Banca de DEFESA: ARTHUR WILLIAN MATIAS GONÇALVES

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : ARTHUR WILLIAN MATIAS GONÇALVES
DATE: 31/03/2026
TIME: 15:00
LOCAL: CCET
TITLE:

The Union of Geometry and Algebra in Education: An Invitation to the Gauss–Lucas Theorem

KEY WORDS:

Gauss-Lucas Theorem; Polynomials; Complex Numbers; Didactic Sequence.

PAGES: 86
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

The central topic of this dissertation is the Gauss–Lucas Theorem, which states that the roots of the derivative of a complex polynomial of degree at least two lie in the convex hull of the set of roots of the original polynomial. We develop the theoretical background necessary for the proof and interpretation of this theorem, addressing fundamental topics such as complex numbers, polynomials, and the Fundamental Theorem of Algebra. We argue that the relevance of this work goes beyond its theoretical content, as it highlights topics from elementary mathematics that, in the current educational landscape, have often been relegated to a secondary role. In this sense, the dissertation also seeks to emphasize the connection between different areas of mathematics, particularly between algebraic and geometric perspectives. As an educational product, the dissertation concludes with a didactic sequence in the form of video lessons, whose aim is to present the Gauss–Lucas Theorem in an accessible way to high school students and other interested audiences, highlighting the rich relationship between algebra and geometry present in this result.

COMMITTEE MEMBERS:
Presidente - 1143007 - ALAN DE ARAUJO GUIMARAES
Interna - 1552847 - DEBORA BORGES FERREIRA
Externo à Instituição - FRANCISCO VIEIRA DE OLIVEIRA - UFERSA