EJMT Abstract

This paper is an expansion of [11], an earlier paper of the first author’s. The discussions in this paper were inspired by a college entrance practice exam from China. The investigations lead us to apply technological tools to explore the reflections along circles. Firstly, we shall see if we choose the incoming and outing light beams to be at a specific angle within a circle, we shall create many nice geometric patterns. Secondly, we prove that the reflections along the circle are periodic if the reflection angle is a rational degree. Thirdly, we replace the straight lines for light beams by two symmetric curves with respect to the corresponding normal line at the point on the circle, we will create nice patterns involving curves. Finally, we use technological tools to explore interesting scenarios when reflections are done along ellipses.