Math of the Mayans

The Mayans created a relatively complex numerical system for their time.  This numerical system was heavily intertwined with their astronomy, religion, and day to day transactions.  It was a base 20 system (vigesimal) that has been conjectured to have been created based upon counting toes and fingers.  Another possible explanation is that the number 20 was representative of life or humans and 400 was representative of the year (when dealing with calendars their number normally representing 400 did not mean 400 but it meant 360).  As shown below, the Mayan glyph for "being" (top) is of similar structure to the Mayan glyph for "twenty": 



The Mayans were one of the first civilizations to use the number zero.  They utilized it as a placeholder in their number system to help with their calendar.  They had symbols representing zero, one, and five that could be used in association with their base system to represent any number they needed to:


Some examples of numbers one through twenty:


As shown above, 20 is represented by a single dot above zero.  To get multiples of 20, 400, 8000..., the Mayans would separate their numbers vertically with the place for the highest number (20 in the case above) being at the top.  Each level up would then represent a higher power of 20.  Larger numbers would appear as follows (without the dotted lines):

 So, 2,072 would be represented by a bar above 3 dots above 2 dots closely above 2 bars.  When completing more complicated calculations, for astronomical purposes for example, numbers could look like the following (again without the dotted lines):


The Mayans were able to quickly and easily represent numbers in the millions and beyond with not many more "digits" than we use today.  Their advanced system of numbers, along with their astronomical prowess allowed them to calculate the exact length of a year to within three decimals as well as the lunar month to within 3 decimals.

Mayan math most likely lacked a direct method of multiplication for their numbers and more certainly for division (they did not have fractions).  Despite this and the fact that the math of the Mayans was isolated from the math of Europe, they still were able to do some remarkable things.




Sources:

Glyphs created with:
http://www.paleoaliens.com/event/mayan_glyphs/
Info gathered from:
http://www-history.mcs.st-and.ac.uk/HistTopics/Mayan_mathematics.html (I used a cached version of the webpage because the original wasn't working)
http://www.hanksville.org/yucatan/mayamath.html
http://www.storyofmathematics.com/mayan.html      

Comments

  1. UnknownSeptember 19, 2017 at 6:08 AM

    Hi Josh, I found your blog post to be extremely interesting! I find it so crazy that the Mayan people could keep all of that notation and all of the symbols straight. The Mayans also amaze me with how close they could calculate the length of a year and lunar month. It seems to me that the Mayans had math, along with many other things, down. I wonder how the Mayans taught their children the number system it would be interesting to compare to how we teach ours.

    -Dayna Ball

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  2. John GoldenOctober 1, 2017 at 3:46 PM

    Very cool, and the images help sell it. They also seem to have had some neat geometry, which makes me wish we had their Euclid, if they had one. If not, what conditions were missing?

    C's 5/5

    Small point: you can make your links actual links!

    ReplyDelete
    Replies
    1. John GoldenOctober 1, 2017 at 3:47 PM

      Forgot the boilerplate:
      These posts are evaluated by:
      Clear- if this shows up as an issue, it’s usually about spelling, grammar or structure.
      Coherent- has a point and an objective
      Complete- looks like 2 hours of work, attends to necessary bits for the point. Sharing your thinking, always a good idea. Cite images or websites you used or referenced.
      Content- math and teaching ideas are accurate. (Does not mean no math mistakes. Mistakes are how we get better!)
      Consolidated- writing has an end. Synthesize the ideas, pose remaining questions, etc. Sometimes I recommend one or more of: 1) What did I say/do?, 2) Why is it important?, 3) What comes next?

      On first writing these are just for feedback. At the end of the semester you pick 3 posts for exemplars. Those can be revised from feedback or just ones you write taking into account the feedback now.

      Delete

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