Corpo, movimento e aprendizagem na psicocinética de Jean Le Boulch

School teachers in the discipline of Physical Education, we find ourselves constantly in question of methodological and epistemological issues of practice. This research aims to identify human body understanding, movement and theoretical learning proposed by examining the work of Jean Le Boulch and his approach to Physical Education. We seek to indicate epistemological elements about Physical Education theory and practice, believing that this approach and dialog comes to contribute with this field of knowledge. Boulch, a French teacher of Physical Education, Medicine and Psychology, had an important influence in Brazilian Physical Education during the 1970s and 1980s. His main contribution was teaching courses and knowledge about psychomotricity. Boulch’s studies helped to build knowledge of human movement; considering his importance in people’s development and a critic to a mechanistic view of body and movement. Our reflections will be based on the concepts brought from psychokinetics presented in the bibliographic references of Le Boulch in Brazil, and other references developed by him in this country including conferences, lectures and interviews. This reflection includes the debaters of his work. We chose a theoretical approach referring to the Phenomenology of philosopher Maurice Merleau-Ponty (1999) as a methodological reference considering the influence of his thought in Le Boulch studies. This thesis examines the learning and practice of teaching the Physical Education field of knowledge. We conclude that the body being an entity that exists for itself in the world and that contact with the world starts from human movement. Ultimately, new trains of thought for the teaching of physical education can be set from the reflection of phenomenological concepts brought by Le Boulch in his theory.

Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem