Sobre la geometría sintética y analíticala elipse y sus construcciones

Abstract

Within the curriculum for the second year in Spanish upper secondary schools (17-18 year old students, appr.) we can find a unit called "conicals", in the subject Geometry. We consider that the development of this unit is essential for the adequate training of prospective university students, since it is assumed in this institution that the programmes are actually fulfilled in secondary schools. Nevertheless, the fact is that, in some Spanish secondary schools, ellipses are not even dealt with in class, studying circumferences at the most. The subsequent consequences in the first year at the university --as a result of not knowing conicals-- are obviously negative to the students. In this paper we suggest a synthetic-analytical approach to the constructions based on the ellipse that we think is motivating and training-orientated for upper secondary school students.