GEOMETRY OF KERF WHEN CURVE SAWING WITH A CIRCULAR RIP-SAW

Rip-sawing following the curvature of a crooked log means advantages for yield. However, the possibility to saw in a narrow curve with a circular saw blade is limited because of the inherently flat geometry of circular saw blades. For a double arbour circular saw the situation is even more problematic because the two blades have a certain overlap and thus, the two arbours are not positioned in the same horizontal position. In this study, a theoretical geometrical study of the creation of a kerf with a single circular saw blade and with a double arbour circular saw with two saw blades was examined. Results for stiff saw blades show that the kerfs become in general curved and inclined (tilted) in the vertical direction and also that the width of the kerfs for double arbour saws becomes wider at the top and bottom of the cant than in the middle. Additionally, the sawn boards obtain varying thickness along their width because of the varying kerf width. A comparison with experimental thickness data from four test sawings at a sawmill indicates that the theoretical results are valid and that curve sawn boards become thinner than straight sawn boards.

Uma Proposta de Ensino de Geometria Plana com GeoGebra A proposal of teaching of flat geometry with GeoGebra

A presente obra aborda alguns aspectos do surgimento da geometria plana no mundo; Como se deu a inclusão no Brasil, exibindo alguns dos acontecimentos que foram importantes para definir o ensino da geometria plana nas escolas públicas brasileiras. Apresenta um software gratuito de matemática dinâmica, o GeoGebra, desenvolvido para o ensino e aprendizagem nos vários níveis de ensino (do básico ao universitário), mostra um exemplo que pode ser usado em sala de aula da aplicação do GeoGebra: O caso de congruência de triângulo, possibilitando, assim, ao professor ir muito além de qualquer barreira que possa ser colocada para dificultar o ensino/aprendizado dos discentes.

Uma Proposta de Ensino de Geometria Plana com GeoGebra A proposal of teaching of flat geometry with GeoGebra

A presente obra aborda alguns aspectos do surgimento da geometria plana no mundo; Como se deu a inclusão no Brasil, exibindo alguns dos acontecimentos que foram importantes para definir o ensino da geometria plana nas escolas públicas brasileiras. Apresenta um software gratuito de matemática dinâmica, o GeoGebra, desenvolvido para o ensino e aprendizagem nos vários níveis de ensino (do básico ao universitário), mostra um exemplo que pode ser usado em sala de aula da aplicação do GeoGebra: O caso de congruência de triângulo, possibilitando, assim, ao professor ir muito além de qualquer barreira que possa ser colocada para dificultar o ensino/aprendizado dos discentes.

O lugar das matemáticas na formação de professores indígenas da região do Alto Solimões/AM

This article approaches the mathematical practices in the Degree Course in Indigenous Teacher Training of the Federal University of Amazonas/Campus of Benjamin Constant, in a context of cultural and linguistic diversity. For reflection on this theme, we take as a starting point the following question: In what formative terms the mathematical practices, through Concrete Material, have repercussions in the ways of teaching and learning of the indigenous students of the group of Alto Solimões/UFAM? In this sense, we aim to describe the different methodological approaches to the teaching and learning of some concepts in the scope of Flat Geometry, together with the indigenous students of the Undergraduate Course in Training of Indigenous Teachers/UFAM. The study has a qualitative approach based on ethnographic research, with the collection and analysis of information: impressions, perceptions and episodes with employees, as well as interdisciplinary, intracultural and intercultural activities enhanced in the understanding of some concepts of Flat Geometry, with emphasis on the baskets of the Ticuna artisans. Our reflections show, among other things, the acquisition of new knowledge, the creation, elaboration and proposition of different activities and mathematical practices for the future teaching actions in the schools of their communities.

Surface Forces Derived from Surface Energies

As it more practical to measure the forces acting between two contacting surfaces then the energies of surfaces, this chapter covers those surface forces that are derived from surface energies. The starting point is Derjaguin’s approximation, which relates the energy between two flat surfaces to the force in other geometries: sphere/flat, sphere/sphere, and crossed cylinders. Next is a discussion of the surface forces in dry contacts with no liquid menisci around the contact points. This discussion covers the cases where adhesion causes significant deformation (JKR theory), where deformation is insignificant (DMT theory), and the cases in between. How surface roughness impacts adhesion is also discussed. The second half of this chapter deals with how liquid menisci around contacts contribute to adhesion forces, both for the sphere-on-flat geometry and for contacting rough surfaces.

The geometry of corank 1 surfaces in ℝ4

We study the geometry of surfaces in ℝ4 with corank 1 singularities. For such surfaces, the singularities are isolated and, at each point, we define the curvature parabola in the normal space. This curve codifies all the second-order information of the surface. Also, using this curve, we define asymptotic and binormal directions, the umbilic curvature and study the flat geometry of the surface. It is shown that we can associate to this singular surface a regular one in ℝ4 and relate their geometry.

Uma experiência de Geometria Plana com Tecnologias no ensino básico: um olhar a partir da Teoria de Van Hiele

Resumo: O presente artigo tem como objetivo apresentar e analisar os resultados de uma sequência de atividades desenvolvidas no software GeoGebra e feitas com estudantes do Ensino Médio. O conteúdo desenvolvido nas atividades foi o de Geometria Plana com ênfase em polígonos e quadriláteros notáveis. O artigo tece também reflexões sobre como a tecnologia pode potencializar e auxiliar o professor no ensino da Geometria. As atividades desenvolvidas tiveram o aporte teórico no modelo de pensamento geométrico de Van Hiele e a utilização dos recursos tecnológicos em sala de aula está fundamentada em uma perspectiva teórica conforme os autores estudados. A reflexão aqui apresentada é fruto de um estudo qualitativo, no qual se utilizou o software GeoGebra como recurso tecnológico. Como intuito de averiguar o desenvolvimento de competências e habilidades geométricas foi realizado com a turma durante o experimento de ensino um pré-teste e um pós-teste. A título de conclusão infere-se que o experimento de ensino possibilitou aos estudantes avançar progressivamente na construção de conhecimentos sobre polígonos e quadriláteros notáveis; e ao professor-pesquisador, refletir sobre a qualidade do ensino da geometria quando se integram recursos tecnológicos ao fazer docente.Palavras-chave: Geometria. Ensino. Aprendizagem. Tecnologias Digitais. An Experience of Flat Geometry with Technologies in Basic Education: a Look from the Van Hiele Theory Abstract: The present article aims to present and analyze the results of a sequence of activities developed in GeoGebra software and made with high school students. The content developed in the activities was that of Flat Geometry with emphasis on polygons and remarkable quadrilaterals. The article also discusses how technology can enhance and assist teachers in the teaching of Geometry. The activities developed had the theoretical contribution in the Van Hiele geometric thinking model and the use of technological resources in the classroom is based on a theoretical perspective according to the authors studied. The reflection presented here is the result of a qualitative study, in which GeoGebra software was used as the technological resource. In order to ascertain the development of geometric skills and abilities, a pre-test and a post-test were performed with the class during the teaching experiment. As a conclusion, it is inferred that the teaching experiment made it possible for the students to progress progressively in the construction of knowledge about remarkable polygons and quadrilaterals; and the teacher-researcher, reflect on the quality of geometry teaching when integrating technological resources when making teachers. Keywords: Geometry. Teaching. Learning. Digital Technologies.