Creating computer graphics and animations based on parametric equations of lines and curves – proposals for mathematics education at upper secondary level

Creating computer visualizations, especially animations, can help students to understand geometric objects (especially straight lines and curves), which are described by parametric equations, as point sets and to discover functional relationships and dynamic aspects. Because creating computer animations is very attractive for students it can help to motivate them to figure out features of parametric descriptions. This paper makes proposals for creating graphics and animations on lines, circles, spirals, parabolas and other curves by describing these curves with parametric equations and shows some examples created by students at upper secondary level. As a prerequisite the students should have basic knowledge in trigonometry and elementary analytic geometry. Computer animations based on parametric equations of lines and curves can be created using computer algebra systems or photorealistic 3d graphics software (like POV-Ray). Examples using both kinds of software will be shown and described.