Motivation och attityderna gentemot matematik är avgörande för elevernas lärande och prestatiner. Forskning visar att bristande motivation och negativa attityder kan leda till minskat intresse samt sämre resultat i ämnet. Trots att detta äv välkännt finns det fortfarande en utmaning för lärare att skapa en stimulerande och engagerande undervisningsmiljö som främjar positiva attityder och ökar motivationen hos eleverna. Denna studie syftar till att utforska hur lärare väljer och använder didaktiska metoder för att öka motivationen och uppmuntra positiva attityder i matematikundervisningen på mellanstadiet. Studiens teoretiska utgångspunkt har i resultat tolkats uttifrån en fenomenografisk metod och därefter applicerat tematisk analys för att systematiskt analysera den insamlade data. Med kvalitativa metoder bestående av semistrukturerade och strukturerade intervjuer  med matematiklärare udnersöker studien olika strategier som används för att engagera elevernas motivation gentemot matematik. Resultaten betonar en stödjande och inkluderande miljö där lärare spelar en avgörande roll för att forma elevernas attityder samt motivation. Genom att förstå dynamiken mellan ämnet, läraren och eleverna strävar studien efter att erbjuda insikter i hur lärare kan anpassa undervisningsmetoder för att främja en gynnsam miljö för matematikinlärning.

En chirurgie vasculaire, l’accès à l’artère fémorale, qu’il soit par une incision chirurgicale ou par une approche percutanée, est très fréquemment utilisé pour une multitude d’interventions vasculaires ou endovasculaires; pour des pontages divers, le traitement d’occlusions artérielles, la réparation d’anévrismes et la pose d’endoprothèses. L’objectif général de ce projet de recherche est de faciliter et réduire les risques des approches de l’artère fémorale par une meilleure compréhension anatomique du triangle fémoral. La méthodologie a été réalisée grâce à l’utilisation de cadavres spécialement embaumés par la méthode développée par Walter Thiel. Les résultats présentés dans ce mémoire ont permis de proposer des solutions en réponse à des problèmes cliniques en chirurgie vasculaire. Dans un premier temps, l’étude de la vascularisation cutanée du triangle fémoral a mené à proposer de nouvelles incisions chirurgicales afin de limiter la dévascularisation cutanée des plaies et ainsi réduire les problèmes de cicatrisation observés. Ensuite, nous avons validé l’identification radiographique et échographique de l’artère fémorale à son croisement avec le ligament inguinal afin de faciliter l’identification d’un site de ponction artérielle adéquat. Enfin, nous avons développé une méthode échographique simple qui facilite l’approche percutanée de l’artère fémorale, même chez les patients obèses. Les retombées de ce projet de recherche sont multiples pour les cliniciens, l’étude fournit une meilleure compréhension anatomique tridimensionnelle du triangle fémoral et les techniques proposées dans ce mémoire pourront apporter une amélioration de la pratique chirurgicale et faciliter le travail des médecins. Toutefois, ces propositions devront maintenant être validées en clinique. / In vascular surgery, access to the femoral artery is frequently used either through a surgical incision of the groin or by a percutaneous approach in a wide variety of vascular and endovascular procedures; for multiple bypasses, treatment of arterial occlusions, aneurysms repair and placement of various stents. The general purpose of this study is to facilitate and reduces the risks of both the surgical and the percutaneous approaches of the femoral artery through a better anatomical understanding of the femoral triangle. The methodology was conducted on specifically embalmed cadavers according to the method developed by Walter Thiel. The results presented in this memory allowed us to propose solutions to clinical problems in vascular surgery. First, the study of the cutaneous vascularisation of the femoral triangle led to suggest new surgical approaches in order to reduce lesions of the cutaneous arteries and the potential devascularization of the borders of the wound yielding a better postoperative outcome. Then, we validated the radiographic and ultrasonographic position and identification of the inguinal ligament and the proximal femoral artery to facilitate the identification of a safe arterial puncture site. Moreover, we developed a simple method for ultrasound-guided arterial puncture, suitable for obese patients, to facilitate the percutaneous approach of the femoral artery. The benefits of this research project are multiple for clinicians, the study provides a better tridimensional anatomic understanding of the femoral triangle and the techniques proposed will lead to an improved surgical practice and facilitate the work of doctors. However, our work and propositions still need to be validated clinically.

A ce jour la détermination de l’angle γ du Triangle d’Unitarité de la matrice de Cabibbo-Kabayashi-Maskawa est statistiquement limitée par la rareté des transitions b→ u. La précision obtenue en combinant les résultats des expériences BABAR et BELLE est proche de 10°. L’expérience LHCb auprès du LHC présente un fort potentiel d’amélioration pour ce paramètre de violation de CP, notamment via la désintégration Bd0 -> D0K*0, un des canaux clés de cette mesure. Les désintégrations D0 -> Kπ, D0 -> Kππ0 et D0 -> Kπππ sont étudiées dans cette thèse. L’utilisation de désintégrations faisant intervenir des π0 nécessite un bon étalonnage en énergie des calorimètres électromagnétiques. Une méthode d’étalonnage intercellules du ECAL basée sur le flux d’énergie, permet d’obtenir une inter-calibration de l’ordre de 1,5 %, l’échelle d’énergie absolue étant obtenue par des méthodes indépendantes non étudiées ici. La détermination du rapport d’embranchement de la désintégration Bs0 -> D0K*0, première étape du programme aboutissant à la mesure de la violation de CP dans le canal Bd0 -> D0K*0, est réalisée relativement au rapport d’embranchement de Bd0 -> D0ρ0. Le résultat final obtenu avec 36 pb−1 de données collectées par LHCb en 2010 reste dominé par l’erreur statistique :BR(Bs0 -> D0K*0)/BR(Bd0 -> D0ρ0) = 1, 48 ± 0, 34 (stat) ± 0, 15 (syst) ± 0, 12 (fd/fs). / The present status on the determination of the angle γ of the Cabibbo-Kabayashi-Maskawa Unitary Triangle is statistically limited by the rarity of b→ u transitions. The obtained precision combining results from the BABAR and BELLE experiments is close to 10°. The LHCb experiment at the LHC has a strong potential to reduce the uncertainty on this CP violation parameter, especially through the Bd0 -> D0K*0 decay, one of the key channels for this measurement. The D0 -> Kπ, D0 -> Kππ0 and D0 -> Kπππ decays are studied in this thesis. Decays involving π0 require an accurate energy calibration of electromagnetic calorimeters. An inter-calibration technique based on the energy flow allows to obtain the 1.5 % level, the absolute scale being obtained from independent methods studied elsewhere. The determination of the Bs0 -> D0K*0 decay branching ratio, first step towards a measurement of CP violation in the Bd0 -> D0K*0 channel, is performed relatively to the Bd0 -> D0ρ0 decay. The final result, obtained with 36 pb−1 of data collected by LHCb in 2010 is dominated by the statistical uncertainty:BR(Bs0 -> D0K*0)/BR(Bd0 -> D0ρ0) = 1, 48 ± 0, 34 (stat) ± 0, 15 (syst) ± 0, 12 (fd/fs).

Le mélange des quarks est décrit dans le modèle standard de la physique des particules par le mécanisme de Cabibbo-Kobayashi-Maskawa (CKM). À ce jour, l'angle gamma du triangle d'unitarité est un des paramètres de ce mécanisme mesuré avec la moins bonne précision. La mesure de cet angle sert de référence pour le modèle standard, puisqu'elle peut être réalisée sans contribution significative de nouvelle physique. La précision actuelle de la meilleure mesure directe de gamma est d'environ 10°, alors que les ajustements globaux des paramètres CKM, potentiellement sujets à une contribution de nouvelle physique, déterminent cet angle à quelques degrés près. Par conséquent, une mesure directe précise de cette quantité est nécessaire pour contraindre d'avantage le triangle d'unitarité de la matrice CKM et ainsi tester la cohérence de ce modèle. Cette thèse présente une mesure de gamma par une analyse de Dalitz du canal B0->DK*0, avec une désintégration du méson D en K0Spipi. Elle est basée sur les 3 fb⁻¹ de données enregistrés par LHCb pendant le Run I du LHC, à une énergie de collision proton-proton dans le centre de masse de 7 et 8 TeV. Ce canal est sensible à gamma par l'interférence entre les transitions b->u et b->c. La mesure des observables de violation de CP réalisée est x- = -0.09 ^{+0.13}_{-0.13} ± 0.09 ± 0.01 , x+ = -0.10 ^{+0.27}_{-0.26} ± 0.06 ± 0.01 , y- = 0.23 ^{+0.15}_{-0.16} ± 0.04 ± 0.01 , y+ = -0.74 ^{+0.23}_{-0.26} ± 0.07 ± 0.01 , où le première incertitude est statistique, la deuxième est l'incertitude systématique expérimentale et la troisième est l'incertitude systématique venant du modèle de Dalitz. Une interprétation fréquentiste de ces observables donne rB0 = 0.39 ± 0.13 , deltaB0 = ( 186^{+24}_{-23} )° , gamma = ( 77^{+23}_{-24})° , où rB0 est le module du rapport des amplitudes des désintégrations supprimées et favorisées et deltaB0 la différence de phase forte entre ces deux désintégrations. Par ailleurs, un travail sur l'optimisation de la reconstruction des photons pour la mise à niveau du détecteur LHCb est aussi présenté. Lors du Run III du LHC, la luminosité instantanée reçue par LHCb sera augmentée d'un facteur cinq, générant un plus grand recouvrement entre les cascades se développant dans le calorimètre électromagnétique. L'étude montre que l'effet de ce recouvrement entre les gerbes est limité en réduisant la taille des clusters utilisés pour la détection des photons, tout en évitant une diminution significative de l'énergie reconstruite. Avec des corrections adaptées, la nouvelle reconstruction développée améliore la résolution en masse de 7 à 12%, suivant la région du calorimètre considérée. / Quark mixing is described in the standard model of particle physics with the Cabibbo-Kobayashi-Maskawa mecanism. The angle gamma of the unitarity triangle is one of the parameters of this mecanism that is still determined with a large uncertainty. It can be measured without significant contribution of new physics, making it a standard model key measurement. The current precision of the best direct measurement of gamma is approximately 10°, whereas the global fits of the CKM parameters determine this angle up to a few degrees. Therefore precise measurement of this quantity is needed to further constrain the Unitarity Triangle of the CKM matrix, and check the consistency of the theory. This thesis reports a measurement of gamma with a Dalitz analysis of the B0->DK*0 channel where the D meson decays into K0Spipi, based on the 3 fb⁻¹ of proton-proton collision data collected by LHCb during the LHC Run I, at the centre-of-mass energy of 7 and 8 TeV. This channel is sensitive to gamma through the interference between the b->u and b->c transitions. The CP violation observables are measured to be x- = -0.09 ^{+0.13}_{-0.13} ± 0.09 ± 0.01 , x+ = -0.10 ^{+0.27}_{-0.26} ± 0.06 ± 0.01 , y- = 0.23 ^{+0.15}_{-0.16} ± 0.04 ± 0.01 , y+ = -0.74 ^{+0.23}_{-0.26} ± 0.07 ± 0.01 , where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is the systematic uncertainty due to the Dalitz model. A frequentist interpretation of these observables leads to rB0 = 0.39±0.13 , deltaB0 = ( 186^{+24}_{-23} )°, gamma = ( 77^{+23}_{-24} )° , where rB0 is the magnitude of the ratio between the suppressed and favoured decays and deltaB0 the strong phase difference between these two decays. In addition, the work performed on the optimisation of the photon reconstruction for the upgraded LHCb detector is reported. During LHC Run III, the LHCb instantaneous luminosity will be increased by a factor five, implying a larger shower overlap in the electromagnetic calorimeter. The study shows that reducing the cluster size used in the photon reconstruction limits the effect of the overlap between the showers, without inducing a significant energy leakage. With some dedicated corrections, the new cluster reconstruction improves the Bs->Phi gamma mass resolution by 7 to 12%, depending on the calorimeter region.

L’objet de notre recherche en didactique des mathématiques est d’étudier l’introduction des technologies numériques comme environnement complémentaire à des manipulations concrètes. Nous définissons les duos d’artefacts comme l’articulation fructueuse entre un artefact numérique et un artefact matériel qui soit une plus-value pour les apprentissages. L’approche instrumentale de Rabardel nous permet d’établir les critères de cette articulation; chaque artefact du duo enrichit l’autre à travers les instruments construits. Un duo d’artefacts provoque des genèses instrumentales associées. Afin de fonder les conditions d’un apprentissage au sens de Brousseau, un duo n’existe que lorsqu’il est mobilisé dans une situation didactique. Notre enjeu est alors d’élaborer un duo d’artefacts incluant le compas matériel en vue de la conceptualisation du triangle à partir de sa construction à la règle et au compas. La composition du duo et son orchestration dans une situation ont pour intention de faire émerger une nouvelle genèse instrumentale du compas et, selon les travaux de Duval, une déconstruction dimensionnelle 1D du triangle. Des expérimentations en classe nous ont permis de valider l’hypothèse selon laquelle la situation et le duo provoquent l’élaboration d’un nouvel instrument compas pour faire pivoter un segment. Le modèle de conceptions de Balacheff nous a aussi permis d’identifier l’évolution des conceptions des élèves sur le triangle et le cercle au fil de la situation, en particulier l’apparition d’une vision 1D du triangle comme une ligne brisée fermée et d’une caractérisation du cercle comme la trajectoire d’une extrémité d’un segment pivoté. / Our research project in didactics of mathematics is to study the use of digital technologies as a complementary environment to concrete manipulations. We define a duo of artefacts as the fruitful link between a digital artefact and a material one in such a way that this linking is an added value for the learning process. The instrumental approach of Rabardel allows us to establish the requirements for this link, each artefact enriching the other through the constructed instruments. A duo of artefacts sets off associated instrumental geneses. In order to base the conditions of the learning process, in the sense of Brousseau, a duo exists only when it is mobilized in a didactic situation. Our issue is to develop a duo of artifacts including the pair of compasses for the conceptualization of the triangle in the teaching of its geometric construction. The composition of the duo and its orchestration in a didactic situation are intended to bring out a new instrumental genesis of the compasses and, according to Duval's work, a 1D dimensional deconstruction of the triangle. Experiments in classes have enabled us to validate the hypothesis that the situation and the duo cause the development of a new pair of compasses instrument to rotate a segment. Balacheff's model of conceptions also allowed us to identify the evolution of pupils' conceptions of the triangle and the circle as the situation progressed, specifically the improvement of a 1D vision of the triangle as a closed broken line and a characterization of the circle as the trajectory of one end of a pivoted segment.

A voltage source inverter is commonly used to supply a variable frequency variable voltage to a three phase induction motor in a variable speed application. A suitable pulse width modulation (PWM) technique is employed to obtain the required output voltage in the line side of the inverter. Real-time methods for PWM generation can be broadly classified into triangle comparison based PWM (TCPWM) and space vector based PWM (SVPWM). In TCPWM methods such as sine-triangle PWM, three phase reference modulating signals are compared against a common triangular carrier to generate the PWM signals for the three phases. In SVPWM methods, a revolving reference voltage vector is provided as voltage reference instead of three phase modulating waves. The magnitude and frequency of the fundamental component in the line side are controlled by the magnitude and frequency, respectively, of the reference vector. The fundamental line side voltage is proportional to the reference magnitude during linear modulation. With sine-triangle PWM, the highest possible peak phase fundamental voltage is 0.5Vdc, where Vdc is the DC bus voltage, in the linear modulation zone. With techniques such as third harmonic injection PWM and space vector based PWM, the peak phase fundamental voltage can be as high as (formula) (i.e., 0:577Vdc)during linear modulation. To increase the line side voltage further, the operation of the VSI must be extended into the overmodulation region. The overmodulation region extends upto the six-step mode, which gives the highest possible ac voltage for a given (formula). In TCPWM based methods, increasing the reference magnitude beyond a certain level leads to pulse dropping, and gradually leads to six-step operation. However, in SVPWM methods, an overmodulation algorithm is required for controlling the line-side voltage during overmodulation and to achieve a smooth transition from PWM to six-step mode. Numerous overmodulation algorithms have been proposed in the literature for space vector modulated inverter. A well known algorithm among these divides the overmodulation zone into two zones, namely zone-I and zone-II. This is termed as the 'existing overmodulation algorithm' here. This algorithm is modified in the present work to reduce computational burden without much increase in the line current distortion. During overmodulation, the fundamental line side voltage and the reference magnitude are not proportional, which is undesirable from the control point of view. The present work ensures a linear relationship between the two. Apart from the fundamental component, the inverter output voltage mainly consists of harmonic components at high frequencies (around switching frequency and the integral multiples) during linear modulation. However, during overmodulation, low order harmonic components such as 5th, 7th, 11th, 13th etc., are also present in the output voltage. These low order harmonic voltages lead to low order harmonic currents in the motor. The sum of the lower order harmonic currents is termed as 'lower order current ripple'. The present thesis proposes a method for estimation of lower order current ripple in real-time. In closed loop current control, the motor current is fed back to the current controller. During overmodulation, the motor current contains low order harmonics, which appear in the current error fed to the controller. These harmonic currents are amplified by the current error amplifier deteriorating the performance of the drive. It is possible to filter the lower order harmonic currents before being fed back. However, filtering introduces delay in the current loop, and reduces the bandwidth even during linear modulation. In the present work, the estimated lower order current ripple is subtracted from the measured current before the latter is fed back to the controller. The estimation of lower order current ripple and the proposed current control are verified through simulation using MATLAB/SIMULINK and also experimentally on a laboratory prototype. The experimental setup comprises of a field programmable gate arrays (FPGA) based digital controller, an IGBT based inverter and a four-pole squirrel cage induction motor. (Pl refer the original document for formula)

Titel: Risk Managements påverkan för utfallet av ERP-projekt Författare: Ann-Magritt Lindemark Engøy och Hanna Maunus Handledare: Pär Vilhelmson Examinator: Sarah Philipson Kurs: Examensarbete företagsekonomi C, 15.0 hp Nyckelord: ERP-projekt, Projekt Management, Risk Management, risker i ERP-projekt, lyckade projekt, misslyckade projekt, The Iron Triangle. Syfte: Att undersöka vilka risker som är mest förekommande vid implementeringen av ERP-system och hur risk management kan reducera dessa. Metod: Kvalitativ metod, hermeneutik, fallstudier, semistrukturerade intervjuer, välgrundad teori. Resultat: Organisationens och projektets ledning hade större kunskaper om vilka risker som ville uppstå och olika risk management strategier än andra anställda och slutanvändarna av systemet.  Standardisering, samordning och automatisering av organisationens kärnprocesser var huvudsyften för att implementera ERP-system i organisationen. God planering av projektet är avgörande för ett lyckat resultat. Det är viktigt med bra kommunikation och tätt samarbete mellan de olika avdelningarna i projektet, och även med externa konsulter som till exempel leverantören av ERP-systemet. Riskanalys var en viktig del av projektens risk management strategi. En skicklig och flexibel projektledning hade stor betydelse för att risk management strategin fungerade. Resursproblem visade sig vara den största risken i de undersökta projekten. Change management visade sig vara en välanvänd metod för att minska organisationens motstånd mot ERP-projekt. Kostnadsbudgeten var inte det viktigaste målet att uppnå och The Iron Triangle visade sig inte vara så avgörande för om projektet ansågs lyckad eller misslyckad. Organisationerna använda sig mycket av upplärning av användarna för att åtgärda de risker som kan uppstå i samband med personalen. Risk management fungerade för projektledningen som ett verktyg för att åtgärda och även kontrollera projektrisker. Slutsatser: De vanligaste riskerna som upptäcktes i undersökningen var olika slags problem med personalen, tekniska problem, samarbetet med leverantören och kommunikationen mellan olika intressenter, att hålla projektets tidsschema och budget, samt tailoring av systemet och att se till att det fungerar i enlighet med syftet. Särskilt personalriskerna var många och utgjorde stora utmaningar för ERP-projekten. Studien visade även att risk management kan påverka utfallet av ERP-projekt positivt och hjälpa ERP-projekt att uppnå sina mål. / Title: Risk Managements influence on the outcome of ERP projects Authors: Ann-Magritt Lindemark Engøy & Hanna Maunus Tutor: Pär Vilhelmson Examiner: Sarah Philipson Course: Bachelor Thesis in Business Administration C, 15.0 hp Keywords: ERP projects, Project Management, Risk Management, risks in ERP projects, successful projects, unsuccessful projects, The Iron Triangle. Purpose: To investigate what risks are most dominant with the implementation of ERP systems and how risk management can reduce these risks. Method: Qualitative method, hermeneutic, case studies, semi-structured interviews, well-grounded theory. Findings: The management had better knowledge about the risks that would arise and different risk management strategies in ERP projects than other employees and end users of the ERP systems. Standardisation, coordination and automation of the organisations core processes were the main purposes for implementing ERP systems in the organisations. Excellent planning of the project is critical for a successful project outcome. It is important to have good communication and close cooperation between the various departments in the projects, as well as with external consultants such as the supplier of the ERP system. Risk analysis was the most important and the most used method of the risk management strategies among our cases. Skilled and flexible project management had a positive impact on the risk management strategy ability to succeed. Resource issues turned out to be the biggest risk in the investigated projects. Change management proved to be a well-used method to reduce the employees resistance against the ERP project. To meet the standards from the cost´ budget was not seen as the most important objective to achieve. It also turned out The Iron Triangle was not a critical factor to determine whether the project in question was seen as a success or a failure. The organisations used training of the end-users to address the risks that may arise in connection with the employees. Risk management worked for the management as a tool to resolve and control the project risks. Conclusions: The most common risks that where discovered in this study was personnel risks, technical issues, the relationship with the supplier and communication between various stakeholders, not to exceed the project budget and schedule, as well as tailoring the system and make sure that it is working as intended. Particularly risks related to the employees constituted major challenges for the ERP projects. Our study showed furthermore that risk management clearly affects the outcome of ERP projects positively and helps ERP projects to achieve their goals.

This thesis aims to show that the notable points of the triangles are not limited to Incentro, circumcenter, Baricentro and Orthocenter which are the best known. In fact, the Encyclopedia of Triangle Centers (ETC), see [5], features over five thousand notable points. Are points with several interesting properties as we will see throughout this work. In addition to the points already mentioned will also present the points of Feuerbach, the Lemoine point, the point Gergonne, the Nagel point, the Spieker point and the points of Fermat. Will be also presented some important theorems, among them we highlight the Ceva theorem that will be used to prove the existence of several points mentioned. We realize that it is a matter of understanding that can be easily inserted into the basic education. / A presente dissertação tem como objetivo mostrar que os pontos notáveis dos triângulos não se resumem ao Incentro, Circuncentro, Baricentro e ao Ortocentro que são os mais conhecidos. Na verdade, a Encyclopedia of Triangle Centers (ETC), ver [5], apresenta mais de cinco mil pontos notáveis. São pontos com várias propriedades interessantes como veremos ao longo deste trabalho. Além dos pontos já citados apresentaremos também os pontos de Feuerbach, o ponto de Lemoine, o ponto de Gergonne, o ponto de Nagel, o ponto de Spieker e os pontos de Fermat. Serão apresentados também alguns teoremas importantes, entre eles podemos destacar o Teorema de Ceva que será usado para provar a existência de vários pontos citados. Podemos perceber que é um assunto de fácil compreensão que pode ser inserido no ensino básico.

Les schémas de subdivision et les schémas de subdivision inverse sont largement utilisés en informatiquegraphique; les uns pour lisser des objets 3D, et les autres pour minimiser le coût d’encodagede l’information. Ce sont les deux aspects abordés dans cette thèse.Les travaux présentés dans le cadre de la subdivision décrivent l’études et la construction d’un nouveautype de schémas de subdivision. Celui-ci unifie deux schémas de subdivision de type géométriquesdifférents. Cela permet de modéliser des objets 3D composés de zones issues de l’applicationd’un schéma approximant et de zones issues de l’application d’un schéma interpolant. Dans le cadrede la subdivision inverse, Nous présentons une méthode de construction des schémas de subdivisionbi-réguliers inverses (quadrilatères et triangles) / Subdivision schemes are commonly used to generate a smooth shape from a much more coarseone. The reverse subdivision is designed to describe a high resolution mesh from a coarse one. Bothof these tools are used in numerous graphical modelisation domains. In this thesis, we focused ontwo distinct aspects: on one hand the construction of quasi-linear subdivision schemes and on theother hand the construction of reverse quad/triangle subdivision schemes. The work, presented inthe context of the subdivision, describes the construction of a new type of subdivision schemes, andtheirs applications to solve some problems coming from the application of linear subdivision schemes.The work presented in the context of the reverse subdivision describes a new method to reverse thequad/triangle subdivision schemes

Orientador: Prof. Dr. Márcio Fabiano da Silva / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, Santo André, 2018. / Nesta dissertação exploramos o número de ouro, ou razão áurea F presente em diferentes contextos como segmento dividido em média e extrema razão, o retângulo áureo, os triângulos áureos e o pentágono regular. Em especial, os triângulos áureos de um pentágono regular, chamados de triângulos centrais de ouro e a obtenção da razão áurea através das relações das áreas dos triângulos; através das relações entre os incentros, ortocentros, circuncentros e lados dos triângulos. Construímos círculos de 9 pontos e destacamos a presença da razão áurea, em sua maioria, na reta central dos triângulos de ouro, limitadas pelo vértice comum e o ponto médio de sua base isósceles e o centro de cada circunferência de 9 pontos. Apresentamos ainda, propostas de atividades, em sala de aula, para abordar de maneira diferenciada com os alunos o número de ouro F, acompanhadas de suas resoluções presentes em um apêndice. / In this dissertation we explore the number of gold, or golden ratio F present in different contexts as segment divided into average and extreme ratio, golden rectangle, golden triangles and regular pentagon. In particular, the golden triangles of a regular pentagon, called central golden triangles and the attainment of the golden ratio through the relations of the triangle areas; through the relationships between the incenters, orthocentres, circumcenters, and sides of the triangles. We construct a circle of 9 points and we emphasize the presence of the golden ratio, for the most part, in the central line of the golden triangles, limited by the common vertex and the midpoint of its isosceles base and the center of each circumference of 9 points. We also present proposals for activities in the classroom to approach students in a differentiated way the number of gold F, accompanied by their resolutions present in an appendix.