A HISTORICAL BIBLIOGRAPHICAL INVESTIGATION OF MATHEMATICAL WHYS ABOUT REGULAR POLYHEDRAL

Abstract

This paper aims to answer two mathematical whys about Regular Polyhedra ‒ Why they so called are and why are only five regular polyhedra? ‒ present in the article Why mathematicians in the Journal of the Maths Teacher from a historical review on this topic. For that, a qualitative research was developed, of the bibliographic type, searching for historical arguments in the literature sufficient for the understanding of these questions. It was necessary to understand and define the polyhedra, as well as to present their historical development on the Platonic Polyhedrons. It has been elucidated, in an etymological explanation, that the Regular Polyhedra are so called due to the regularity of the polygons that compose them and are also called Platonic Polyhedra. We could further observe that, however closely related to Plato and his mystical form, it was the Pythagoreans who began to study them. We also note with the aid of the History of Mathematics that the explanation of only five is presented under a geometric bias by Euclid and a mystic of Plato in relating them to the elements of nature: fire, earth, water, air and universe. We understand, then, that many of today's questions can be elucidated by the History of Mathematics.