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http://dx.doi.org/10.7468/mathedu.2014.53.3.313

A study on tangent of quadratic curves and cycloid curves using vectors  

Lee, Dong Won (Changshin High School)
Chung, Young Woo (Department of Mathematics, Kyungsung University)
Kim, Boo Yoon (Department of Mathematics Education, Pusan National University)
Publication Information
The Mathematical Education / v.53, no.3, 2014 , pp. 313-327 More about this Journal
Abstract
'Tangent' is one of the most important concepts in the middle and high school mathematics, especially in dealing with calculus. The concept of tangent in the current textbook consists of the ways which make use of discriminant or differentiation. These ways, however, do not present dynamic view points, that is, the concept of variation. In this paper, after applying 'Roberval's way of finding tangent using vectors in terms of kinematics to parabola, ellipse, circle, hyperbola, cycloid, hypocycloid and epicycloid, we will identify that this is the tangent of those curves. This trial is the educational link of mathematics and physics, and it will also suggest the appropriate example of applying vector. We will also help students to understand the tangent by connecting this method to the existing ones.
Keywords
tangent; vector; parabola; ellipse; circle hyperbola; cycloid;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
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