19 December 2007 Geometry in Pre-Columbian Cultures in the Americas Euclidean Geometry usually comes to mind first, when we speak about geometry. People often forget that much of modern geometry was inherited from our pre-Columbian cultures, especially from the Aztecs, the Incas, and the Mayas. Geometry was integrated into almost all aspects of our pre-Columbian cultures life, such as the daily activities, shape of buildings and streets, the design of their cities, as well as weavings and ceramics. Interesting enough, but geometry and geometry legacy is also found in the Aztecs and Mayan languages. Garcilaso de la Vega in his The Incas: The Royal Commentaries of the Inca tells that the pre-Columbian cultures had an excellent knowledge of geometry, which they had to have in order to survey and portion out the land (Jolas, 1961, p.43).
Although the knowledge of geometry was, to a certain extent, empirical, and not speculative, as they made their allotments and calculations using little stones and pieces of cord, the way the pre-Columbian cultures made their calculations, was still quite remarkable. The cities built by the pre-Columbian cultures were carefully planned, as one can easily find the geometric shapes and patterns in the Mayan and Incas surroundings.
The accomplishments of the Maya civilization that required mathematical skills and the use of geometry were also found in their ancient cities Palenque, Quirigua, Chichen Itza, Copan, Tikal, and Tulum. The scientists have also found a really impressive relationship to Astronomy and exact sciences, as their spatial orientation of the four corners of the universe was based by our intercardinal points, or, probably, toward two directions in the east and two in the west, that is to say, sunrise at winter and summer solstices, and sunset at the same two solstices” (Leon-Portillo, 1988, p. 130).
... Sagrario Metropolitano is an example of building over the pre-Columbian Aztec city and making use of the ancient materials as construction materials ... important features of pre-Columbian architecture as found in Mexico, it is important to understand how these societies and respective cultures are influential ...
In addition, according to the researchers, the examples of pre-Columbian architecture confirm the coordination and alignment of the Mayan and Aztecan temples with the celestial bodies. Some of their temples were built and located in such a way, that they were located towards the sunrise at winter, while some of them (for example, alignment of the Stelas 10 and 12 in Copan, Honduras) were aimed to show the time of the year, when the fields should be burned to prepare for the planting of crops (Morales).
In addition, there is an assumption that pre-Columbian cultures used two almost vertical tubes to mark the zenith sun, and the June solstice.
The buildings that were built by the pre-Columbian cultures were also carefully planned. Indeed, the vast majority of the buildings and temples are rectangular prisms, truncated tetrahedrons, and even cylinders (some of the examples of Mayan cylinder-shaped buildings were found in Ceibal).
The buildings also have much in common with the celestial bodies, and this fact also indicates that the pre-Columbian cultures carefully calculated and planned their architectural works. Geometrical calculations also helped Mayas to build interesting architectural elements, such as the Mayan false arch that was often used in their architectural works (Morley, 1983, p. 267).
Some buildings created by the pre-Columbian cultures are perfect examples of symmetry (for example, the murals of Coba) (Morales).
The remains of ceramics found by the archaeologists also prove that geometry was widely used in the pre-Columbian cultures. They found a wide variety of bichromatic strip patterns and frieze patterns used in the pottery. The very shape of the Mayan, Aztecan, and Incas ceramics is well-designed; in geometrical figures, such as curves, triangles, circles, and others are often present in the exterior and exterior of the Mayan and Inca’s vessels. Rubio (1992, p.6) also proves that in Maya ceramics three basic forms are found: jugs, bowls, glasses, plates and vessels with a restricted mouth”, and each of these categories significantly differs from the other because they have different geometric shapes. The pre-Columbian cultures often decorated their ceramics with various kinds of intertwined and spiral curves, and, as these lines, curves and geometric figures were widely used in pre-Columbian cultures arts, each geometric shape and figure (i.e. align, side, row, line, edge, curve, and others) existed in expressions and terms in their languages.
... the Pre-Columbian era to the forming of New World there was lot of oppression and greed. Some aspects of cultures were lost ... there is more to it than meets the eye. The Pre-Columbian Era is the time period before the famous voyage of ... onto the people that were already there causing the cultures to merge. The Columbian Exchange is said to have altered millions of ...
The researchers prove the assumption that the presence of these terms in the languages of indigenous people serve as the evidence of the existence of geometry in pre-Columbian cultures. For example, one of the studies confirm that geometric terms were present in various Mayan languages (i.e. rainbow – xoquik’ab, cylindrical bolbo, square caxucut, quadrilateral fumru and rok, distance najt and xnajtil, row tzol, etc) (Morales).
The patterns of geometry were also found in embroidery and weaving, as pre- Columbian cultures used a wide range of mosaic designs. One of such mosaic designs is shown in picture. As we can see, the mosaic contains the repeating triangles in the rows, diagonally and horizontally. The geometric figures are repeated, and form the mosaic pattern. In such a way, we can make a conclusion that geometry was used in the weaving and artwork in pre-Columbian cultures.
In conclusion it may be said that geometry was widely used in pre-Columbian cultures. The excellent examples of geometry can be found in architecture works, in the remains of ceramics, in languages, and in weaving and embroidery. The Mayas, the Aztecs, the Incas and other cultures used geometry in their daily activities, and although sometimes geometry went unnoticed, it still was the essence of the attractive and balanced world of the ancient pre-Columbian cultures. Works Cited Jolas, Maria. The Incas: The Royal Commentaries of the Inca, Garcilaso de la Vega, 1539-1616. New York: Orion Press, 1961. Leon-Portilla, Miguel.
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Time and Reality in the Thought of the Maya. Oklahoma: University of Oklahoma, 1988. Morales, Leonel. “Mayan Geometry.” December 1993. International Study Group on Ethnomathematics (ISGEm) Newsletter. 19 December 2007 . Morley, Sylvanus. The Ancient Maya.
California: Stanford University Press, 1983. Rubio, Rolando. Introduccion a la ArqueologIa Maya. Guatemala: Cuaderno de Trabajo, Museo Popol Vuh, Universidad Francisco MarroquIn, 1992..