By: San CristÓbal de Las Casas,
I live in Chiapas, Mexico, where I work as a math tutor. As part of that work, I have prepared a booklet on how to do calculations with Mayan numbers, including the square-root procedure that children learn in school. The booklet includes addition and subtraction tables for Mayan numbers.
Why Did I Write This?
Two years ago, my wife took a course in Tzotzil (a Mayan dialect) in San Cristóbal's Universidad Maya. One day she told me that when the professor was teaching them about Mayan numbers, the students had asked him, "What are they good for? For example, can you add and subtract with them?"
I've done a lot of volunteer tutoring in math, and I've found that students do better when they understand the properties of numbers—for example, the commutative, the distributive, and the associative. For some students, a light comes on when I then proceed to show that our procedures for adding, subtracting, multiplying, and dividing are nothing more than convenient ways to take advantage of those properties.
Perhaps these experiences explain why the Tzotzil students' question made me think, "Our procedures for adding, etc., should work with Mayan numbers, too. After all, Mayan numbers have a place-value system and a symbol for zero just like our Hindu-Arabic numbers. The fact that Mayan numbers are base 20 rather than base 10 shouldn't make any difference." So I tried a few calculations with Mayan numerals, and it turned out that the same procedures did indeed work.
I went on to make this collection of calculations for my wife's professor and classmates. Included are an addition, a subtraction, two multiplications, a division, and—as something really different-a square root. I hope this will be sufficient; if you want to see how to do cube roots or logarithms with Mayan numerals, you'll have to look elsewhere! (Or do them yourself, using the ideas presented here).
How to Calculate with Mayan Numbers
Mayan numbers aren't just a curiosity—they're a completely practical tool for doing calculations. Just like Hindu-Arabic (HA) numbers, Mayan numbers have a place-value system, a consistent base (20 instead of 10), and a placeholder symbol, analogous to our zero, to show when a place is empty.
Thanks to these features of the Mayan number system, we can add, subtract, multiply, divide, and even find square roots using the same techniques that work with HA numerals. (For example, borrowing and carrying digits). Of course, it's necessary to carry out these operations according to Mayan addition and multiplication tables.
We'll begin by presenting the Mayan digits and an example of how to write a multiple-digit numeral. Then, we'll see how to do the above-mentioned calculations.
Mayan Digits, and How to Write Multiple-Digit Numbers
Here are the Mayan digits. Unlike HA (Hindu-Arabic) digits, the bigger the number represented, the more space the digit occupies (except in the case of zero).
- Download the free Maya Mathematics: 15-page booklet in English [pdf format]
- Download the free Maya Mathematics: 15-page booklet in Spanish [pdf format]
- Download the free Apéndice B Algebra Notes in Spanish
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- Mayan Numbers - Possible glyphs for numbers used by the Mayan civilization
- The Symbolism of the Mayan Numbers
- Mayan Math Lesson Plan
- The Mayan Calendar
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- Popol Vuh: The Definitive Edition Of The Mayan Book Of The Dawn Of Life And The Glories Of by Dennis Tedlock
- An Illustrated Dictionary of the Gods and Symbols of Ancient Mexico and the Maya by Mary Miller and Karl Taube
- Secrets of Mayan Science/Religion by Hunbatz Men