The “Circle” and the “Philosophy” of Geometry: Teaching Proposal for Students of Second Class of Senior High School

Thanasoulia Georgia1 , Gakis Panagiotis1 , Afratis Georgios2

(1. Modular High School of Patras, University of Peloponese, Greece; 2. Secondary Education of Achaia, Greece)

Abstract: This presentation deals with the presentation of a didactic proposal addressed to students of the second class of senior high school. The aim of this educational activity is to actively engage the student, in order to shape a “researcher” attitude, taking advantage of the possibilities of supervision and experimentation provided by a computer. In addition, an innovative aspect of cognitive reality arises, specifically interdisciplinary teaching. As far as philosophy is concerned, students realize the relationship between philosophy and mathematics, as well as the geometric triangulation that dominates the daily life of ancient Greece, art and poetry (in this case, comedy). Students realize the presence of mathematical rules in their daily lives. Students discover and ascertain the relationship of the perimeters of inscribed and delineated regular polygons to the length of the circle circumference. Geogebra software was used to implement this activity, a free and multi-platform application in the teaching of mathematics at all levels of education, which incorporates Geometry, Algebra, tables, graphs and Calculus. This paper presents the theoretical framework for planning and implementing the activity, as well as the mathematical approach to the problem and finally the presentation of the teaching process in classroom conditions.

Key words: number π, “geometry” of thoughts