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Full-Text Articles in Physical Sciences and Mathematics
Students' Reasoning About The Concept Of Limit In The Context Of Reinventing The Formal Definition, Craig Alan Swinyard
Students' Reasoning About The Concept Of Limit In The Context Of Reinventing The Formal Definition, Craig Alan Swinyard
Dissertations and Theses
Many researchers (Artigue, 2000; Bezuidenhout, 2001; Cornu, 1991; Dorier, 1995) have noted the vital role limit plays as a foundational concept in analysis. The vast majority of topics encountered in calculus and undergraduate analysis are built upon understanding the concept of limit and being able to work flexibly with its formal definition (Bezuidenhout, 2001). The purpose of this study was to: (1) Develop insight into students' reasoning about limit in relation to their engagement in instruction designed to support their reinventing the formal definition of limit, and; (2) Inform the design of principled instruction that might support students' attempts to …
A Closer Look At The Crease Length Problem, Sean F. Ellermeyer
A Closer Look At The Crease Length Problem, Sean F. Ellermeyer
Faculty and Research Publications
An optimization problem that appears as an exercise in most modern calculus textbooks is the crease length problem. Here, Ellermeyer provides a solution of the general crease length problem in which all possible foldings of a corner to the opposite edge are taken into account. One of his findings will be that the minimum crease length is never produced by a Case 2 fold and hence that the general crease length problem always yields a different minimum than the constrained problem that is treated in the textbooks. He discovers a criterion that determines which foldings must be performed in order …