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 The Mayan Culture is otherwise know as

Mesoamerican civilization.Mesoamerican civilization.• The are known for the only fully developed The are known for the only fully developed

written language of the pre-Columbian written language of the pre-Columbian Americas.Americas.

• The Maya remain to this day in contemporary The Maya remain to this day in contemporary Mesoamerican societies, and maintain a Mesoamerican societies, and maintain a distinctive set of traditions and beliefs.distinctive set of traditions and beliefs.

• The have almost exclusively adopted the Roman The have almost exclusively adopted the Roman Catholic religion.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

• 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 Calendar20 Day Monthly Mayan Calendar

• There were 13 days in the week, and 20 days in the month There were 13 days in the week, and 20 days in the month each with a different name that had a different meanings. each with a different name that had a different meanings.

• Listed below are the names & their approximate meaningsListed below are the names & their approximate meaningsImix – WaterlilyImix – Waterlily Chuwen – FrogChuwen – FrogIk’ – WindIk’ – Wind Eb – SkullEb – SkullAk’bal – NightAk’bal – Night Ben – Corn stalkBen – Corn stalkK’an – CornK’an – Corn Ix – JaguarIx – JaguarChikchan – SnakeChikchan – Snake Men – EagleMen – EagleKimi – Death headKimi – Death head Kib – shellKib – shellManik’ – HandManik’ – Hand Kaban – EarthKaban – EarthLamat – VenusLamat – Venus Etz’nab – FlintEtz’nab – FlintMuluk – WaterMuluk – Water Kawak – Storm CloudKawak – Storm CloudOk – DogOk – Dog Ahaw - LordAhaw - Lord

Month Names and Approximate MeaningsMonth Names and Approximate MeaningsEach month also had a different name with a special Each month also had a different name with a special meaning associated to it. Listed below are those name and meaning associated to it. Listed below are those name and meanings if known.meanings if known.

Pohp – MatPohp – Mat Yax – GreenYax – GreenWo – UnknownWo – Unknown Zak – WhiteZak – WhiteSip – UnknownSip – Unknown Keh – RedKeh – RedSotz’ – BatSotz’ – Bat Mak – UnknownMak – UnknownSek – UnknownSek – Unknown K’ank’in – UnknownK’ank’in – UnknownXul – DogXul – Dog Muwan – OwlMuwan – OwlYaxk’in – New SunYaxk’in – New Sun Pax – UnknownPax – UnknownMol – WaterMol – Water K’ayab - TurtleK’ayab - Turtle

Mathematics and Astronomy

• Mayans were able to compute the length of the Mayans were able to compute the length of the Earth’s revolution around the Sun to within a Earth’s revolution around the Sun to within a thousandth of a decimal point of the current thousandth of a decimal point of the current modern calculations using modern technology.modern calculations using modern technology.

• They kept calendars on the lunation and eclipse They kept calendars on the lunation and eclipse cycles, equinox and solstices.cycles, equinox and solstices.

• They were able to do this using a numerical They were able to do this using a numerical system that counted by twenties and used only system that counted by twenties and used only three notational symbols.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 20*1=20 20*2=40 20*3=60 6*20=120 0= 0 1= 1 1= 1 1= 1 2= 2 = 20 = 21 =41 =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.

BibliographyBerlinghoff, 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