Mayan Culture
A Mathematical Trip Back in Time
250 A.D. – 900 A.D.
Who are the Mayan’s?
• The Mayan Culture is otherwise know as
Mesoamerican civilization.
• The are known for the only fully developed
written language of the pre-Columbian
Americas.
• The Maya remain to this day in contemporary
Mesoamerican societies, and maintain a
distinctive set of traditions and beliefs.
• The have almost exclusively adopted the Roman
Catholic religion.
Mesoamerica Civilization
• This civilization is know for its amazing art,
phenomenal architecture, fully developed
written language, astronomical systems,
and its sophisticated mathematical
knowledge.
• A typical Classic Period Mayan state was
a small hierarchical kingdom headed by a
hereditary ruler.
Where is the Mesoamerican
Civilization?
• The area of the Maya civilization extended
throughout the northern Central American
Region, including Guatemala, Belize,
Western Honduras, El Salvador, as well as
some southern Mexican states.
Mathematical Discoveries
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They created a calendar to measure time.
They used numbers to calculate finances.
They were exceptional astronomers.
They chronicled the lives of rulers.
They used tables to chart the movement of
planets
Mayan Calendar
• The Mayans used more than 17 different calendars.
• The Mayan people were very sophisticated in their
mathematics and time concepts. No other culture had
the same level of understanding.
• One calendar was made up of 260 days, this was called
the “sacred count calendar.” It was used throughout
Mesoamerica for centuries.
• Calendars were very important to the early Mayan’s.
Both gods and men were identified by the day they were
born.
20 Day Monthly Mayan Calendar
• There were 13 days in the week, and 20 days in the month
each with a different name that had a different meanings.
• Listed below are the names & their approximate meanings
Imix – Waterlily
Chuwen – Frog
Ik’ – Wind
Eb – Skull
Ak’bal – Night
Ben – Corn stalk
K’an – Corn
Ix – Jaguar
Chikchan – Snake
Men – Eagle
Kimi – Death head
Kib – shell
Manik’ – Hand
Kaban – Earth
Lamat – Venus
Etz’nab – Flint
Muluk – Water
Kawak – Storm Cloud
Ok – Dog
Ahaw - Lord
Month Names and Approximate Meanings
Each month also had a different name with a special
meaning associated to it. Listed below are those name
and meanings if known.
Pohp – Mat
Wo – Unknown
Sip – Unknown
Sotz’ – Bat
Sek – Unknown
Xul – Dog
Yaxk’in – New Sun
Mol – Water
Yax – Green
Zak – White
Keh – Red
Mak – Unknown
K’ank’in – Unknown
Muwan – Owl
Pax – Unknown
K’ayab - Turtle
Mathematics and Astronomy
• Mayans were able to compute the length of the
Earth’s revolution around the Sun to within a
thousandth of a decimal point of the current
modern calculations using modern technology.
• They kept calendars on the lunation and eclipse
cycles, equinox and solstices.
• They were able to do this using a numerical
system that counted by twenties and used only
three notational symbols.
Mayan Numerical System
• The Mayan number system is based on the number 20, not the
number 10 as in our own system. This means that they count by 20
instead of 10.
• They count from 0 to 19 before moving to the next order. Whereas,
in our number system we count from 0 to 9 then move to the 10’s
position.
• This base 20 system is called vegismal.
• Using this number system and having a value for zero, they were
able to have clear place values. Such as a dot for 20 could also
mean one without a placeholder to indicate that the dot goes in 20
position.
• The symbols they use for counting are bars, dots and a shell.
 The dot has a value of one.
 The bar has a value of five.
 The shell has a value of zero.
Zero
• The Mayan symbol for zero is considered
one of the greatest achievements of their
civilization.
• They depicted zero in the form of a shell
because it has great spiritual implications.
• Having a symbol which is equivalent to the
Arabic zero allowed the Mayans to
express any whole number using place
value notation.
Number System
Numbers written from 1 to 20
Numbers 20 and Larger
• Unlike our number system the Mayan
numbers are arranged vertically instead
of horizontally.
• The bottom row (1st row) is single units
(1-19)
• The next row (2nd row) is multiplied by
20.
• The 3rd row is 18*20
• The 4th row is 18*202
Larger Numbers
20*1=20
0= 0
= 20
20*1=20 20*2=40
1= 1
1= 1
= 21
=41
20*3=60 6*20=120
1= 1
2= 2
=61
=122
Why were their Mathematical
Discoveries Important?
• Their ability to write numbers enabled
them to add and subtract with ease.
• They were able to maintain financial
records.
• They maintained several calendars.
• They were exceptional astronomers.
• Without a number system these things
could not have occurred.
Bibliography
Berlinghoff, W. P. & Gouvea, F. Q. (2004). Math through the ages.
Publication Place: Oxton House Publishers and the Mathematical
Association of America.
The classic Maya (n.d.). Retrieved February 23, 2007, from
http://www.13moon.com/ABOUT%20THE%20MAYA.htm
Fought, S. (1997). The Mayan symbol for zero. Retrieved February 23,
2007 from Drexel University, The Math Forum Web site:
http://mathforum.org/k12/mayan.math/
Maya civilization. (2007) Retrieved February 26, 2007, from Wikpedia
Web site: http://en.wikipedia.org/wiki/Maya_civilization