GeoGebra as facilitator of a hypotrochoid generalization in an initiation scientific research project at undergraduate level

Abstract

An initiation to scientific research project was proposed for two undergraduate students in Environmental Engineering, with the porpuse of studing a generalization of the hypotrochoid and epitrochoid curves.  The GeoGebra software is the facilitator of the team of two professors and the students. The difficulties of the mathematical proofs become, in the environment of the dynamic geometry, exercises of construction of curves that, arranged in sequence, determined the generalization of the well-known hypotrochoid curve, result that is the detailed in this work. From this first discovery, the transition to epitrochoid curves or more general curve,s becomes an iterative application and an applicattion of mathematical induction. This study   has demonstrated the importance of the computational tool, specially for its contribution in the visualization of theoretical results as well as for its simplicity in coding.