The deltoid as envelope of line in high school: A constructive approach in the classroom

This paper presents a design of educational module (EM) aimed on the one hand at retrieving to the teaching of the traditional syllabus some mathematical terms connected to geometrical constructions, and on the other to ntroduce, by virtue of the new issues posed by dynamic geometry software (DGS), different teaching perspectives from the traditional ones so that students can be encouraged to experience the true meaning of mathematical discovery. The focus is based on the tracing of the deltoid curve - triangular curve - derived by an envelope of lines. The peculiarity of EM lies in the methodological approach which privileges a practical strategy based on the combination of the usual tools like ruler and compasses with their modern versions offered by a DGS like GeoGebra. In the concluding paragraph we will report a coherent analysis of the method and the results obtained from the experimentation in class.