Estudo histórico e pedagógico sobre ternos pitagóricos à luz de eugène bahier

At the present investigation had the purpose to achieve a descritive analysis pedagogy in the work of Recherche méthodique et propriétés des triangles rectangles en nombres entiers. According to the analysis achieved, we made and applyed the teaching module called Pitagories: one of tools to comprehension Pitagory Theorema, there were studying by public students in mathematic course in the UFRN , the new mathematic teachers in future. The analysis the was made with writen test the was showed that all students got the view comprehension in the teaching approach module, to apointed the difference in the learning qualytative with other reseach that was made with quastionaire and enterview. With this module that was made with the new future teacheres there was more attention the better comprehension with the Pitagory Theorema, that was good focus in the pitagory about the potential historical pedagogyc in the work studied.

Atribuição de significado ao conceito de proporcionalidade: contribuições da história da matemática

This study is the result of a work which approaches the Mathematics History how source of the meaning s attribution in the proportionality concept. We adopt the methodology of the source qualitative and we work with a group of teachers from instruction s public system of the fundamental and medium level from Pocinhos City Paraíba. For the data collection, we use the field notes, the questionnaire, a sequence of activities and the interview semistructured like instruments. The study had how objective to know the significates attributeds to proportionality concept through of the activity mediate from Mathematics History, besides to investigate if a approach of the nature enables modification according to this sense. The results obtaineds though the data analysis indicate that the activities bring contributions which refer to achieve objectives. On the other hand they also showed that we have a long trajectory to be trailed in the meaning of to turn the Mathematics History a subsidy effective in the teachers practice, in view of the formation absence in the knowledge area, besides the necessity of the approach adequated of the Mathematics History in the didatics books of Mathematic

Um estudo sobre o ensino-aprendizagem das demonstrações matemáticas

Demonstrations are fundamental instruments for Mathematics and, as such, are frequently used by mathematicians, math teachers and students. In fact, demonstrations are part of every Mathematics teaching environment, because Mathematics considers something true when it can be demonstrated. This is in contrast to other fields of knowledge that employ observation and experimentation to validate truth. This dissertation presents a study of the teaching and learning of demonstrations in Mathematics, describing a Teaching Module applied in a course on the Theory of Numbers offered by the Mathematics Department of the Universidade Federal do Rio Grande do Norte for mathematics majors. The objective of the dissertation was to propose and test a Teaching Module that can serve as a model for teaching demonstrations. The Teaching Module consisted of the following five steps: the application of a survey to determine the students‟ profiles and their previous knowledge of mathematical language and techniques of demonstration; the analysis of a series of dialogues containing arguments in everyday language; the investigation and analysis of the structure of some important techniques of demonstration; a written assessment; and, finally, an interview to further verify the principal results of the Teaching Module. The analysis of the data obtained though the classroom activities, written assessments and interviews led to the conclusion that there was a significant amount of assimilation of the issue at the level of relational understanding, (SKEMP, 1980). These instruments verified that the students attained considerable improvement in their use of mathematical language and of the techniques of demonstration presented. Thus, the evidence supports the conclusion that the proposed Teaching Module is an effective means for the teaching/learning of mathematical demonstration and, as such, provides a methodological guide which may lay the foundations for a new approach to this important subject

Vídeo-aula de história da matemática: uma possibilidade didática para o ensino de matemática

In this work we are disagreeing with the possibility of production and of the use of video-class for the disciplines of history of mathematics by the teachers of elementary e middle school as a way to contribute to the development of their classes. Our goal is to provide to the mathematics teachers the option of connecting social, scientific, cognitive, and didactic aspects of topics in math thoughts to their students. That shall be based in the presence of mathematics in the history of humanity. Thus, we consider possible that teachers and their students can link and relate mathematics to other sciences, education culture, and reflect about the many ways of represent them, as well as the patters of organization of nature and of culture. In this way, they shall be able to observe and interpret situations that involve mathematical questions associated to the various means of historic-epistemological studies already done by other researchers and scholars in the field of history of mathematics who works in creating video-classes. In addition to that, we can use all the available media in order to give edifying dynamics to the mathematical formulations established throughout history. In this sense, we are based and focused on the objectives, which are sustained by educational computer technology, techniques for video making, as well as mathematical teaching proposals and the historical inquiring made by Mendes (2001, 2009a, 2009b). The validating experimentation allowed us to conclude that the techniques we used in the production of the history of mathematics video-classes proved they to be valid ones. They are able to be executed with the minimum of technological resources. In addition, they have the same efficacy as far as classroom use

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

Elaboração de uma sequência didática sobre os conceitos geométricos preliminares ao estudo da trigonometria

This study is qualitative, including literature search and preparation of teaching materials. Your goal is to report the study of geometric problems of character presented in the application of trigonometry and work on the preparation of detailed activities that help in overcoming these difficulties. For this, we read some papers on teaching and learning of trigonometry in order to identify the difficulties encountered during their journey. Then separate the geometric difficulties of character and prepare a list of geometric content and procedures associated with them. Thus, we can organize a notebook with activities that would address most of these concepts. Finally we present the specification of activities called Activity on introductory concepts to the study of trigonometry

Os artigos de Euler sobre os números amigáveis

Among the many methodological resources that the mathematics teacher can use in the classroom, we can cite the History of Mathematics which has contributed to the development of activities that promotes students curiosity about mathematics and its history. In this regard, the present dissertation aims to translate and analyze, mathematically and historically, the three works of Euler about amicable numbers that were writed during the Eighteenth century with the same title: De numeris amicabilibus. These works, despite being written in 1747 when Euler lived in Berlin, were published in different times and places. The first, published in 1747 in Nova Acta Eruditorum and which received the number E100 in the Eneström index, summarizes the historical context of amicable numbers, mentions the formula 2nxy & 2nz used by his precursors and presents a table containing thirty pairs of amicable numbers. The second work, E152, was published in 1750 in Opuscula varii argument. It is the result of a comprehensive review of Euler s research on amicable numbers which resulted in a catalog containing 61 pairs, a quantity which had never been achieved by any mathematician before Euler. Finally, the third work, E798, which was published in 1849 at the Opera postuma, was probably the first among the three works, to be written by Euler

Utilizando as ciências espaciais e a astronáutica na construção de atividades práticas em ensino de física

In this work we consider the use of new technologies fron the Space Science and Astronautical, in the learning process, incorporating technical and conceptions of physics Spatial what can take on the response of some problems what there are a lot insistent in populate the mind of professors and followers regarding agreement of these conceptions into the level Average. Intending to bring another contribution to Physics teaching practice, especially Classical Mechanics, but introducing many introductory concepts from Modern Physics, since this topic is considered of great interest for teachers and students, for it involves high technology. It s advanced manufacturing demand certain processes that make possible the application of those concepts

Imunoexpressão das claudinas -1 e -7 em ameloblastomas e germes dentais humanos

We investigated the immunohistochemistry expression of claudins -1 and -7 in ameloblastoma and in human dental germs on the pattern of distribution (focal, regional or diffuse), the cells that expressed (if central or peripheral) and the location of that expression in the cell components recital membrane, cytoplasm and nucleus. Among the 29 cases of ameloblastoma, 24 were type solid and 6 unicystic. In 7 mandibular specimens of human fetuses found dental germs from the stage of bud to the crown. We note that the pattern of expression in the dental germs was variable for claudinas studied according to the cell type and stage of differentiation and was invariate only in the cells of stellate reticulum. In epithelium internal of enamel organ, claudin-1 has been decreasing with the progression of differentiation as to claudina-7 that was found in the cells of the peripheral papilla. For ameloblastoma the expression was more significant than that observed in dental germs. Fisher s exact test no found association between the expression of claudinas cells in central and peripheral and the type of ameloblastoma (solid or unicystic). Thus, in general the claudin-1 was positive in the central cell of 93,1% of the cases and in peripheral cells of 51,7%. The claudin-7 was expressed in the cells of all cases central and peripheral cells from 89,7%. For both claudins the distribution was predominantly diffuse cells both in central and peripheral cells. Given our findings it is suggested that the expression of claudins may be indicative of the involvement of these molecules in morphogenetics events culminating with the dental development and that possibly influence the development of neoplastic ameloblastoma

Resposta celular Th1 /Th2 na doença periodontal experimental, em ratos: um estudo imuno-histoquímico

Host response plays a major role in the pathogenesis of periodontal disease. Mediators such as inflammatory cytokines which are secreted during the immune response to bacterial challenges have ambiguous functions that may or may not lead to protection of the attacked tissue. In this context, experimental evidence suggests that T-helper 1 (Th-1) and T-helper 2 (Th-2) mediated responses are potentially important during the disease process. The aims of this study therefore were to further clarify the role played by Th2 cells during different time points of the active phase of periodontal disease, as well as, to investigate whether there was any evidence of a Th1 response in the periodontal disease microenvironment. Experimental periodontitis was induced in 30 Wistar male rats by placing cotton ligatures around the mandibular first molars. The rats were then randomly divided into two groups. Group1 (G1=15) and Group 2 (G2=15). In G1 the ligatures were maintained for 2 days, whereas in G2 the ligatures were left for 15 days, a time point that corresponds to the advanced stage of periodontal disease The contra-lateral teeth served as controls (no ligatures). Immunohistochemical investigation for the presence in gingival tissue of Th2 specific transcription factor (GATA3) and the subunit of the IFN-γ receptor was carried out after the disease induction period. Light microscopy analysis revealed a decrease in the expression of GATA-3 as bone loss progressed. On the other hand, although IFN-γ R1 was detected at an early stage of the active phase of disease its expression remained unaltered during the remaining period of the study. These results indicate that the Th2 response have a protective role during the pathogenesis of periodontal disease and that the progression of the periodontal disease is related with the unbalance of the responses Th1/Th2

Análise comparativa na influência da técnica de moldagem funcional em arcos parcialmente edêntulos sobre os pontos de contato oclusais, a integridade da fibromucosa e a extensão da base da prótese

There is a lack of clinical studies evaluating techniques of functional impression for partially edentulous arches. The aim of this double-blind non-randomized controlled clinical trial was to compare the efficacy of altered cast impression (ACI) and direct functional impression (DFI) techniques. The efficacy was evaluated regarding the number of occlusal units on denture teeth, mucosa integrity at 24-hour follow-up and denture base extension. The sample included 51 patients (female and male) with mean age of 58.96 years treated at Dental Department of UFRN. The patients, exhibiting edentulous maxilla and mandibular Kennedy class I, were divided into two groups (group ACI, n=29; group DFI, n=22). Clinical evaluation was based on the number of occlusal units on natural and/or artificial teeth, mucosa integrity at 24-hour follow-up, and denture base extension. Statistical analysis was conducted using the software SPSS 17.0® (SPSS Inc., Chicago, Illinois). Student T-test was used to reveal association between number of occlusal units and impression technique while chi-square test showed association between mucosa integrity and impression technique. Fischer s exact test was applied for association between denture base extension and impression technique at 95% level of significance. No significant difference was observed between the groups regarding number of occlusal units, mucosa integrity and denture base extension. The altered cast technique did not provide significant improvement in comparison to the direct technique when the number of occlusal units, mucosa integrity and denture base extension

Avaliação mecânica in vitro utilizando miniplacas quadradas e retangulares do sistema 2.0 mm em fraturas da região anterior de mandíbula

The aim of this study was to comparatively evaluate the mechanical strength of squared and rectangular 2.0 mm system miniplates comparing them to the standard configuration with 2 straight miniplates in stabilizing fractures in the anterior mandible. Ninety synthetic polyurethane mandible replicas were used in mechanical test. The samples were divided into six groups of three different methods for fixation. Groups 1, 2 and 3 showed complete fractures in symphysis, characterized by a linear separation between the medial incisor, and groups 4, 5 and 6 showed complete fractures in parasymphysis with oblique design. Groups 1 and 4 were represented by the standard technique with two straight miniplates parallel to each other. Groups 2 and 5 were stabilized by squared miniplates and groups 3 and 6 were fixed by rectangular design. Each group was subjected to a mechanical test at a displacement speed of 10 mm/min on a universal testing machine, receiving linear vertical load on the region of the left first molar. The values of the maximum load and when displacements reached 5 mm were obtained and statistically analyzed by calculating the confidence interval of 95%. Fixation systems using squared (G2) and rectangular (G3) miniplates obtained similar results. No statistically significant differences with respect to the maximum load and the load at 5 mm displacement were found when compared to standard method in symphyseal fractures (G1). In parasymphysis the fixation method using squared miniplates (G5) obtained results without significant differences regarding the maximum load and the load at 5 mm when compared to the standard configuration (G4). The fixation method using rectangular miniplates (G6) showed inferior results which were statistically significant when compared to the standard configuration (G4) for parasymphysis fractures. The mechanical behavior of the fixation methods was similar, except when rectangular miniplates were used. The fixation methods showed better results with statistical significance in symphyseal fractures

Eficiência mastigatória e impacto da saúde oral na qualidade de vida em pacientes reabilitados com próteses totais removíveis implanto-suportadas

Edentulous patients with complaint about mandibular conventional denture might experience poor masticatory function and negative impact of oral health on quality of life. The aim of this controlled clinical trial was to evaluate the effect of mandibular overdenture on oral health-related quality of life and masticatory efficacy in patients wearing mandibular complete dentures. The edentulous patients (n=16) were rehabilitated with new maxillary and mandibular complete dentures and, after 3 months, mandibular overdentures retained by 2 implants (bar-clip system) were fabricated. The Brazilian version of OHIP-Edent questionnaire was used to assess the oral healthrelated quality of life. Masticatory efficacy was evaluated through a colorimetric method with chewing capsules. The mean OHIP-Edent score was 8.5 with conventional dentures and 2.0 with mandibular overdenture, which means a positive impact of oral health on quality of life with overdentures (p=0.001). The mean absorbance for masticatory efficacy was 0.025 for conventional dentures and 0.073 for overdentures. There was statistically significant difference for masticatory efficacy before and after implants rehabilitation (p=0.003). However, there was no correlation between masticatory efficacy and OHIP (p>0.05). So, mandibular overdenture retained by 2 implants improved the quality of life and masticatory efficacy of edentulous patients with complaint about mandibular conventional complete dentures

Falhas e complicações com o uso de prótese parcial removível inferior de extremidade livre bilateral

Aim: To determine the frequency and type of complications related to removable partial denture (RPD) less, Kennedy Class I, over time . Materials and Methods: This observational study consisted of a sample of 65 users PPR lower arches in Kennedy Class I and dentures, rehabilitated in the Department of Dentistry, Federal University of Rio Grande do Norte (UFRN). Patients were followed through periodic controls during periods of 60 days, 6 months and 1 year from installation. After the first year of control had other returns annually. The occurrence of complications or prosthetic failure was observed and recorded in a specific clinical record over 39 months. The patterns of failures observed were classified in the following situations: occurrence of traumatic ulcers after 2 months of installation, lack of retention, fracture or caries in the rest, fracture or dislocation of the artificial teeth, the larger connector fracture, fracture clip fracture support, poor support (need to reline the denture) and prosthesis fracture. Results: The incidence of complications was low frequency, being higher in the second year of use of the prosthesis. Among the complications that occurred more is the loss of retention (31.57%). Failures more severe and difficult to solve as the fracture elements of the metal structure of the PPR had low occurrence and were represented by only one case of the larger connector (5.3%) fractures. Conclusion: Removable partial dentures mandibular free end opposing of the conventional dentures have a low complication rate after 39 months of use when subjected to periodic controls

Avaliação da eficiência da técnica de obturação pela compressão hidrùlica vertical após instrumentação automatizada

The purpose of this study was to evaluate through radiographic and microscopic analysis the efficiency of the filling techniques by vertical hidraulic compression after the root canal mechanical instrumentation in vitro as well to evaluate the marginal apical leakage through macroscopic and microscopic analysis. Thirty human mandibular molars were used , they were divided on three groups, these were subdivided on six subgroups with five specimens each, come down to 106 root canals filled. Initially, the teeth were instrumented with Profile system series 29 and filled with two ways: single accessory cone or single cone associated with gutta-percha secundary cone, with Fill Canal sealer or Sealer 26. Completed the filling, the teeth were coated with araldit and finger -nail polish except for the apical 2 mm and dried for 3 hours, thep radiographs were taken of the teeth in orto and disto-radiai directions. Next, the coronal seal was carried out with composite resin photopolymerized and with their process of making impermeable. Teeth of positive controls were used without araldit and finger-nail polish whereas the negative controls were used with total coat of araldit and finger-nail polish. The specimens were placed in 2% Methylene Blue dye for 24 hours and thermocycled for 7 days. Afterwards, sections were made of each tooth at mesial and distal roat, after this the teeth were radiographed at buccolíngual direction for a macroscopic analysis and at buccolingual and mesiodistal directions for assessment of the marginal apical leakage. Cross sections were made 3 mm to 3mm since the tooth apice. The sections obtained for each group were observed with a stereomicroscope to evaluate the quality of the root canal filling and the marginal apical leakage. The results showed that: In the four techniques the marginal dye leakage was present in the apical third; in all groups the quality of the root canal filling in the radiography was better at mesial root canal and the single cone technique showed inefficient when only a single distal root canal was present. In the radiographic evaluation the best quality of the root canal filling was observed in the 1A group (single accessory cone + FiIl Canal), as in the mesial root as in the distal root wich Shcwed twe root canals: when the distaI root had only one canal. the best result was showed by 28 group (single accessory cone associated with secundary cone + Fill Canal) In the macroscopic analysis of longitudinal !eaKage (outside surface). less leakage was showed as In the mesial root as in the distal root in the negative control group (3) followed 2A group (single accessory cone + Sealer 26). When the microscopic analysis of tranversal leakage of both roots (inside surface) was carried out. the groups that showed less dye leakage were the negative control (38) followed the 28 group (single acessory cone associated with secundary cone + Sealer 26). The homogeneity o filling was best noted in the 1 A group (.single accessoty cone + Fill Canal). The groups that showed less dye penetration in the tranversal leakage (total area) were negative control (3B) and 2B