TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra

A proposta deste trabalho é estudar as teorias de análise de qualidade de rede GPS, baseando-se nas teorias de confiabilidade de rede propostas por Baarda, em 1968. As hipóteses estatísticas para detecção de "outliers" constituem a base desse estudo, pois são fundamentais para elaboração dos testes de detecção de "outliers", localização e eliminação de erros grosseiros e, também, para a análise da confiabilidade da rede. A confiabilidade, que traduz a controlabilidade da rede e depende do número de redundância, é estudada em dois aspectos: confiabilidade interna e confiabilidade externa. A rede de referência cadastral do município de Vitória – ES, escolhida para o estudo de caso foi estabelecida por GPS, em 2001, tendo como concepção básica a implantação de 37 pares de vértices intervisíveis, privilegiando locais públicos e de livre acesso. Essa rede foi ajustada em 2001 pela Prefeitura Municipal de Vitória, e as coordenadas ajustadas dos vértices são usadas, deste então, para apoiar todos os levantamentos topográficos e cadastrais realizados no município. O ajustamento dessa rede, em 2001, constituiu-se de um ajustamento simples em que os testes estatísticos de detecção de "outliers", a localização e eliminação dos erros grosseiros não foram levados em conta. A parte prática desta pesquisa compreendeu a medição de 21 novos vetores (linhas bases) para formar uma rede de controle, conforme estabelece a NBR-14166, o ajustamento dessa rede de controle (15 vértices) e o ajustamento da rede principal (78 vértices), tendo por injunção a rede de controle previamente ajustada. A principal diferença ente o ajustamento de 2001, feito pela Prefeitura Municipal de Vitória, e ajustamento de 2004, feito para esta pesquisa, foi a consideração no novo ajustamento dos testes estatísticos baseados nas teorias de confiabilidade propostas por Baarda. A comparação entre os resultados dos dois ajustamentos da rede cadastral de Vitória não apontou diferenças significativas entre as coordenadas ajustadas / The proposal of this work is to study the theories of analysis of network quality GPS, basing on the theories of reliability network proposed by Baarda, in 1968. The statistical hypotheses for outlier's detection constitute the base of this study, because they are fundamental for elaboration of the tests of outlier's detection tests, location and elimination of observations with gross errors as well as for the analysis of the realiability of the network. The reliability, that translates the controllability of the network and it depends of the redundancy number, it was studied in two aspects: internal reliability and external reliability. The network of cadastral reference of the municipal district of Vitória (ES), chosen for the case study it established by GPS, in 2001. The basic conception of this network was the implantation of 37 pair of vertexes inter-visible, privileging public places (of free access), as sidewalks and central stonemasons. This network adjusted in 2001 by the Municipal City Hall of Vitória, and the adjusted coordinates of the vertexes used, of this then, to support all topographical and cadastral survey accomplished in the municipal district. The adjustment of this network, in 2001, constituted of a simple adjustment in that did not take into account the statistical tests of outlier's detection and location and elimination of observations with gross errors. The practical part of this research was constituted of the measurement of 21 new vectors (line bases) to form a control network, as it establishes NBR-14166, the adjustment of that control network (15 vertexes) and the adjustment of the main network (78 vertexes), tends previously for injunction the control network adjusted. To principal it differentiates being the adjustment of 2001, done by the Municipal City Hall of Vitória, and adjustment of 2004, done for this research; it was the consideration in the new adjustment of the based statistical tests, mainly, in the reliability theories proposed by Baarda. The results of the adjustment of 2001 and of 2004 compared, and it verified that, in the case of the cadastral network of Vitória, there was not significant difference among results found in the two adjustments

The skin cancer is the abnormal and uncontrolled growth of the cells that compose the skin, disposing in formats different from borders, colors, sizes and symmetry creating different types. In general lines, the forms of the stains are geometrically irregular. As many forms in the nature cannot be explained in the molds of the conventional geometry, scientists developed the geometry fractal to classify certain objects that don't possess dimension whole, but fractional. The dimension fractal can characterize group or object, for the first it is the number that informs us how densely the group it occupies the metric space where he meets and for the second, the irregularity of your contour. The illustrations can be also differentiated through the index of compactness, in the index of variation of colors and your way through the first idiosyncrasy of the ellipse. This group of parameters was applied for the differentiation of skin stains. In this work grew a software to esteem the dimension fractal of skin stains (benign and malignant) using the called method Box Counting for the estimate of the dimension fractal, the index of variation of colors to quantify the number of colors of the stain, the index of compactness to evaluate the existent relationship between the area of the illustration and the area of the circle with same perimeter of the illustration and the first idiosyncrasy of the ellipse for comparison with a circumference. The parameter that allowed to differentiate the skin stains was the dimension fractal. / O câncer de pele é o crescimento anormal e descontrolado das células que compõem a pele. Dispõe-se em formatos diferentes de bordas, cores, tamanhos e simetria, dando origem a diferentes tipos. As formas das manchas de pele são geometricamente irregulares. Como muitas formas na natureza não podem ser explicadas nos moldes da geometria convencional, cientistas desenvolveram a geometria fractal para classificar certos objetos intrincados que não possuem dimensão inteira, mas sim fracionária. A dimensão fractal pode caracterizar conjunto ou objeto, para o conjunto é o número que nos informa o quão densamente o conjunto ocupa o espaço métrico onde ele se encontra e, para o segundo objeto, a irregularidade do seu contorno. As figuras podem ser também diferenciadas por meio do índice de compacidade, do índice de variação de cores e sua forma por meio da primeira excentricidade da elipse. Este conjunto de parâmetros aplicou-se para a diferenciação de manchas de pele. Neste trabalho desenvolveu-se um software para estimar a dimensão fractal de manchas de pele (benignas e malignas), estruturado na aplicação do método chamado Box Counting para a estimativa da dimensão fractal, o índice de variação de cores para quantificar o número de cores da mancha, o índice de compacidade para avaliar a relação existente entre a área da figura e a área do círculo com mesmo perímetro da figura e a primeira excentricidade da elipse para comparação com uma circunferência. O parâmetro que permitiu diferenciar quantitativamente as manchas de pele foi a dimensão fractal.

Made available in DSpace on 2015-05-15T11:46:22Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1908357 bytes, checksum: 3762912e093a6400855708f530b6cd4d (MD5) Previous issue date: 2013-05-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We study the geometry of surfaces immersed in R4 through the singularities of their families of height functions. Inflection points on the surfaces are shown to be umbilic points from their families of height functions. Furthermore, we see that inflection points of imaginary type are isolated points of the curve --1(0). As a consequence we prove that any dive generic convexly embedded S2 in R4 has inflexion points. / Neste trabalho estudamos a geometria das superfícies em R4 através da variedade canal e das singularidades das famílias de funções altura das superfícies. Provaremos que os pontos de inflexão das superfície são os pontos umbílicos das famílias de funções altura. Além disso, veremos que pontos de inflexão do tipo imaginário serão pontos isolados da curva --1(0). Como uma consequência deste estudo provaremos que qualquer mergulho genérico convexo de S2 em R4 tem pelo menos um ponto de inflexão.

TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra

One of the important parameters observed during extruded fibre fabrication is its diameter. The diameter can be measured with a single scanning camera assuming that the fibre section has a circular shape. As proved in practice, another important parameter is ovality, that is the rate of fibre flattening. This paper assumes that the fibre section shape is elliptical. In such a case, at least three different views on examined fibre are needed. Mathematical part of this paper is concerned with analytical description of fibre ovality measurement using two different approaches based on the knowledge of linear algebra, projective geometry and conic sections theory. Main goal of this paper is thus to use both mathematical theory and image analysis methods for ovality and diameter determination. Precise calcluation of such quantities is, however, conditioned on precise camera system calibration, which is described in the paper as well. Additionally, the work contains a brief mention of technical realization of ovality measurement and its possible difficulties.

By entering the diploma thesis is to create an architectural study of the sacral object and the Salesian community center in Brno - Líšeň. The first mention of the creating church appeared in 1987 and because of this reason Salesians came to this city, they focus on working with children and youth, according to Don Bosca. Their method od education was reflected in the overall project concept. The building will be linked to the existing object of the Salesian Youth Center, but it will also serve for a wider circle of believers. The consecration of the church will be a third divine person - the Holy Spirit. The object will be on the Horníková ulica, on the parcels no. 5037/30,32. On the plot with parc. No.5037/32 is currently a building, that is the property of the Nadácia pre radosť, and it will by removed during construction. The proposal is based on urban analyzes performed and responds to the surrounding buildings. It also affects the conditions of the building plot and uses terrain sloping. The proposal consists of one object that includes a church with a capacity for 400 seat and 100-standing persons with chorus, sacristy, adoration chapel and technical and hygienic backgrounds. Furthermore, there is a educational/multifunction room, workshop and store of religious products, farther the parish part with the apartments, office for priests and underground garage. In addition to the building, there was created paved areas for pedestrian which responding to existing communications. Due to the removal of the parking lot in the northern part of the solved territory, the existing parking lot was extended on the south side and there was also created a new communication for cars, which connects the Northern Street Horníková with Western. In this communication, it is necessary to create a suitable road signage to prevent the supply of vehicles and it must not be used as an abbreviation in the traffic jam at the 2nd grade road communication.

Cette thèse propose une étude transversale des principales réalisations de DO dans l'anaphore verbale en anglais, à savoir : do this/that/it, do so, ellipse post-auxiliaire (EPA) et DO britannique. Chaque anaphorique fait l'objet d'une étude approfondie fondée sur un échantillon de plusieurs centaines d'occurrences authentiques prélevées dans le BNC et le COCA, ainsi que le corpus de Bos & Spenader (2011). Plusieurs variables sont analysées, notamment le registre, la nature grammaticale de DO, les propriétés sémantiques et syntaxiques du déclencheur d'antécédent, l’identité de sujet et d'état de choses, les alternances de polarité, de modalité, d'aspect, de temps et de voix ainsi que la présence éventuelle d'adjoints contrastifs ou non contrastifs.Une attention particulière est portée au DO britannique, c'est-à-dire l'emploi de formes non finies de DO anaphorique essentiellement limité au registre conversationnel de l'anglais britannique, qui n'a jamais fait l'objet d'une étude empirique auparavant. A partir d’un échantillon de 483 occurrences prélevées dans la composante orale du BNC et vérifiées systématiquement à l'écoute, cette étude met en lumière certaines caractéristiques socio-culturelles et situationnelles qui favorisent son utilisation, en plus de ses propriétés linguistiques et discursives. Ainsi, cette étude aboutit à la conclusion que le DO britannique constitue une réalisation particulière de l'EPA, qui met en œuvre des formes non finies du DO auxiliaire. / This dissertation presents research across the main types of verb-phrase anaphora involving DO, viz. do this/that/it anaphora, do so anaphora, post-auxiliary ellipsis (PAE) and British English DO. Each anaphor underwent close analysis based on a sample of several hundreds of occurrences retrieved from the BNC and the COCA, as well as Bos & Spenader's (2011) corpus. Different variables were studied including register, the grammatical status of DO, semantic and syntactic properties of antecedent triggers, identity of subjects and states of affairs, the presence or absence of contrastive and non-contrastive adjuncts, as well as polar, modal, aspectual, temporal and voice alternations.One item of particular interest involves British English DO which bears a strong resemblance to PAE, except that it involves non-finite forms of DO and is generally restricted to British conversational English. Unlike PAE, British English DO has never before been the focus of study based on empirical data. In this research, 483 naturally-occurring examples taken from the Spoken component of the BNC as well as the accompanying metadata and recorded material were fully examined. Sociolinguistic and situational information was investigated, as were the linguistic properties and discourse conditions that make the use of British English DO felicitous. The result has led to a far better understanding of the phenomenon. In particular, it was found that British English DO can be considered a sub-type of PAE, which involves non-finite forms of auxiliary DO.

The present thesis contributes to the theory of generalized Minkowski spaces as a continuation of Minkowski geometry, i.e., the geometry of finite-dimensional normed spaces over the field of real numbers. In a generalized Minkowski space, distance and length measurement is provided by a gauge, whose definition mimics the definition of a norm but lacks the symmetry requirement. This seemingly minor change in the definition is deliberately chosen. On the one hand, many techniques from Minkowski spaces can be adapted to generalized Minkowski spaces because several phenomena in Minkowski geometry simply do not depend on the symmetry of distance measurement. On the other hand, the possible asymmetry of the distance measurement set up by gauges is nonetheless meaningful and interesting for applications, e.g., in location science. In this spirit, the presentation of this thesis is led mainly by minimization problems from convex optimization and location science which are appealing to convex geometers, too. In addition, we study metrically defined objects, which may receive a new interpretation when we measure distances asymmetrically. To this end, we use a combination of methods from convex analysis and convex geometry to relate the properties of these objects to the shape of the unit ball of the generalized Minkowski space under consideration.

<p>У Докторској дисертацији је извршена методичкa трансформација садржа-<br />ја&nbsp; аналитичке&nbsp; геометрије,&nbsp; у&nbsp; наставном&nbsp; систему&ndash; настава&nbsp; уз&nbsp; помоћ<br />рачунара,&nbsp; адекватним&nbsp; избором&nbsp; садржаја,&nbsp; израдом&nbsp; одговарајућих<br />генеричких органи-затора уз коришћење образовног софтвераGeoGebra и<br />Mathematica. Обрађен је дидактички систем настава уз помоћ рачунара,<br />анализом међусобне зависности фактора наставе, анализом дидактичких<br />принципа,&nbsp; класификацијом&nbsp; и&nbsp; приказом&nbsp; наставних&nbsp; метода,&nbsp; уз&nbsp; подесно<br />формиране&nbsp; генеричке&nbsp; организаторе.&nbsp; Експериментално&nbsp; истраживање&nbsp; је<br />потврдило могућност примене наставе уз помоћ рачунара, као и позитиван<br />утицај на реализацију циљева и задатака, на укупан образовни учинак и<br />подизање нивоа ефикасности савремене наставе.</p> / <p>U Doktorskoj disertaciji je izvršena metodička transformacija sadrža-<br />ja&nbsp; analitičke&nbsp; geometrije,&nbsp; u&nbsp; nastavnom&nbsp; sistemu&ndash; nastava&nbsp; uz&nbsp; pomoć<br />računara,&nbsp; adekvatnim&nbsp; izborom&nbsp; sadržaja,&nbsp; izradom&nbsp; odgovarajućih<br />generičkih organi-zatora uz korišćenje obrazovnog softveraGeoGebra i<br />Mathematica. Obrađen je didaktički sistem nastava uz pomoć računara,<br />analizom međusobne zavisnosti faktora nastave, analizom didaktičkih<br />principa,&nbsp; klasifikacijom&nbsp; i&nbsp; prikazom&nbsp; nastavnih&nbsp; metoda,&nbsp; uz&nbsp; podesno<br />formirane&nbsp; generičke&nbsp; organizatore.&nbsp; Eksperimentalno&nbsp; istraživanje&nbsp; je<br />potvrdilo mogućnost primene nastave uz pomoć računara, kao i pozitivan<br />uticaj na realizaciju ciljeva i zadataka, na ukupan obrazovni učinak i<br />podizanje nivoa efikasnosti savremene nastave.</p> / <p>In this doctoral dissertation, methodical transformation of content analytic<br />geometry, is carried out, in the educational system - a computer-assisted<br />teaching, by appropriate selection of content, making appropriate generic<br />organizers using educational software GeoGebra and Mathematica.<br />Didactic teaching system, computer-assisted teaching, was processed, by<br />analyzing the factors of teaching and didactic principles, classification and<br />presentation of teaching methods, with the adequately created generic<br />organizers. Experimental research has confirmed the apossibility of<br />computer-assisted teaching, as well as a positive impact on the realization<br />of goals and tasks, on the overall educational impact and raising the<br />efficiency of modern teaching.</p>