Using GeoGebra as an Expressive Modeling Tool: Discovering theAnatomy of the Cycloid’s Parametric Equation

In Greek geometry, curves were defined as objects, which are geometric and static. For example, a parabola is defined as the intersection of a cone and plane like other conics, which are first introduced by Apollonius of Perga (262 BC – 190 BC). Alternatively, 17th century European mathematicians have preferred to define the curves as the trajectory of a moving point. In his Dialogue Concerning Two New Science of 1638, Galileo found the trajectory of a canon ball. Assuming a vacuum, the trajectory is a parabola (Barbin, 1996). We can understand that some of the scientists, who studied on curves, actually were interested in the problems of applied science, like Galileo as an astronomer and a physician, Nicholas of Cusa as an astronomer etc. Some of the scientist, who lived approximately in the same century, took further the research on the curves as a mathematician (e.g. Roberval, Mersenne, Descartes and Wren).