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Borrowing from the Past: Using 17th Century Technology to Inform 21st Century Undergraduate Mathematics

Honor Student Borrowing from the Past: Using 17th Century Technology to Inform 21st Century Undergraduate Mathematics

Department: Mathematics
Symposium Year: 2013
Student(s): Deborah Wiles
Faculty Mentor(s): Dr. Mark Hughes

 

There is interest in undergraduate mathematics for close study of proofs for various planar loci in the Cartesian plane. They add significantly to a student’s understanding of trigonometry, geometry, and to the ability to think of mathematical structures in abstract terms. Certainly, application-style problems using the procedures and theorems of trigonometric concepts provide necessary introduction into the sort of real-world situations encountered by future engineers and analysts. But studying the underlying structures and abstract nature of mathematics at a pre-calculus or early calculus stage, as well as studying the history behind the development of these ideas, would go a long way toward enriching the experiences of early mathematics students. In particular, the seventeenth century provides an interesting confluence of mathematical ideas surrounding conic sections and coordinate geometry from the ancient Greeks to Descartes that would soon lead to the development of the calculus in Europe. This project draws upon the mathematical understanding and technology available in the seventeenth century in order to create interesting problems and lessons for the twenty-first century undergraduate classroom. Historical perspectives, profiles of various mathematicians, and mathematical proofs are presented, as well as animated graphics of planar loci that describe conic sections. Additionally, one or more problems for classroom use will be offered. 

 

 

 

Present in 2014

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