Mayan Mathematics
Denise Brown
Professor of Mathematics
I have always been interested in the indigenous cultures of Mexico, Central and South America. A study grant will allow me to increase my knowledge of the Mayans and how their society dictated their Mathematical system.
The ancient Maya of Mexico and Central America were the most advanced mathematicians in the entire New World. They were the only culture in the Pre-Columbian Americas to create the concept of “zero”. Their complex calendar system remains one of the most accurate ever created. With it, Mayans were able to calculate astronomical events thousands of years into the future or the past. More recent studies have begun to show that they were also adept users of “sacred geometry” otherwise known as the basic geometric forms and proportions that are found in nature.
Mathematics is a broad topic but I would like to break their system into three parts : their number system, measurement system, and geometry. My main question is what drove the Maya to create their Mathematical system ? I plan to research the daily life of the Maya, their social structure including religion, architecture, astronomy, and calendar system.
The Mayan Number system
Our system is decimal (base 10) and uses 10 digits to represent numbers theirs is vigesimal (base 20) but uses only three symbols to represent numbers. These are: a dot (1 unit), a bar (5 units) and zero which is symbolized by a shell. These symbols allowed even the uneducated to add and subtract for purposes of trade and commerce. It is argued that their number system was used by priests and astronomers for astronomical and calendar calculations. Some questions I have are : What arithmetic operations were used? Did they have a way of expressing fractions?
The Mayan Calendar
One is a ritual composed of 260 days with 13 months of 20 day each. The twenty days were numbered from 0 to 19. The second calendar was a 365-day civil calendar consisting of 18 months, each named after agricultural or religious events. Some questions I have about calendars are: Why are there two calendars with different numbers of days? How was time measured ?
Mayan Astronomy
Mayans carried out astronomical measurements with remarkable accuracy yet they had no instruments other than sticks. Many of their buildings are thought to be observatories. Many of the windows on their buildings are positioned to line up with significant lines of sight such as the setting of the sun on the spring equinox and certain lines of sight relating to the moon. With their crude instruments they were able to calculate the length of a year to be 365.242 days and also the length of the lunar month to be 29.5302 days.
Mayan Geometry
I am interested the geometry that is found in the various aspects of the daily activities of the Maya, such as design of cities, and the shape of buildings, ceramics and weavings The great majority of Mayan temples are truncated tetrahedrons, rectangular prisms, or, in some cases, cylinders. My question is what geometric terms are included in their language? Do they have words for point, line, plane, curve etc. How did nature influence their designs? What about the ideas of proportionality, symmetry, rotations and translation influence their weavings? Is there a special ratio like the “golden ratio” that is prevalent in Mayan art and architecture?
I will my research in Math 1351 Foundations in Mathematics II, which is required for future elementary and middle school teachers. The results of my research could be presented at various conferences I attend. I also could use a scaled down version for the annual Bowman Day of Science.
I will research all of the above during the Summer II semester. The SMU library has all of the texts and articles listed on my reading list. I plan to spend 4 –5 days a week at the SMU library .
Reading List
I will read all or parts of the following
Closs, Michael P.
1986(editor)Native American Mathematics, University of Texas Press, Austin.
A good collection of papers about mathematics in New World cultures from Chile to Canada.
Lounsbury, Floyd
1978 “Maya Numeration, Computation and Calendarical Astronomy,” Dictionary of Scientific Biography, Volume 15, supplement 1, Charles Scribners Sons, New York.
An article describing the nature of Maya mathematics from one of the foremost authorities.
Aveni, Anthony F.
1992(editor)The Sky in Mayan Literature, Oxford University Press, Oxford.
A collection of articles about Maya astronomy as understood through hieroglyphic texts.
2000Sky Watchers of Ancient Mexico, Revised Edition, University of Texas Press,Austin.
The single best source for information on Mesoamerican Archaeoastronomy written by one of the forefathers of the field of Archaeoastronomy.
Carlson, John
1990 America's Ancient Skywatchers. National Geographic, Vol. 177, No. 3,March 1990, pp76-107.
An article explaining the cosmologies of multiple Pre-Columbian cultures. John Carlson is one of the foremost authorities on ancient Maya astronomy.
Freidel, David, Linda Schele and Joy Parker
1993 Maya Cosmos - Three Thousand Years on the Shaman's Path. William Morrows and Company Inc., New York.
A groundsbreaking study of the connections between modern Maya star lore and ancient Maya astronomy.
Milbrath, Susan
1999Star Gods of the Maya – Astronomy in Art, Folklore and Calendars, University of Texas Press, Austin.
A detailed review of both modern and ancient Maya astronomy ordered by observation phenomena.
Coe, Michael D.
1999aThe Maya, fifth Edition, Thames and Hudson Ltd., London.
A very well written textbook on Maya Civilization in its fifth edition.
Schele, Linda and David Friedel
1990 A Forest of Kings - The Untold Story of the Ancient Maya. WilliamMorrows, New York.
A portrayal of ancient Maya life presented in the form of vignettes about days in the lives of Maya kings.
Schele, Linda and Peter Mathews
1998The Code of Kings, William Morrows, New York.
The functions of Maya buildings discussed by building types and supported by translations and artifact assemblages.
Sharer, Robert
1994The Ancient Maya, 5th Edition, Stanford.
An exhaustive textbook of almost 900 pages that covers all aspects and time periods of ancient Maya Civilization.
Tedlock, Barbara
1992Time and The Highland Maya, Revised Edition, University of New MexicoPress, Albuquerque.
An ethnography about the daykeeper shamans of highland Guatemala written by an American scholar who was herself initiated as a shaman.
Tedlock, Dennis
1998Popol Vu, A Translation, 2nd Edition. Simon and Schuster, New York.
The story of the Maya creation myth. It is key to understanding Maya religion.