June 26, 2011
June 26, 2011
June 29, 2011
22.1046.1 - 22.1046.17
Mathematics and Architecture of the Incas in PeruAbstractThis study-abroad January (J-term) course co-taught by the authors (mathematics, mechanicalengineering) is described in detail. Background and motivation for the course is discussed,including previous work, study abroad programs at The University of X, the student population,and structure of the course. Additionally, samples of student work, assessment, and lessonslearned are provided that offer practical advice for others considering offering similar courses.The lead author and course originator is an expert on the topic of mathematical symmetry and isalso an international traveler, often to visit sites that exhibit interesting symmetry attributes.Symmetry appears in many places including manmade forms, such as textiles and impressivelyin architecture, which, to maximize appreciation, makes sense to be physically on-site. At theUniversity of X, the study-abroad program is well-established and takes on one of two forms,either internally offered courses, or in our case, through a regional school consortium, wherestudents in participating schools are eligible. The niche market for this course is students (26total) who have completed 3 semesters of Calculus, which narrowed it down to mostly upperclassman in engineering and/or mathematics, although other technical majors, such as chemistrywere represented. The course can be used as either a 4 credit mathematics or engineering course,appealing to many who are seeking a minor, typically in mathematics. Because of the emphasison, and the ubiquitous nature of symmetry, the course offers some flexibility with regard to itsvenue. In fact, prior to the January 2010 offering, the course had been taught twice in Spain.The course is structured such that there are different elements that work together synergistically,such as on-site visits (possibly with on-site instruction), travel, readings, lectures, studentpresentations (technical & tourist) to promote ownership, and homework in a workbook.The course evolves as a journey, both academically and geographically. Most topics weredirectly related to the Incas or symmetry, although due to the proximity of other sites ofacademic interest, several other topics were covered. Students learned about topics such asQuipas (a complex system of knot-tying for recording numerical and other data), the La Yacupa(an ancient calculating device that was used for addition, subtraction, multiplication, anddivision), geometrical symmetry of frieze and wallpaper patterns commonly depicted onbuildings and in textiles, and the stability of structures (important because of the commonoccurrence of earthquakes). In addition, the famous enigmatic Nazca Lines and the steamship,Yavari, on the highest elevation commercial lake in the world, (Lake Titicaca -- 12,000 ft) werestudied. This adventurous course, whether by land, air, or water, traversed through much of Peru(0-14,000 ft), including the cities of Lima, Nazca, Arequipa, Puno and Lake Titicaca (island ofTaquile), Cusco, Aquas Calientes, and the beach community of Huanchaco Trujillo. Thehighlight of the course was visiting the famous lost city of the Incas, Machu Picchu.Generally, the course was a success and we are in the process of customizing the course materialfor a similar January 2012 course in Europe.
Shakiban, C., & Hennessey, M. P. (2011, June), Mathematics and Architecture of the Incas in Peru Paper presented at 2011 ASEE Annual Conference & Exposition, Vancouver, BC. 10.18260/1-2--18327
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