Dynamic construction of a family of octic curves as geometric loci

Abstract

We explore the construction of curves of degree 8 (octics) appearing as geometric loci of points defined by moving points on an ellipse and its director circle. To achieve this goal we develop different computer algebra methods, dealing with trigonometric or with rational parametric representations, as well as through implicit polynomial equations, of the given curves. Finally, we highlight the involved mathematical or computational issues arising when reflecting on the outputs obtained in each case.

Keywords

• plane curves
• geometric locus
• octic curve
• interactive construction
• dynamic geometry
• geogebra
• symbolic computation
• maple
• implicitization