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Mayan Mathematics and Numbers - Symbols of Their Culture

Cynthia is a writer, artist, and teacher. She loves studying language, arts, and culture, and sharing that knowledge.

Mayan Math Is Not That Hard

My fascination with the ancient Mayan culture has finally led me to a math lesson. While I readily admit that math wasn’t my favorite subject in school, I definitely can appreciate the Mayan approach to math. They were quite advanced for their time.

This article explores the more simple aspect of Mayan math: how they wrote their numbers and how their numbers related to their concept of time.

Where the Mayans Lived - Present Day Central America, Including the Yucatan Peninsula

The Concept of Zero

By the end of the third century, the Mayans had already figured how to use the number zero. They used a shell to represent it. They figured that though it didn’t presently have “matter,” it could actually have matter at some future point in time.

Interestingly, the Mayans had the number zero figured out ahead of many other civilizations.

Hmm, so the Mayans used numbers that had "ones" and "twenties" places?  I drew this little guy to "contemplate" Mayan numbers.

Hmm, so the Mayans used numbers that had "ones" and "twenties" places? I drew this little guy to "contemplate" Mayan numbers.

The Mayan Numeral System Was Directly Tied to Their Calendar and to the Concept of Time

The Mayan calendar told them when to plant crops, marked the changing seasons, and even when to celebrate their religious rites.

Because of the Mayans’ ability to use the number zero and write just about any number they could imagine, they could use their calendar to predict events thousands of years into the future.

The calendar was made of two wheels. They meshed together to make a 365-day year.

The year looked different than our present method of keeping track of days, months and years. Their calendar was 18 months long, with each month containing 20 days each. The Mayans considered the 5 days at the end of the year to be bad luck.

The Mayan notion of a day was that each day had a certain amount of “contents.” At the end of the day, when empty, another day would arrive, ready with its own contents.

The Mayan concept of time wasn’t linear, either. To them, it was cyclical. Because of their use of the wheel, they expected events to repeat themselves in the future.

For a particular day to repeat itself, though, 52 years had to pass. The Calendar Wheel was a cycle of 52 years. It is noteworthy, though, that for the Mayans, time neither had a beginning nor an end.

The Mayan Math System Used a Base 20 Approach

Remember how the Mayan calendar had 20 days in each month? That’s a reflection of their way of doing numbers.

In the United States and in many other industrialized societies, the decimal system is the mathematical approach of these cultures. The root deci means “ten.” It is a system that uses base 10.

The Mayans, however, used a base 20 form of mathematics.

Their mathematical symbols comprised of three characters: a shell, dots and bars.

The shell = 0.

The dot = 1.

The bar = 5.

Thus, the numbers 1-19 were made of the shell, dots and numbers. (See photo.)

The number 36 could be written as a power of 20: 1 x 20 = 20 and 20 + 16 = 36. If you compare that to the decimal system, it looks different: 3 x 10 = 30 and 30 + 6 = 36.

Here’s where it gets a little more complicated. Since the Mayan system was base 20, things changed after number 19: they moved to the next place value.

Another interesting point is that the Mayans wrote their place values vertically. The smallest number went on the bottom, and progressively higher numbers went on top, based on powers of 20. (see table)

The 1s place was at the bottom, then the 20s (20 x 1) place above that, then the 400s place (20 x 20), followed by the 8000s (20 x 20 x 20), then the 160,000 (20 x 20 x 20 x 20), and so on.

Thus, if you wanted to write the number 35 (see examples in red below), you would use all 19 numbers in the ones place, and a "twenty" in the 20s place.

Mayan numbers 1-19.  They would "start" over again in the next place value.

Mayan numbers 1-19. They would "start" over again in the next place value.

Mayan Numbers 85, 37 and 92 Written Out

Some Mayan numbers written out.

Some Mayan numbers written out.

The Number 18,425 in Mayan Numbers

The Mayans had an interesting way of writing all their numbers - all with just three characters. Their mathematical system was as complex as ours today. (Note: the number in the third row should be a dot with a bar under it to stand for 2,400, but

Power of 20Total PowerIn WordsMayan NumberActual Number

20 x 20 x 20 x 20

160,000

-

-

-

20 x 20 x 20

8,000

2 eight thousands

••

16,000

20 x 20

400

6 four hundreds

_•

2.400

20 x 1

20

1 twenty

20

1 x 0

1

5 ones

-----

5

 

 

 

 

18,425

© 2012 Cynthia Calhoun

Comments

Cynthia Calhoun (author) from Western NC on August 18, 2012:

Austinstar - I'm always learning new things about them. They are indeed unique. They were incredibly inventive. I find it fascinating that so much of what they came up with was because of their study of the stars. Thanks so much for coming by!

Lela from Somewhere near the heart of Texas on August 18, 2012:

Most math is way over my head, but since the Mayans built their systems by studying astronomy, I occasionally get a glimpse into their math. The more you study their rich culture and building construction, the more fascinating the Mayans become.

They are a very unique group!

Cynthia Calhoun (author) from Western NC on August 18, 2012:

Mary - hehe, thank you so much! I did do a lot of research, but it was so FUN! :D Thanks for the mention about my other HOTD...I'm always a little slack about getting those right up on my profile. LOL Hubhugs!

Jools99 - awesome! The Mayans are one of my favorite ancient civilizations to study. :) Thank you so much for stopping by!!

Einy51 - They really did have a great system. It's amazing that they were able to develop it on their own. :)

Stephanie - It's fun, isn't it? I had a lot of fun when I was trying to teach myself this base 20 system. LOL. Thank you so much for stopping by. :)

Stephanie Henkel from USA on August 17, 2012:

I loved the Mayan math lesson! Having used the system of tens all my life, it was easy to believe this was the only math system. Thanks for a fresh look at very ancient mathematics. Your presentation was so simple and logical that it was easy to grasp the basic concepts. Fun read, voted up, useful and interesting!

Einy51 from Gampaha,Srilanka on August 17, 2012:

Agreed! I think they had very developed mathematics knowledge than us.

Jools Hogg from North-East UK on August 17, 2012:

Cyndi - What a well researched and interesting hub. I knew nothing at all about the Mayans so this has been a brand new learning experience for me (my favourite kind :o)

Mary Hyatt from Florida on August 17, 2012:

My goodness, girl! You might just have another HOTD with this one. You really did a lot of research on this, and it was worth it. I love your drawings, too.

I voted it up, etc. and will share.

I just noticed on your profile, you don't mention your HOTD about the OWL. Mary

Cynthia Calhoun (author) from Western NC on August 17, 2012:

Kelley - Before writing this, I knew vaguely about Mayan math, but I really loved researching this. Thanks for coming by.

Jainismus - The theory goes that many NA groups may have crossed the Bering Land Bridge thousands of years ago on migratory routes and then dispersed throughout the Americas. There is suggestive evidence of this being the case, both by anthropologists and geneticists. :)

Mahaveer Sanglikar from Pune, India on August 17, 2012:

Interesting hub. My question is, though unrelated with Mayan mathematics but related to Mayans is: Were Mayans a part of the people migrated from eastern end of Russia to Alaska and then to Canada, US and further south? Or they were original inhabitants of America?

kelleyward on August 17, 2012:

What a great topic for a hub. I admit I didn't know much about Mayan Mathematics until I read your fascinating hub. Voted up, useful, interesting, and shared! Take care, Kelley

Cynthia Calhoun (author) from Western NC on June 29, 2012:

Joanveronica - wow! I LOVE getting compliments from teachers, and a math teacher on a math hub. YES! That means I get an "A" right? Hehehe. Just kidding. I teach Spanish, so I can understand. Thank you so much for your awesome feedback and comments. I hope you also have a wonderful day. Cheers!

Joan Veronica Robertson from Concepcion, Chile on June 29, 2012:

Very interesting Hub. Thank you for sharing this information. As a Math teacher I of course had worked with different number bases, but had not connected it to the Mayas. Voted up, awesome and interesting! Have a good day and be happy!

Cynthia Calhoun (author) from Western NC on May 03, 2012:

Mayra - thanks for stopping by. :) Just click the "share" button and you'll see the "link to this page" option. You can also use the contact button underneath my picture if you need to ask me any more questions. I hope your project goes well.

mayra on May 03, 2012:

I'm trying to cite this page. Can i have your name and the year you wrote it?

Cynthia Calhoun (author) from Western NC on April 24, 2012:

Obvious - well, if it weren't for math, you wouldn't have a computer to type on. Sorry, but it's here to stay. Even the ancients got that.

Cynthia Calhoun (author) from Western NC on April 24, 2012:

AAMR - thanks for stopping by and commenting. I'm glad you found this interesting. :)

Obvious Troll is Obvious on April 24, 2012:

Lame, who cares about old math? Math is stupid NOW, it was lamer a long time ago too.

Anyonymous Ancient Mayan Researcher on April 24, 2012:

Interesting. I had not know that the Mayans had perfected Zero first.

Cynthia Calhoun (author) from Western NC on April 15, 2012:

clevercat - great to see you!! Thanks for stopping by and sharing your insights. :) Thank you so much for the kudos. (HUGS)

Rachel Vega from Massachusetts on April 15, 2012:

Love it! Fascinating and well-written. What a cool research idea. Voted up and beautiful.

Cynthia Calhoun (author) from Western NC on April 12, 2012:

aviannovice - thanks for stopping by again as always. :) I look forward to your insightful comments. :) (HUGS)

Cynthia Calhoun (author) from Western NC on April 12, 2012:

randomcreative - thanks for stopping by. Can I just tell you that I love your user name. I *so* wish I had been more creative with mine. :) (HUGS)

Cynthia Calhoun (author) from Western NC on April 12, 2012:

Austinstar - yes, I wanted to emphasize that because there's so much emphasis on it this year. lol Thanks for stopping by. I am going to have to take you up on that "collaborating" idea. :)

Cynthia Calhoun (author) from Western NC on April 12, 2012:

Haha, too funny, Eric. Wow, thinking of a hexidecimal system makes my brain hurt. Base 6? Eeek. Fantasy novel? Now that will be AWESOME to read!! :)

Deb Hirt from Stillwater, OK on April 12, 2012:

Great job, CC. I didn't know about the math in this depth that the Mayans were responsible for.

Rose Clearfield from Milwaukee, Wisconsin on April 12, 2012:

This is a great resource, Cyndi! Thanks!

Lela from Somewhere near the heart of Texas on April 12, 2012:

I love that you mentioned that the Mayan calendar has no beginning and no end. This is correct. Calendars are just a man made measure of what we call 'time'.

Eric Newland from Dayton, Ohio on April 12, 2012:

Interesting read. I know a bit about non-base-ten systems (e.g. hexidecimal), but it's fascinating how they wrote their numbers out.

Also didn't know their calendar worked that way. I'm working on a fantasy novel in which the fictional world uses twelve 30-day months with a "year-end" period for the extra days. All this time I thought I was being original!

Cynthia Calhoun (author) from Western NC on April 12, 2012:

So, true, alocsin. The ancient Maya used this system, for sure. So much of it was destroyed after the Conquest, but Mayan, Aztec, Olmec, Toltec and so many others have living descendants today. I know many uphold the traditions of their ancient ancestors, as well. Thank you for pointing that out. :) Thank you also for your comments, feedback and insights as always. (HUGS)

Aurelio Locsin from Orange County, CA on April 12, 2012:

I'm not a big math buff either but tying the subject to this civilization makes it interesting. They obviously used all their fingers and toes to come up with the base 20 system while Western civilization just based it on the fingers. One thing I'd like to point out is that the Maya are very much alive and well and still living in the Yucatan peninsula. In fact, one of my friends was of Mayan ancestry, though he was born in this country. When he returned from his first trip to the Yucatan, he remarked that all the locals there and in the ancient wall paintings looked like him! Your hub is, of course, referring to the ancient Maya, who are ancestors of the modern ones. Voting this Up and Interesting.

Cynthia Calhoun (author) from Western NC on April 12, 2012:

Vellur - it's always great to see you. Thank you for your kind words and feedback. It was interesting to research this - an entirely different way of doing things, yet still remarkably the same. I appreciate your votes and time. :)

Cynthia Calhoun (author) from Western NC on April 12, 2012:

teaches - great to see you! I always look forward to your wonderful, insightful comments. :) This was fun to research - I definitely learned a lot, too. (HUGS)

Cynthia Calhoun (author) from Western NC on April 12, 2012:

scottgruber - When I started researching this, it took me a little while to wrap my head around the base 20 stuff. In a number of ways, already, I have found this to be EASIER than the base 10 system, if you can believe that. Those bars make it easy, because they simplify things. Anyway, thanks for stopping by! Cheers!

Nithya Venkat from Dubai on April 11, 2012:

Interesting and informative. A view into the Mayan way of calculations presented very well. Great hub, voted up.

Dianna Mendez on April 11, 2012:

This was fascinating and very educational. They really were an advanced civilization in many areas. Great coverage of this concept.

scottcgruber from USA on April 11, 2012:

Interesting stuff! I had no idea they used a base 20 system. Thank you for a great hub!

Cynthia Calhoun (author) from Western NC on April 11, 2012:

HubHugs to you, K9! :) I just love it when I get feedback that tells me you have learned a lot. Yes!! Thank you so much for your comments and insights. (HUGS)

India Arnold from Northern, California on April 11, 2012:

Incredibly informative hub! I learned a ton about Mayan Math. You made it very simple to grasp, and the images you provide are fantastic. Nice article! A very fun read.

HubHugs~