Mathematics and Architecture of the Incas in Peru

Cheri Shakiban; Michael P. Hennessey

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Conference: 2011 ASEE Annual Conference & Exposition
Location: Vancouver, BC
Publication Date: June 26, 2011
Start Date: June 26, 2011
End Date: June 29, 2011
ISSN: 2153-5965
Conference Session: Computers and Software in Teaching Mathmatics
Tagged Division: Mathematics
Page Count: 17
Page Numbers: 22.1046.1 - 22.1046.17
DOI: 10.18260/1-2--18327
Permanent URL: https://peer.asee.org/18327
Download Count: 2795

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Paper Authors

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Cheri Shakiban University of St. Thomas

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I am a professor of mathematics at the University of St. Thomas in St. Paul, Minnesota, where I have been a faculty member since 1983. I received my Ph.D. in 1979 from Brown University in Formal Calculus of Variations. My recent area of research is mostly in computer vision, with applications to object recognition. My publications are in diverse areas of mathematics and engineering. I love to work with undergraduate students, in particular, underrepresented students, to get them involved in doing research in mathematics and encourage them to give conference presentations/posters and submit their work for publication. In addition to teaching regular math courses, I also like to create and teach innovative courses such as "Mathematical symmetry of Southern Spain" and "Mathematics and Architecture of the Incas in Peru", which I have taught as study abroad courses several times.

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Michael P. Hennessey University of St. Thomas

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Michael P. Hennessey (Mike) joined the full-time faculty as an Assistant Professor fall semester 2000. He is an expert in machine design, computer-aided-engineering, and in the kinematics, dynamics, and control of mechanical systems, along with related areas of applied mathematics. Presently, he has published 41 technical papers (published or accepted), in journals (nine), conferences (31), or magazines (one). In 2006, he was tenured and promoted to the rank of Associate Professor. Mike gained 10 years of industrial and academic research lab experience at 3M, FMC, and the University of Minnesota prior to embarking on an academic career at Rochester Institute of Technology (three years) and Minnesota State University, Mankato (two years). Mike holds a Bachelor of Mathematics from the University of Minnesota (with distinction), an MS in Mechanical Engineering from MIT, and a Ph.D. in Mechanical Engineering from the University of Minnesota. He is also a member of ASME, SIAM, and ASEE.

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Abstract

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.

Citation
Format

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

TY  - CPAPER
AB  -                  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 &amp; 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.
AU  - Cheri Shakiban
AU  - Michael P. Hennessey
CY  - Vancouver, BC
DA  - 2011/06/26
PB  - ASEE Conferences
TI  - Mathematics and Architecture of the Incas in Peru
UR  - https://peer.asee.org/18327
DO  - 10.18260/1-2--18327
ER  -