# Ancient number systems in XeTeX

I am teaching a history of mathematics class this semester. We are beginning with a brief discussion of ancient number systems: Egyptian, Babylonian, Mayan, Chinese, Incan, GreekRoman, and Hindu-Arabic. As I was writing up the first homework assignment it occured to me that I should investigate whether these numbers could be typeset using LaTeX.

It quickly became apparent that, because fonts are involved, I would have to use XeTeX rather than LaTeX. It was a fun (although time consuming) exercise. In the end I was able to typeset Egyptian hieroglyphics, Babylonian cuneiform, and Chinese rod numerals. Because the syntax was often messy, I spent a while burying the complicated TeX in the headers so that the numbers would be easy to work with in the document.

For example, to generate the Egyptian hieroglyphics for 123 I write

\Ehun\Eten\Eten\Eone\Eone\Eone.

The fraction 1/123 is

\Efrac{\Ehun\Eten\Eten\Eone\Eone\Eone}.

To express 123 in cuneiform all I have to write is

\Bnum{123}.

To create a number board with the Chinese counting rods representing 123 I type

\Cnum{|x|x|x|}{\Cvone & \Chtwo & \Cvthree}.

If you would like to give this a try, download my .tex files:

I’d love to be able to do something similar with the Mayan numbers. I tried for a while, but couldn’t get them to work.

[Update: I figured out how to generate Mayan numerals. Here’s a Tex file with all four number systems—Egyptian, Babylonian, Chinese, and Mayan.]

Disclaimer: I know my way around TeX pretty well, but I’m not a power user. It took me quite a while to get all this to work. I’m not sure I can offer much trouble-shooting advice if you can’t get this to work on your computer.

1. fanofreds says:

That’s quite cool! We don’t offer a “History of Mathematics” type course at my college…but I’ll file this post away just in case we eventually do.

2. kaleb40 says:

I don’t have a reason to use this right now, but this is so cool. Thanks for sharing.

3. kaleb40 says:

This is great! Thanks for sharing.

4. cosas says:

Hi Professor Richeson, is it possible that you can share that History of Mathematics course with us?, maybe the reading list, the topics that you cover, some lectures notes, whatever.

1. A few people have asked me that. Unfortunately, for day-to-day operations everything is on Moodle (our CMS), and thus it requires a password. But I’ll see what I can do at the end of the semester. It would be nice to do something like you suggest.

5. Frédéric Grosshans says:

About Mayan numbers : your difficulty probably comes from the fact that they are not yet encoded in unicode. However, LaTeX packages exists to type Mayan http://www.math.univ-toulouse.fr/~orevkov/mayaps.html and Epi-Olmec http://obelix.ee.duth.gr/~apostolo/Epi-Olmec/ . Since both these writing systems use the same mesoamerican numbers, you can probably use any of the 2 packages for your purpose.

1. Thanks! I’ll be sure to look at those links.