Assessment of divine proportion in the cranial structure of individuals with Angle Class II malocclusion on lateral cephalograms

INTRODUCTION: The study of the Divine Proportion (Φ = 1.618) began with the Greeks, having as main researchers the mathematician Pythagoras and the sculptor Phidias. In Dentistry, Ricketts (1981-82) was an early to study this issue. OBJECTIVE: This study proposed to evaluate how some cephalometric measures are presented in relation to the Divine Proportion, with the total of 52 proportions, formed by 28 cephalometric landmarks. METHODS: Lateral cephalograms of 40 Class II adults patients aging from 17 to 45 years (13 male and 27 female) were evaluated. The linear distances between the landmarks were measured using Radiocef Studio software. RESULTS: After statistical analysis, the data shown an average of 65,48% in the Divine Proportion, 17,5% in the relation Ans-Op/V1S-DM16 and 97,5% in the relations Na-Me/Na-PoNa e Na-PoNa/Na-Gn. CONCLUSION: Among all cephalometric measurements investigated, the lower facial third and the dental arches showed the smallest percentages of Divine Proportion.

Students' foregrounds: Hope, despair, uncertainty

A foreground is formed through the possibilities, tendencies, propensities, obstructions, barriers, hindrances, et cetera, which his or her context provides for a person. Simultaneously, a foreground is formed through the person's interpretations of these possibilities, tendencies, propensities, obstructions, barriers, hindrances. A foreground is a fragmented, partial, and inconsistent constellation of bits and pieces of aspirations, hopes, and frustrations. It might be both promising and frightening; it is always being rebuilt and restructured. Foregrounds are multiple as one person might see very different possibilities; at the same time they are collective and established through processes of communication. In this article educational meaning is discussed in terms of relationships between the students' foregrounds and activities in the classroom. I illustrate how students' dreams might be kept in cages, and how this has implications for how they engage or do not engage in learning processes. I investigate how a foreground might be ruined, and in what sense a ruined foreground might turn into a learning obstacle. Finally, I discuss processes of inclusion and exclusion with reference to the notion of foreground. © 2012. The Authors.

Números transcedentes e de Liouville

Pós-graduação em Matemática em Rede Nacional - IBILCE

Teorema de Pitágoras: algumas extensões/generalizações e atividades com o Software GeoGebra

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Considerações históricas sobre o infinito e alguns de seus paradoxos

This research aims to elucidate some of the historical aspects of the idea of infinity during the creation of calculus and set theory. It also seeks to raise discussions about the nature of infinity: current infinite and potential infinite. For this, we conducted a survey with a qualitative approach in the form of exploratory study. This study was based on books of Mathematics' History and other scientific works such as articles, theses and dissertations on the subject. This work will bring the view of some philosophers and thinkers about the infinite, such as: Pythagoras, Plato, Aristotle, Galilei, Augustine, Cantor. The research will be presented according to chronological order. The objective of the research is to understand the infinite from ancient Greece with the paradoxes of Zeno, during the time which the conflict between the conceptions atomistic and continuity were dominant, and in this context that Zeno launches its paradoxes which contradict much a concept as another, until the theory Cantor set, bringing some paradoxes related to this theory, namely paradox of Russell and Hilbert's paradox. The study also presents these paradoxes mentioned under the mathematical point of view and the light of calculus and set theory