A forgotten little chapter on isoperimetric inequalities. On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter

[EN]Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which it shares a diameter, a problem stemming from the theory of isoperimetric inequalities. In this paper such a bound is constructed and shown to be attained for a particular area. It is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle

Analysis of competitiveness in the NBA regular seasons

[EN] Research background and hypothesis. Several attempts have been made to understand some modalities of sport from the point of view of complexity. Most of these studies deal with this phenomenon with regard to the mechanics of the game itself (in isolation). Nevertheless, some research has been conducted from the perspective of competition between teams. Our hypothesis was that for the study of competitiveness levels in the system of league competition our analysis model (Shannon entropy), is a useful and highly sensitive tool to determine the degree of global competitiveness of a league. Research aim. The aim of our study was to develop a model for the analysis of competitiveness level in team sport competitions based on the uncertainty level that might exist for each confrontation. Research methods. Degree of uncertainty or randomness of the competition was analyzed as a factor of competitiveness. It was calculated on the basis of the Shannon entropy. Research results. We studied 17 NBA regular seasons, which showed a fairly steady entropic tendency. There were seasons less competitive (? 0.9800) than the overall average (0.9835), and periods where the competitiveness remained at higher levels (range: 0.9851 to 0.9902). Discussion and conclusions. A league is more competitive when it is more random. Thus, it is harder to predict the fi nal outcome. However, when the competition is less random, the degree of competitiveness will decrease signifi cantly. The NBA is a very competitive league, there is a high degree of uncertainty of knowing the fi nal result.

Correlatos da participação no desporto escolar nos ensinos regular e militar, o papel do sexo, idade, estatuto socioeconómico e das atitudes

[POR] Introdução: Em Portugal, além das aulas de educação física, as escolas oferecem tempos destinados ao desporto escolar (DE), que poderão aumentar os níveis de actividade física dos alunos. Objectivo: Analisar os níveis e os correlatos da participação no DEnos ensinos regular e militar, identificando a su a relação com variáveis sociodomográficas e atitudes.