Abstract

We present a unified point of view on conics, the invariant of the study being the angle under which a given conic is viewed. The geometric locus of points from which a given ellipse or hyperbola is viewed under a fixed angle θ (θ -isoptic curve of the conic) is a quartic named spiric curve. We show how to characterize the number of components of the θ -isoptic curve and reconstruct it as a toric section. This work has been done in parallel to a course on Analytic Geometry for in-service teachers in Israel. At the beginning, not all of them had a strong CAS literacy, but they underwent an interesting instrumental genesis. As far as we are concerned by improving the regular curriculum, the work shows how the usage of a Computer Algebra System enables the teacher to enrich the curriculum by the means of a revival of classical topics in mathematics.