I preface this by saying zero original research went into this other than my interest in the subject and the God-given ability to Google stuff.
You probably already know that we use a base-10 number system to count stuff – 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. But there are other number bases – some of which you already know about, even if you didn’t realize it.
The language of computers, binary, is nothing more than a base-2 system, where every digit can be represented by zeroes and ones. Thus, when converting from base-2 to base-10, you’d count 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010…and so on. Here is what these base-2 numbers equate to:
0 = 0
1 = 1
10 = 3
11 = 4
100 = 5
101 = 6
110 = 7
and so on, so that (for example):
111001 = 57
(Links are at the bottom of the page if you want to explore this, as well as the other things discussed below)
But there are other bases – an infinite number of bases, actually. The Babylonians used a base-60(!) number system, and Mayans used a base-20 system. Hexadecimal (base-16) systems are relatively common, used in everything from computer programming (as a way to condense binary) to our everyday usage of pounds and ounces.
In fact, you use an octovigesimal system every day. Better known as base-28, this is what our current Gregorian calendar is (loosely) based upon.
So, what if I wanted to see if my name is represented in the digits of π? How would this even be possible? What would be the best way to convert the base-10 digits of π to letters?
Well, we’d want to use base-27 for this. Base-27 is represented thus:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O and P
To convert this to alpha, we’d assign 1=A, 2=B, 3=C and so on, letting zero represent a space, i.e. 0=””.
Doing this let’s us then convert π in base-27 from 3.3MQ53… to C.CVEZC. And we’re off and running!
(“Why not use base-26?” I hear you thinking. Well, we want to be able to represent each letter of the alphabet with a letter so that A=1, B=2, etc., and we need a 27th place to capture our zero value, so base-27 it is!)
There is a conversion tool online (also linked below) that allows you to enter your name (or any word, really) to see if it is represented in this converted base-27 π. My name, STEVE, appears starting with the 8,857,158th digit of π:
Some fun facts about the occurrence of words in (this version of) π-27:
The first spelled-out number appears at the 4,259th position: SIX
The first ordinal number appears at the 222,386th position, and of course it’s FIRST
JEDI appears at position 1,126,698, but the SITH overpowers them at the earlier position of 804,693.
Within the first 30,000,000 digits of our converted π-27, the word MATHEMATICS does not appear. Hopefully it will show up in the second group of thirty million characters…
And where does PI appear? Not surprisingly (given that it’s only two letters long), it pops up for the first time starting at position 18.
So, click on the link below (or right here if you’re impatient) and see where your name first appears!
One caveat, though – this database only includes the first ~30 million converted digits of π, and your chances of finding your name decreases substantially as the length of your name grows longer. If your name is three (or fewer) letters long, you have virtually a 100% chance of finding it. Five letter names (like mine) carry a 56% chance of success, but seven letter names have virtually zero chance of being represented.
Good luck, and let me know in the comments if you’ve found your name in the first thirty million digits of π!
Here are the links I promised:
Check π for your name here: http://www.dr-mikes-math-games-for-kids.com/your-name-in-pi.html
How π in base-27 works: https://www.atractor.pt/mat/fromPI/pib27-_en.html
How counting in different bases works: http://mae.engr.ucdavis.edu/dsouza/Classes/ECS15-W13/counting.pdf
Math.com’s π facts page: http://www.math.com/tables/constants/pi.htm
More stuff about π-27: http://www.dr-mikes-math-games-for-kids.com/your-name-in-pi-notes.html