By Michael Hartley
On this website is a page where you can find your name in pi. This page explains how that works. If you're a teacher, you might want to read the teacher's notes too.
How can my name be in pi?
I converted pi to base 27 (if you don't know what that means, read the section What does base 27 mean below). I took the digits to represent letters, according to 1=A, 2=B, and so on. The digit 0 is punctuation.
In this way, the expansion of pi looks like a long string of letters (with occasional punctuation), namely \[\pi=C.CVEZ\dots=C+\frac{C}{27}+\frac{V}{27^2}+\frac{E}{27^3}+\frac{Z}{27^4}+\dots\] where A=1, B=2, C=3,..., Z=26.
How many digits of pi do you have?
I started with over 1,000,000 digits in base 27. This represents the same accuracy as 1,500,000 decimal digits. If that sounds like a lot, it still only gave an 82% chance of finding a given 4 letter name! If your name has 5 letters, the chances were only about 7.2%!
Now I have over 30 million digits in base 27 (thirty-one million, four hundred and fifteen thousand, nine hundred and twenty nine, to be precise), so a five letter name has an almost 90% chance of being found! Perhaps I'll push it up even further one day.
Why did you choose base 27 and not 26?
Base 27 is the neatest way which allows me to represent the digit 1 as A, 2 as B, ..., and 26 as Z. With Base 26, I would have to use A=0, B=1, etc... or A=1, B=2, ..., Y=25, Z=0. I think my system is the prettiest. If you don't like it, you can always set up your own search page...
How did you get the digits?
When I first made this page, in about 1998, I downloaded a program from a website. The website was in Japanese, so I don't know much about it. The program used a very efficient algorithm to calculate decimal digits of pi. I changed the program a little bit so that it would calculate in base 27. It took 3 days to calculate the 1,048,400 digits. To calculate the 16,000,000 I hoped to obtain on the computer I had back then would have taken over 2 months!
In July 2005 I raised the number of digits to 31,415,929, using a program called APFLOAT (and a much better computer). I started it running at 4pm, and by a bit past 9pm it was done!
In August 2012 I moved the web page over to this site, Dr Mike's Math Games for Kids. This makes "Your Name In Pi" the oldest game on this site, pre-dating the site by 7 years or so!
Why did you do it?
Do I need a reason?? :-)
Interesting pi facts
Here are some interesting features of this way to represent pi.
- The first animal: The first animal is the EMU, at the 26th place. Proud to be Australian.
- The first country: The African country MALI, population about 12 million, is the first country, coming in at position 30098. Thanks to Mark Nicholas for pointing this out! When I tried to find the first country, I didn't check them all, and I missed this one. I don;t know if Mark Nicholas was completely thorough, so if you find a closer one, please let me know... Abbreviations like UK don't count!
- The first name: At the 40th place, the first name in pi is MOBY. Ok, I didn't say it had to be a human name, did I?
- The first number: E appears in the third place after the decimal. If you insist on whole numbers, the first is SIX, at the 4259th position. Unless you count NIL, which comes in at 2335.
- The first ordinal: The first - it had to be, really - is FIRST, appearing at the 266386th place of pi
- The first book of the Bible: Coming in at the 1383rd position is LUKE, beating JOB by miles...
- The first planet: The first planet is the fourth - MARS appears at the 556697th place of pi. Hopefully this is not the number of days we will wait before we land there!
- The first chemical element: TIN is first (at the 61059th place). Well, what did you expect? PRASEODYMIUM or something?
- JEDI comes in at position 1126698, but SITH have their revenge, pipping them by 322005 places.
- The first of the Fellowship of the Ring is, of course SAM, at position 11352. Unless you insist he use his full name "Samwise". Then MERRY becomes Meriadoc, and the Chosen One is FRODO, at position 16957553 (beating GIMLI by just under 2 million places).
- And the most amazing of all: The first English word in pi is... wait for it... PI, coming in at position 18. Now isn't that something?
What does "base 27" mean?
Most people know that pi, the ratio of a the distance around a circle to the distance across, is 3.14159... This actually means that \[\pi=3+\frac{1}{10}+\frac{4}{10^2}+\frac{1}{10^3}+\frac{5}{10^4}+\frac{9}{10^5}+\dots\]
Because the number "10" keeps appearing in the denominator, we say this is pi in "base 10". It is also why we have 10 different digits.
There is no reason why we have to use 10. The ancient Babylonians used 60 different digits! Even today, computer scientists sometimes use base 16 (with 16 digits 0 to 9 and A to F), base 8 (with digits 0 to 7) or even base 2 (with only two digits 0 and 1!).
If we were using base 16, we would say pi was 3.243F6..., meaning \[\pi=3+\frac{2}{16}+\frac{4}{16^2}+\frac{3}{16^3}+\frac{F}{16^4}+\frac{6}{16^5}+\dots\]
Here, the "F" represents the "digit" 15. In base 16, there are 16 digits, usually represented as 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F.
I wanted people to be able to look for their name in pi. The alphabet has 26 letters, and it would be nice if A was 1, B was 2, C was 3 and so on. But there has to be a zero digit! So I decided to work out pi in "base 27", with the 27 digits 0,A,B,C,...,Y and Z.
That's how your name can be in pi!