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A Mathematical Journey Through the Land of the Maya Philip Scalisi Bridgewater State College, Pscalisi@Bridgew.Edu Bridgewater Review Volume 24 | Issue 2 Article 6 Dec-2005 A Mathematical Journey through the Land of the Maya Philip Scalisi Bridgewater State College, [email protected] Paul Fairbanks Bridgewater State College, [email protected] Recommended Citation Scalisi, Philip and Fairbanks, Paul (2005). A Mathematical Journey through the Land of the Maya. Bridgewater Review, 24(2), 8-13. Available at: http://vc.bridgew.edu/br_rev/vol24/iss2/6 This item is available as part of Virtual Commons, the open-access institutional repository of Bridgewater State University, Bridgewater, Massachusetts. A Mathematical Journey Several of us were fortunate to enter the interior of El The next day our group journeyed to Dzibilchaltún, Castillo as a smaller pyramid exists inside it! After a city noted for having one of the longest histories of through the ascending 62 narrow slippery stairs in a steamy, dark unbroken occupation of any Mayan site, from c. 500 and dank atmosphere, we came upon the chamber of B.C. to c. 1500 A.D. The most important structure here Land of the Maya the Chac-mool, a reclining figure with its head looking is the Temple of the Seven Dolls, named after seven by Philip Scalisi and Paul Fairbanks sideways. Its posture represents a figure descending into crudely modeled figurines found in it. At dawn on the the underworld. Beyond this statue is the throne of the spring and autumn equinoxes, the rising sun beams (all photographs by Philip Scalisi) AIRBANKS Red Jaguar, a painted altar inlaid with jade, bone, and directly though the east and west doors of the Temple mirrors. This was a memorable experience. and along the line of the Sacbé, the main path connect- UL F The MAA’s (Mathematical Association of America) Mayan underworld. Stairs on all four sides lead to the ing the two centers of Dzibilchaltún. The equinoxes A Another important structure at Chichén Itza is the Third Annual Mathematical Study Tour took place temple at its peak. The north staircase is lined on either were of great importance to the Mayans as they were Caracol (the Snail) or Observatory. It was designed between May 23rd and June 2nd, 2005. It was the first side with carvings of plumed serpents leading down to indicators for the change in seasons used in their agri- for tracking the movements of the moon and planets. joint MAA-MEC (Maya Exploration Center) venture. giant serpent heads at the bottom. On the spring and cultural cycles. This intricate filtering of light into the Initially built c. 800 A.D., it was altered and added on The purpose was to study ancient Mayan mathematics autumn equinoxes (March 21st and September 21st), a inner chambers at specified times enhanced the glory to over many centuries. The Caracol tower’s interior in the Yucatán Peninsula of Mexico. Twenty eight MAA play of light and shadow by the afternoon sun (around and “godliness” of the emperors. Later that afternoon is often described as a spiral, but in reality, it is a series members, ourselves included, traveled through four 4:00 PM) causes an image of a serpent “coming alive,” we returned to Mérida for a seminar on Mayan calen- of concentric circles. The inner core consists of a spiral Mexican states: Yucatán, Campeche, drical calculations using the Mayan modified vigesimal staircase (hence the “snail”) which leads to the upper Chiapas, and Tabasco. Guiding us and (base 20) numeration system. We shall give more details level. There are three window slits in the sides. One sharing their immense expertise were on these topics later. points due South, a second towards the setting of the three renowned MEC archaeologists: moon at the spring equinox (March 21st), and the third The following day was spent visiting the ruins at PHILIP SCALISI AND P Alonso Mendez, Alfonso Morales, and points to the west towards the setting of the sun on Mayapán, the Spanish missionary monastery at Maní, Christopher Powell. One thing we’d both equinoxes and the summer solstice (June 21st). and the caves of Loltún. Mayapán was the last Mayan A like you to keep in mind as we Y capital of the Yucatán, describe this fascinating journey: the Chichén Itza contains the rising to prominence temperature was consistently above Great Ball Court which is between 1200 and 110 F with high humidity. However the largest in Mesoamerica 1440 A.D. It imitated our guides were so knowledgeable and (168 meters [550 feet] long Chichén Itza by build- the structures so fascinating that we and 70 meters [230 feet] ing smaller but cruder were able to concentrate—generally. wide). In addition, versions of Chichén’s Chichén boasts of having THE TOUR El Castillo and Caracol. perhaps the most spectac- The tour began in Mérida, capital Our group visited the ular natural phenomenon of Yucatán state. There we attended various structures at in the Yucatán, the Sacred seminars on the ancient Mayan Mayapán to take mea- Cenote. This natural sink- numeration system, geometry, surements that verified hole containing water was calendrics, and archaeoastronomy. some of the geometric used primarily for sacred The next day was spent entirely at formulas discovered by ceremonies, and it was Chichén Itza, probably the most Christopher Powell. here that Mayan priests famous of all Mayan cities. Chichén We were also able to cast children, young vir- extends over an area of 32 square kilo- meet with various site gins, and jewel laden war- meters containing structures exhibit- staff archaeologists and riors in order to appease ing a number of diverse architectural witness new excava- the rain god Chaac. The styles: Puuc, Chenes, and Maya- tions and restorations. appeal of the Cenote to Yucateco. Many buildings also show the Mayans may have the influence of the Toltecs and descending to its head in March and ascending from its been partly due to the geo- Teotihuacános from central Mexico. Most conspicuous head in September. This is an extraordinary example of graphic phenomenon that of these is the great pyramid El Castillo, also known as the combination of Mayan architectural, astronomical, there are no above ground Far Left, Top, the Pyramid of Kukulcán. It is 24 meters (78 feet) high TICAL JOURNEY THROUGH THE LAND OF MA and mathematical skills. Chichén’s plumed serpent is rivers or lakes throughout Scalisi and Fairbanks with a 60 meter (196 feet) wide platform at the base. at Golondrinas Falls. associated with the god-king Kukulcán, the Yucatecan the Yucatán Peninsula. This was the first opportunity for our 28 mathemati- Far Left, Center, equivalent of the Teotihuacáno god Quetzalcoatl, cians to scamper up a Mayan structure; the steps are Olmec Head. who was introduced from Central Mexico c. 900 A.D. THEMA much steeper than we’re accustomed to in modern Left, Kukulcán remained as a major Yucatecan cult until the stairways, and the stones used are often loose and slip- Altar and Temple Spanish conquest around 1530 A.D. of the Seven Dolls. pery. Quite a challenge and quite a sight! The pyra- A MA mid’s nine tiers represent the symbolic number of the BRIDGEWATER REVIEW DECEMBER 2005 9 A Mathematical Journey Several of us were fortunate to enter the interior of El The next day our group journeyed to Dzibilchaltún, Castillo as a smaller pyramid exists inside it! After a city noted for having one of the longest histories of through the ascending 62 narrow slippery stairs in a steamy, dark unbroken occupation of any Mayan site, from c. 500 and dank atmosphere, we came upon the chamber of B.C. to c. 1500 A.D. The most important structure here Land of the Maya the Chac-mool, a reclining figure with its head looking is the Temple of the Seven Dolls, named after seven by Philip Scalisi and Paul Fairbanks sideways. Its posture represents a figure descending into crudely modeled figurines found in it. At dawn on the the underworld. Beyond this statue is the throne of the spring and autumn equinoxes, the rising sun beams (all photographs by Philip Scalisi) AIRBANKS Red Jaguar, a painted altar inlaid with jade, bone, and directly though the east and west doors of the Temple mirrors. This was a memorable experience. and along the line of the Sacbé, the main path connect- UL F The MAA’s (Mathematical Association of America) Mayan underworld. Stairs on all four sides lead to the ing the two centers of Dzibilchaltún. The equinoxes A Another important structure at Chichén Itza is the Third Annual Mathematical Study Tour took place temple at its peak. The north staircase is lined on either were of great importance to the Mayans as they were Caracol (the Snail) or Observatory. It was designed between May 23rd and June 2nd, 2005. It was the first side with carvings of plumed serpents leading down to indicators for the change in seasons used in their agri- for tracking the movements of the moon and planets. joint MAA-MEC (Maya Exploration Center) venture. giant serpent heads at the bottom. On the spring and cultural cycles. This intricate filtering of light into the Initially built c. 800 A.D., it was altered and added on The purpose was to study ancient Mayan mathematics autumn equinoxes (March 21st and September 21st), a inner chambers at specified times enhanced the glory to over many centuries. The Caracol tower’s interior in the Yucatán Peninsula of Mexico. Twenty eight MAA play of light and shadow by the afternoon sun (around and “godliness” of the emperors. Later that afternoon is often described as a spiral, but in reality, it is a series members, ourselves included, traveled through four 4:00 PM) causes an image of a serpent “coming alive,” we returned to Mérida for a seminar on Mayan calen- of concentric circles.
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