Pixel International Conferences

Optical illusions attract young people because they are surprising and mysterious. They can also be used as a starting point for a mathematical topic such as parametrization of planar curves. From a mathematical point of view, this paper describes the path of fixed points on a circle while whirling inside a larger circle. A surprising linear path is evoked under specific conditions and is analyzed by mathematical parameterization, which can be used to start discussing parameterizations of planar curves in a calculus course at university first degree level. Moreover, we provide Maple-code to foster student exploration of paths on whirling inner circles. A description of the implementation and students’ reactions in our own calculus classes is added.

Keywords: parameter; modeling; geometry.

References:

[1] ADAMS, R. & ESSEX, C. (2013) Calculus. Canada: Pearson.
[2] HARRISON, M.C. & AFIMA (1993) Parametric curves: an introduction to curve design. Teaching Mathematics and it Applications, 4 (1), 167-173.
[3] ROSE-HENIG, A. & SHAPIRO, A. (2013) A comparison of hypocycloid perception produced by two different elemental constructions. Journal of Vison, 13 (9), 819–819