Displaying parametric curves with virtual and physical tools

Abstract

Parametric curves play an important role in mathematics and engineering education. The purpose of this paper is to introduce the hypotrochoid family of curves and to provide ideas and tools for teaching the topic. We give the general parametric equations of hypotrochoids and show that several special curves can be derived from these equations. To display the curves we use the Hypotrochoid Equation Tracer, which is a dynamic application made by Desmos graphic calculator. In addition we have created a LEGO robot called Spikograph, that models a Spirograph and draws different hypotrochoids providing a physical experience for students. Finally, we have compiled a student project to practice and deepen the knowledge about hypotrochoids.

Task Design for Teaching Cardioid Curve With Dynamic Geometry Software and Educational Robotics in University Practice

“…The Desmos graphing calculator is a user-friendly and easy-to-use tool DGS. The findings from the papers of Chorney (2022), Körei and Szilágyi (2022) and Chechan et al (2023) also support that using Desmos as a technological tool for learning mathematics improves students' performance and helps them develop conceptual understanding through visualisation.…”

“…They value hands-on experiences and real-world applications of their learning (Seemiller & Grace, 2016). Computer science students enjoy working with dynamic geometry software and creating animations is a powerful motivator for them (Körei & Szilágyi, 2022).…”

Discovering epitrochoid curves with STEAM-based learning methods

“…Hypotrochoids can be generated similarly to epitrochoids, but in this case, the rolling circle is inside the fixed one. For the parametric equations of hypotrochoids, see [11], where we outline a learning project to study these curves.…”

Untitled

“…Although the spirograph appeared as a toy in the marketplace in 20 th century in physical form, at present it is very popular in digital forms [26,27,28,29,30,31]. The different versions of drawing robots are being marketed to draw curves and their attractive patterns.…”