Figure 1. 2011 MAA Study Trip participants in Copan, Honduras (Photo by John Wilkins, used with permission)
|Figure 2. Maya ruins in Copan, Honduras (Photo by Cynthia Woodburn, 2011)|
Almost every year since 2003, the MAA has sponsored a study trip to a location of mathematical interest, such as Greece, Egypt, and China. The 2011 study tour had an emphasis on Maya mathematics and included sites in Guatemala and Honduras. Although the timing of the trip coincided with interest in the Maya long count calendar system and the end of a cycle in the year 2012, the group was also exposed to other information which has not received as much publicity and is not as well known. The focus of this article is on some of that information, namely Maya geometry and ways it can be used in the mathematics classroom. (For more information on Maya calendars, check out the Loci: Convergence articles “Maya Calendar Conversions” and “Maya Cycles of Time.”)
The 2011 MAA study tour was organized through the Maya Exploration Center with guide Christopher Powell. Powell (seated at far left in the first row in Figure 1 above) is an archaeologist with over twenty years of field experience. In addition to giving onsite explanations of Maya ruins, Powell presented several lectures to the group. One of these included material from his 2010 Ph.D. dissertation, The Shapes of Sacred Spaces, in which he introduced how the Maya used ratios in their art and architecture, as well as their ingenious way of using a knotted cord to form right angles.
In this article, we start with some background information on the Maya and then explain different ways that the Maya used geometry, going into detail on how the Maya formed right angles and rectangles with sides in various ratios by using knotted cords. Animations and videos created by the first author are included to illustrate the processes. The article concludes with related classroom activities that are tied to the Common Core Standards.
|Figure 3. Maya stela in Copan, Honduras (Photo by Cynthia Woodburn, 2011)|
The classic Maya period ran roughly from 250 to 900 CE (or AD) [Coe, p. 26] during which time the Maya constructed hundreds of cities in a contiguous area from what is now southern Mexico across the Yucatan Peninsula to western Honduras and El Salvador, including what is now Guatemala and Belize. Maps of the Maya world can be seen at Latin American Studies: The Maya. The Maya Exploration Center also has maps of several Maya cities. Currently there are about 10 million modern Maya [Coe, p. 11].
The classic Maya made extensive use of geometry in their architecture. There is also evidence that they used geometry in their art. However, efforts to find a measurement system used by the Maya have been mostly unsuccessful. It does appear that they used body parts as units of measure, e.g. a uinic, which is a person’s height or “wingspan” from fingertip to fingertip. There are also several references to the use of a measuring cord in religious ceremonies and when buildings were being laid out. A measuring cord is even mentioned at the beginning of the Maya religious text Popol Vuh in the description of the creation of the universe. Powell, who conducted ethnography interviews of modern Maya shaman priests and master builders, discovered that measuring cords are still in use today.