Banca de DEFESA: NATÁLIO JOÃO SILVA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : NATÁLIO JOÃO SILVA
DATE: 31/08/2023
TIME: 14:00
LOCAL: Google Meet: https://meet.google.com/foo-wkwf-zxz
TITLE:

THE ARBELOS OF ARCHIMEDES: AN EXTENSION TO THE ELIPSES AND A ALTERNATIVE PROOF

 OF PAPPUS THEOREM WITHOUT USING INVERSION

KEY WORDS:

Arbelos. Parbelos. Pappus Chain. Pappus Theorem. 

PAGES: 76
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

The present work aims to study and expand the properties of Archimedes’ Arbelos and the Pappus

Chain. An Arbelo is a structure composed of three semicircles that are pairwise tangent and have

the diameters on the same line. Such a structure was studied by the mathematician Archimedes,

who found several interesting geometric properties. Initially we will have an introduction

followed by a brief historical account of the life and work of Archimedes of Syracuse and Pappus

of Alexandria. In the preliminary concepts, we present configurations and results about circles

and ellipses that will be of extreme importance for the good understanding of this work. In

the section dedicated to the results, we present an extension of two properties of the arbelos to

the ellipses, provided that the ellipses involved have the same eccentricity. We prove Pappus’ 

Theorem using only plane geometry and analytic geometry, which differs substantially from

what is traditionally done: construction using the inversion technique, normally not seen in High

School. Finally, as an educational product, we present a didactic sequence devoted for teaching 

of concept of circles and ellipses, such activities can be applied to all levels of high school.

BANKING MEMBERS:
Presidente - FRANCISCO DE ASSIS BENJAMIM FILHO
Interno - FRANCISCO PEREIRA CHAVES
Externo à Instituição - RENIVALDO SODRÉ DE SENA - IFCE