Banca de DEFESA: ADILSON TAVARES DE BRITO JÚNIOR

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : ADILSON TAVARES DE BRITO JÚNIOR
DATE: 28/08/2025
TIME: 14:30
LOCAL: CCET
TITLE:

Similarity Between Conics and Cubic Curves: Curious and Novel Results Explained in High School Language

KEY WORDS:

Similarity; conics; polynomials of 3-degree

PAGES: 71
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

In this dissertation, we investigate the notion of similarity between curves, understood as a natural generalization of the concept of similarity between triangles. Based on this definition, we analyze criteria for determining when parabolas, ellipses, and hyperbolas are similar. We then propose a didactic activity aimed at providing teachers with a pedagogical approach that allows high school students to understand that any two parabolas are similar. Finally, we present a theorem that guarantees that the graph of any cubic polynomial can be obtained from the graph of the function $y = x^3$ through similarity functions and a shear transformation. As a consequence of this result, we establish a criterion that makes it possible to verify when the graph of a degree-3 polynomial is similar to the graph of $y = x^3$.

COMMITTEE MEMBERS:
Presidente - 1143007 - ALAN DE ARAUJO GUIMARAES
Interno - 1549905 - FAGNER LEMOS DE SANTANA
Externo à Instituição - DAVID LEVI DA SILVA MACÊDO - UFCG