- A study on tangent of quadratic curves and cycloid curves using vectors
- Lee, Dong Won ; Chung, Young Woo ; Kim, Boo Yoon ;
- The Mathematical Education, volume 53, issue 3, 2014, Pages 313~327
- DOI : 10.7468/mathedu.2014.53.3.313

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.