A geometria do compasso (1797) de Mascheroni (1750 – 1800) em atividades com o GeoGebra

The present work aims to show a possible relationship between the use of the History of Mathematics and Information and Communication Technologies (TIC) in teaching Mathematics through activities that use geometric constructions of the “Geometry of the Compass” (1797) by Lorenzo Mascheroni (1750-1800). For this, it was performed a qualitative research characterized by an historical exploration of bibliographical character followed by an empirical intervention based on use of the History of Mathematics combined with TIC through Mathematical Investigation. Thus, studies were performed in papers dealing with the topic, as well as a survey to highlight problems and /or episodes of the history of mathematics that can be solved with the help of TIC, allowing the production of a notebook of activities addressing the resolution of historical problems in a computer environment. In this search, we came across the problems of geometry that are presented by Mascheroni stated previously in the work that we propose solutions and investigations using GeoGebra software. The research resulted in the elaboration of an educational product, a notebook of activities, which was structure to allow during its implementation, students can conduct historical and/or Mathematics research, therefore, we present the procedures for realization of each construction, followed at some moments by original solution of the work. At the same time, we encourage students to investigate/reflect its construction (GeoGebra), in addition to making comparisons with the solution Mascheroni. This notebook was applied to two classes of the course of Didactics of Mathematics I (MAT0367) Course in Mathematics UFRN in 2014. Knowing the existence of some unfavorable arguments regarding the use of history of mathematics, such as loss of time, it was found that this factor can be mitigated with the aid of computational resource, because we can make checks using only the dynamism of and software without repeating the construction. It is noteworthy that the minimized time does not mean loss of reflection or maturation of ideas, when we adopted the process of historical and/or Mathematics Investigation

Aprendizagem significativa: uma proposta de ensino e aprendizagem da geometria euclidiana espacial no ensino médio

This dissertation is a research based on the Meaningful Learning Theory, with students from the second year of High School, in the city named Capinzal do Norte, state of Maranhão. The pedagogic approach of this research focuses on what to do and how to do so students can better grasp knowledge inherent to the Euclidean Special Geometry in a more meaningful and changing way, also that information may be kept longer in their brain, so it can last longer in the present and future. The methodological strategy adopted was the research-action, followed by the constant observance of a researcher on the matter with the purpose to ensure consistent results, which come from the use of a variety of data collector instruments, such as: Concept Maps, manipulatives, educational softwares and application of evaluative tests, besides the observations made throughout the process of investigation and the diagnosis itself. It is all due to the fact that we rely on the premise that knowledge is assimilated in particular and idiosyncratic ways, which means each and every student learns in different ways and in different periods of time. That is why it is so important to develop diversified methodologies to the same subject. This research adds to the other ones related to the theoretical frameworks of the Meaningful Learning Theory, of Concept Maps, of the use of technology on the educational process and of manipulatives, which purpose is to connect their common dots. This pedagogical intervention also focuses on the construction of the educational orientations with applicability directly on class, directed specially by the Mathematics teacher of the basic education, who might use them during your teaching practice. Such guidelines established here as an educational product aim to follow the Theory's assumptions that serves as basis to this research, thus becoming an educational element with a relevant significance. The results, with which we are faced, proved overwhelming to the proposed objectives in terms of learning, which were evident in the construction of Conceptual Maps, as well as in the use of Concrete Materials, in addition to serving as a motivational element to participating students of research. The results obtained are indeed reliable in terms of learning, considered the expected goals, and made us certain that the way we have approached the subject is consistent with a holistic education and that at the same time values the tiniest details, which are fundamental to all the learning-teaching process.

Efeito da geometria do implante dentário e do protocolo de fresagem óssea na estabilidade primária e na osseointegração inicial: estudo experimental em cães

CHAPTER 1 - This study histologically evaluated two implant designs: a classic thread design versus another specifically designed for healing chamber formation placed with two drilling protocols. Forty dental implants (4.1 mm diameter) with two different macrogeometries were inserted in the tibia of 10 Beagle dogs, and maximum insertion torque was recorded. Drilling techniques were: until 3.75 mm (regular-group); and until 4.0 mm diameter (overdrillinggroup) for both implant designs. At 2 and 4 weeks, samples were retrieved and processed for histomorphometric analysis. For torque and BIC (bone-to-implant contact) and BAFO (bone area fraction occupied), a general-linear model was employed including instrumentation technique and time in vivo as independent. The insertion torque recorded for each implant design and drilling group significantly decreased as a function of increasing drilling diameter for both implant designs (p<0.001). No significant differences were detected between implant designs for each drilling technique (p>0.18). A significant increase in BIC was observed from 2 to 4 weeks for both implants placed with the overdrilling technique (p<0.03) only, but not for those placed in the 3.75 mm drilling sites (p>0.32). Despite the differences between implant designs and drilling technique an intramembranous-like healing mode with newly formed woven bone prevailed. CHAPTER 2 - The objective of this preliminary histologic study was to determine whether the alteration of drilling protocols (oversized, intermediate, undersized drilling) present different biologic responses at early healing periods of 2 weeks in vivo in a beagle dog model. Ten beagle dogs were acquired and subjected to surgeries in the tibia 2 weeks before euthanasia. During surgery, 3 implants, 4 mm in diameter by 10 mm in length, were placed in bone sites drilled to 3.5 mm, 3.75 mm, and 4.0 mm in final diameter. The insertion and removal torque was recorded for all samples. Statistical significance was set to 95% level of confidence and the number of dogs was considered as the statistical unit for all comparisons. For the torque and BIC and BAFO, a general linear model was employed including instrumentation technique and time in vivo as independent. Overall, the insertion torque increased as a function of drilling diameter from 4.0 mm, to 3.75 mm, to 3.5 mm, with a significant difference in torque levels between all groups (p<0.001). Statistical assessment of BIC and BAFO showed significantly higher values for the 3.75 mm (recommended) drilling group was observed relative to the other two groups (p<0.001). Different drilling dimensions resulted in variations in insertion torque values (primary stability) and different pattern of healing and interfacial remodeling was observed for the different groups. CHAPTER 3 - The present study evaluated the effect of different drilling dimensions (undersized, regular, and oversized) in the insertion and removal torques of dental implants in a beagle dog model. Six beagle dogs were acquired and subjected to bilateral surgeries in the radii 1 and 3 weeks before euthanasia. During surgery, 3 implants, 4 mm in diameter by 10 mm in length, were placed in bone sites drilled to 3.2 mm, 3.5 mm, and 3.8 mm in final diameter. The insertion and removal torque was recorded for all samples. Statistical analysis was performed by paired t tests for repeated measures and by t tests assuming unequal variances (all at the 95% level of significance). Overall, the insertion torque and removal torque levels obtained were inversely proportional to the drilling dimension, with a significant difference detected between the 3.2 mm and 3.5 mm relative to the 3.8 mm groups (P < 0.03). Although insertion torque–removal torque paired observations was statis- tically maintained for the 3.5 mm and 3.8 mm groups, a significant decrease in removal torque values relative to insertion torque levels was observed for the 3.2 mm group. A different pattern of healing and interfacial remodeling was observed for the different groups. Different drilling dimensions resulted in variations in insertion torque values (primary stability) and stability maintenance over the first weeks of bone healing.

Estratégias de trabalho com blogs no ensino de geometria em turmas de 5° ano do ensino fundamental

This paper presents a survey conducted through collaborative work, which took place in a suburb school in the city of Uberlandia-MG. The research is characterized as case study and has a qualitative approach. Had the objective to look for different strategies of teaching and learning through the use of technology in pedagogical practice. Regarding the methodology in this research, we analyzed the work with the support of blogs, whose pages were used for student records and discussions directed to the geometry content. The students who were attending the fifth (5th) year of elementary school were invited to participate in this project. However, the research subjects were only those students who accepted the invitation to participate in the study through statement signed by parents. The project was developed with 30 students in the second half of 2014 and another 30 in the first half of 2015. The physical space at school, where most of the project activities were done was at the computer lab. In the process of compiling the data, at school, the following instruments were used: field notes produced by the entire project team, photographs and footage of the activities produced in the computer lab and in classroom (recorded by the research team) questionnaires, interviews, virtual space records: the blogs. The results of this research mainly focused on the analysis of the fifth year student‟s productions records in blogs. Regarding the conclusion, the research has shown that blogs, software and differentiated dynamic studies attracted the student‟s attention, leaving them mostly instigated by the unknown. Gradually, students built their own knowledge from their mistakes and successes. The entire work process enabled the computer lab to be an environment that is used not just to solving computerized and tedious drills. The blogs production work in groups, developed in students the reading and writing of both the mother language as symbols and mathematical nomenclature. The interaction between students became noticeable throughout the project, since it provided the student‟s personal growth, respect, tolerance and mutual cooperation. In this sense, we concluded that the project greatly contributed to the students' literacy process in the mother language, mathematics and computer literacy.

Studio di un'imbarcazione a motore dotato di foiling a geometria variabile

Il presente elaborato tratta la progettazione preliminare di un’imbarcazione dotata di foils a geometria variabile. In particolare, il progetto riguarda un’imbarcazione da turismo che, sfruttando l’utilizzo di appendici al di sotto dello scafo, emerga completamente dall’acqua permettendo l’abbattimento della resistenza e consentendo il raggiungimento di velocità elevate anche mediante una motorizzazione modesta. A questo scopo sono state esaminate alcune componenti al fine di raggiungere gli obbiettivi proposti. In primo luogo, è stata fatta un’analisi dei concorrenti per avere un confronto con altre realtà già presenti sul mercato. In seguito, è stata eseguita una stima fondamentale per ogni parte del progetto successiva. La riduzione del peso dell’imbarcazione consente alla stessa di raggiungere velocità più elevate. Per tale ragione sono state discussi due possibili modelli dell’imbarcazione ovvero una con lo scafo costituito completamente da carbonio, l’altro costituito da un sandwich di carbonio e termanto. In seguito si è analizzata l’analisi statica dell’imbarcazione per cercare di comprendere se i pesi stimati in precedenza consentissero al natante di avere un assetto corretto. Alla luce delle predette risultanze, si sono affrontate le tematiche più complesse: l’analisi della resistenza all’avanzamento e lo studio delle appendici che permettano il foiling. Per quanto attiene l’analisi della resistenza si sono dovuti considerare sia il caso di avanzamento in dislocamento e planata sia il caso di avanzamento in foiling. Per il raggiungimento del foiling è stato necessario dimensionare le ali da applicare all’imbarcazione. Innanzitutto è stata eseguita un’analisi idrodinamica e in seguito un’analisi dell’equilibrio dell’imbarcazione, considerando tutte le sollecitazioni applicate. Infine, sono stati generati dei layout possibili per i foils in modo che tutte le caratteristiche determinate precedentemente sulla base degli studi fossero rispettate.

Geometria espacial no ensino médio: sugestões de atividades e avaliações para o conteúdo de prismas e pirâmides

Este Trabalho de Conclusão de Curso sugere uma sequência de atividades para desenvolver conteúdos de Geometria Espacial, particularmente prismas e pirâmides, com alunos do Ensino Médio, priorizando a visualização dos sólidos no espaço, identificando as diferenças quanto ao formato e às características de seus elementos, sem a necessidade de memorização de fórmulas. Enfatiza-se também a importância da recapitulação de conceitos da Geometria Plana e da forma de avaliar a aprendizagem. A cada ano que passa, os alunos estão encontrando cada vez mais dificuldades na Matemática Básica e isto tem consequência direta na aprendizagem por parte desses alunos nos conteúdos relativos ao Ensino Médio. Muitas vezes os alunos conseguem entender o que o professor explica, mas não conseguem resolver os exercícios. Para verificar a veracidade desta afirmação, foi realizada uma pesquisa através de um questionário com professores que trabalham com Geometria Espacial em sete escolas de Ensino Médio da cidade de Rio Grande, RS. Este trabalho pretende sugerir atividades simples que introduzem e complementam o conteúdo que encontra-se nos livros didáticos tradicionais, que os professores, mesmo com poucos recursos, podem realizar com seus alunos no sentido de tentar contornar essas dificuldades. Pretende-se também ressaltar a importância da exigência por parte dos professores por ocasião de suas avaliações, a fim de que seja preservada a qualidade do ensino.

Uma introdução à geometria projetiva para o ensino fundamental

A Geometria Projetiva é o ramo da matemática que estuda as propriedades geométricas invariantes de uma projeção. Ela surge no século XVII da tentativa de compreender matematicamente as técnicas de desenho em perspectiva empregadas pelos artistas da Renascença. Por outro lado, a Geometria Descritiva também se utiliza de projeções para representar objetos tridimensional em um plano bidimensional. Desta forma, a Geometria Projetiva dialoga com o desenho artístico através das regras de perspectiva, e com o desenho técnico através da Geometria Descritiva. A partir das relações entre estes três campos do conhecimento, elaboramos uma proposta didática para o ensino da Geometria Projetiva a alunos do 9 ∘ ano do ensino fundamental. Este trabalho apresenta esta proposta e busca embasá-la matematicamente, relacionando-a aos principais fundamentos da Geometria Projetiva.

Proposta de ensino de geometria euclidiana plana para o sexto ano do ensino fundamental sob a ótica do raciocínio lógico-dedutivo

This study will introduce a brief history of the Geometry development, focused in the appearing of the organization in the logical deductive structure achieved by Euclid. Following will be discussed the situation of the learning and teaching of geometry topics since antiquity until the present day, where we will notice that it does not happen with the logical-deductive perspective. After this contextualization, we will propose the realization of a geometry workshop for students of the sixth grade of elementary school, focusing to the development of logical-deductive reasoning. Applied to workshop, changes were observed in the organization of thought of the participating students in the research, furthering the understanding of the concepts and properties of flat euclidean geometry.

Currículo universitário: da geometria cartesiana à relatividade einsteiniana

A dimensão das questões curriculares, no ensino superior universitário, transcende, cada vez mais, os tradicionais, mas de crescente complexidade, campos do ensino e da aprendizagem. Na Universidade, para além de se ensinar e aprender, também se vive. Vive-se um dos períodos mais marcantes das vidas de cada um: a época em que se é jovem adulto. A uma organização curricular, institucionalmente ortodoxa, baseada na rigidez dos planos de estudo, dos horários e locais de trabalho e dos conhecimentos a adquirir, contrapõe-se, cada vez mais, uma procura personalizada de produtos educativos personalizados, flexíveis e adaptáveis às características, necessidades e contextos de quem os procura. O design curricular, no âmbito universitário, deverá caminhar no sentido da decrescente rigidez organizacional e da crescente flexibilidade (conferindo maior possibilidade de escolha do que se quer aprender) nunca abdicando das necessárias condições uniformizadas de certificação, que se constituem uma condição indispensável para o reconhecimento académico, profissional e social da formação recebida e/ou construída na Universidade. A presente comunicação pretende dar um contributo para a necessária reflexão que urge fazer sobre a missão da Universidade dos nossos dias.

A Geometria (Alentejana) do Desenvolvimento

Pensar, falar e promover o Desenvolvimento no Alentejo é um exercício de geometria particular. Neste espaço e tempo geográficos, humanos e sociais em que o Alentejo vive, é absolutamente fundamental pensar-se e falar-se acerca do Desenvolvimento, ao mesmo tempo que este vai acontecendo com as especificidades próprias e peculiares de cada canto desta região.

Contribuição do origami para a exploração de conteúdos de geometria no ensino básico: propostas de tarefas

A arte de dobrar papel teve origem na China no século I ou II d.C., e difundiu-se pelo Japão no século VI. Esta arte milenar tem cativado a atenção dos estudiosos ao longo de séculos. Inicialmente ligada ao culto religioso, adoptada posteriormente pelos samurais como entretenimento, é hoje mundialmente aceite como uma arte. Transmitido de mães para filhas durante gerações, foi no século XIX, pela mão do pedagogo Frõebel, introduzido no currículo escolar alemão, sendo desde então considerado por muitos como um instrumento primordial na aquisição de conhecimentos, especialmente na área a geometria e por outros um elemento básico de interdisciplinaridade. Este trabalho pretende demonstrar as potencialidades do Origami como instrumento essencial nas diversas áreas curriculares, especialmente no estudo de conceitos matemáticos, nomeadamente no âmbito da geometria e a sua inclusão no currículo escolar. O uso do Origami na sala de aula inspira curiosidade e motiva a criatividade. ABSTRACT: The art of paper folding arose in China during the first or second century A.D. By the sixth century, it had spread to Japan. This millenary art got the scientific community's attention for centuries. At the beginning, folding was associated with a ceremonial act, later on it was use by Samurais as entertainment, and today it is accepted as an art by all. Transmitted from mothers to children during generations, it was introduced by Frõebel in the German curriculum and since then has been considered by some as an instrument for teaching basic geometry and by others as essential in interdisciplinary concepts. With this work we would like to show the Origami potentialities as an instrument connecting different curriculum areas, especially in mathematics, particularly in geometry and his inclusion in education curriculum. The use of Origami in the classroom helps children to obtain and consolidate basic concepts and inspire curiosity and promote their creativity.

Plásticos reforçados a base de tecidos híbridos: efeitos da anisotropia e geometria normativa na caracterização mecânica e da fratura

As most current studies, reinforced plastics have been, in recent years, a viable alternative in building structural elements of medium and large, since the lightness accompanied by high performance possible. The design of hybrid polymer composites (combination of different types of reinforcements) may enable structural applications thereof, facing the most severe service conditions. Within this class of composite materials, reinforced the underlying tissues hybrid high performance are taking space when your application requires high load bearing and high rigidity. The objective of this research work is to study the challenges in designing these fabrics bring these materials as to its mechanical characterization and fracture mechanisms involved. Some parameters associated with the process and / or form of hybridization stand out as influential factors in the final performance of the material such as the presence of anisotropy, so the fabric weave, the process of making the same, normative geometry of the specimens, among others. This sense, four laminates were developed based hybrid reinforcement fabrics involving AS4 carbon fiber, kevlar and glass 49-E as the matrix epoxy vinyl ester resin (DERAKANE 411-350). All laminates were formed each with four layers of reinforcements. Depending on the hybrid fabric, all the influencing factors mentioned above have been studied for laminates. All laminates were manufactured industrially used being the lamination process manual (hand-lay-up). All mechanical characterization and study of the mechanism of fracture (fracture mechanics) was developed for laminates subjected to uniaxial tensile test, bending in three and uniaxial compression. The analysis of fracture mechanisms were held involving the macroscopic, optical microscopy and scanning electron microscopy

Para todo contenido de geometria plana: ¿existiran movimientos que lo sistematizan?

Este trabajo recoge algunos ejercicios de una colección para sistematizar contenidos de geometría plana, manteniendo vigente en todos, el concepto de movimiento. De acuerdo con las sugerencias de la investigación “Cómo transcurre la línea directriz geometría en secundaria básica”, se proponen ejercicios, sin complicaciones extremas, donde se crean condiciones para la creatividad de los alumnos pues, son de respuestas abiertas y los maestros los pueden utilizar para la creación de otros y elevar el protagonismo de los educandos.

Da geometria dos fibrados vectoriais com métricas esfericamente simétricas

Apontamento sobre a construção de métricas com simetria esférica em fibrados vectoriais riemannianos sobre variedades riemannianas.

Curiosidades historiográficas: un hondureño le escribe a Marx en 1872

IntroducciónHace poco, un colega historiador, me hizo llegar una copia de una carta que su tutor de estudios en Barcelona, a su vez, pusiera en sus manos. La carta en cuestión es una de esas curiosidades histográficas que, en el trayecto de la labor de archivo, a veces, se tiene suerte de encontrar. en ocaciones, tales hallazgos pueden conducir a trabajos de excepcional importancia, como sucedió a Carlos Guinzburg en una comunidad.