot Set fractal. Most of this is, sadly, beyond the level of lower school math students.

Second, when you search pi using this page, you are searching the base 27 digits of pi (the digits are treated as , A, B, C, ..., Z). Note every lower school child will know what this means, nor will it be easy to explain. After all, just teaching our normal everyday base 10 number system occupies a good chunk of kindy and grade 1 math. However, if you are able to get across to the pupil what base 27 means, it will be an important step towards helping them grasp that numbers are not the same things as the particular way we write them down. We write eighty-four as 84, but the number a concept behind the two digits '8' and '4' that is independent of it.

Enough caveats, you want ideas. So, here's a small collection of ideas for how you could use this web page in a classroom setting.

Consider asking students to find their names in pi, printing out the results, and pasting them all over the classroom. Keep in mind, though, that some students' names will not be found in my small collection of only 31 million digits.

Alternatively, see how many names of celebrities, or cities, or states, or teacher's names, or sports. See who can find the first sport in pi, or the celebrity whose name appears the most often.

All this could be in the context of trying to explain that pi's decimal places forms an endless stream of random-looking digits - the famous 22/7 is just a rough approximation, only slightly better than "3.14". Or, trying to explain what it means for numbers to be written in other bases or other number systems.

Or, you could get your kids to play with the pi search engine around about "pi day" - March 14, or 3/14. If you're in a country where people typically write 14 March as 14/3, well, the 31st of April (31/4) doesn't come around often enough to make it an interesting date for a day to celebrate pi. Just celebrate pi day on March 14, as more and more people are doing, and take it as an opportunity to explain about different ways people write the date in different countries. There are many suggestions on the web for ways to celebrate pi day - for example, eating pie, or other circle-shaped party foods. Now you can add "search for your name in pi" to the list.

This search engine works because the digits of pi, at least all the digits anyone has calculated and tested, appear to have no pattern. That means that almost every three- and four-letter name appears in the first 31 million base 27 digits. By contrast, there would not be much point me making a page for you to "search for your name in the digits of one quarter". On the other hand, mathematicians don't actually know for sure that this randomness continues forever. It's entirely possible, for example, that the word "MATHEMATICS" never actually appears in the base 27 digits of pi. If the digits of pi act just like random numbers, I'd need the equivalent of 8 million billion decimal digits to have a reasonable chance of finding "MATHEMATICS" in pi. And even if it didn't appear in the first 80 million billion digits, it still would't prove it was never going to appear - it might, for all we know, first appear in position 80 million billion and one. This is well beyond the record for the number of digits of pi ever computed, and even further beyond the storage capacity of my webserver!

Whether or not any name can eventually be found in pi is yet another pi-shaped mystery. We may never know the answer.