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This thesis deals with the straight-line surfaces, their division, and properties. Because these surfaces are spatial formations, in their view it is necessary to select the appropriate type of screening. For this purpose is selected rectangular axonometric, which also deals with the work. In conclusion, the findings of these two parts are connected together and selected straight-line surfaces are shown using rectangular axonometric. Because today is more comfort use for the purposes of mathematics, especially geometry, different software, is for creating images in this thesis used programs GeoGebra and AutoCAD.

Este trabalho busca, num primeiro momento, caracterizar a problemática aprendizagem do número real na Escola Básica, aplicando questionários-sondagem, analisando livros didáticos e comparando-os com os Parâmetros Curriculares Nacionais. Num segundo momento desenvolvemos um efetivo estudo de Matemática: as maneiras mais comuns de se construir números reais e a equivalência entre todas elas. Mostramos também como, a partir de cada uma destas abordagens, chega-se à representação decimal de um número real positivo. Finalizamos com uma proposta pedagógica para o Ensino Fundamental, e uma experiência didática, numa 8ª série, de construção de um número real via medição exata de segmentos de reta. / The first part of this work is an attempt to characterize the problem of learning the concept of real number in Elementary School, making use of questionnaires and analyzing school books as well as the National Parameters for the teaching of Mathematics. The second part deals with the Mathematics involved in the construction of the real numbers, namely, different ways of constructing this set and also the equivalence between all those constructions. We also show how each one of those constructions leads to the decimal representation of a positive real number. The last part of this work consists of a pedagogic proposal for the construction of the real number making use of the (exact) measure of a line segment and the description and conclusions of its implementation in an 8th year of Elementary School.

The author presents novel algorithms to design unconstrained handwriting recognition systems organized in three parts: In Part One, novel algorithms are presented for processing of Arabic text prior to recognition. Algorithms are described to convert a thinned image of a stroke to a straight line approximation. Novel heuristic algorithms and novel theorems are presented to determine start and end vertices of an off-line image of a stroke. A straight line approximation of an off-line stroke is converted to a one-dimensional representation by a novel algorithm which aims to recover the original sequence of writing. The resulting ordering of the stroke segments is a suitable preprocessed representation for subsequent handwriting recognition algorithms as it helps to segment the stroke. The algorithm was tested against one data set of isolated handwritten characters and another data set of cursive handwriting, each provided by 20 subjects, and has been 91.9% and 91.8% successful for these two data sets, respectively. In Part Two, an entirely novel fuzzy set-sequential machine character recognition system is presented. Fuzzy sequential machines are defined to work as recognizers of handwritten strokes. An algorithm to obtain a deterministic fuzzy sequential machine from a stroke representation, that is capable of recognizing that stroke and its variants, is presented. An algorithm is developed to merge two fuzzy machines into one machine. The learning algorithm is a combination of many described algorithms. The system was tested against isolated handwritten characters provided by 20 subjects resulting in 95.8% recognition rate which is encouraging and shows that the system is highly flexible in dealing with shape and size variations. In Part Three, also an entirely novel text recognition system, capable of recognizing off-line handwritten Arabic cursive text having a high variability is presented. This system is an extension of the above recognition system. Tokens are extracted from a onedimensional representation of a stroke. Fuzzy sequential machines are defined to work as recognizers of tokens. It is shown how to obtain a deterministic fuzzy sequential machine from a token representation that is capable'of recognizing that token and its variants. An algorithm for token learning is presented. The tokens of a stroke are re-combined to meaningful strings of tokens. Algorithms to recognize and learn token strings are described. The. recognition stage uses algorithms of the learning stage. The process of extracting the best set of basic shapes which represent the best set of token strings that constitute an unknown stroke is described. A method is developed to extract lines from pages of handwritten text, arrange main strokes of extracted lines in the same order as they were written, and present secondary strokes to main strokes. Presented secondary strokes are combined with basic shapes to obtain the final characters by formulating and solving assignment problems for this purpose. Some secondary strokes which remain unassigned are individually manipulated. The system was tested against the handwritings of 20 subjects yielding overall subword and character recognition rates of 55.4% and 51.1%, respectively.

Este trabalho busca, num primeiro momento, caracterizar a problemática aprendizagem do número real na Escola Básica, aplicando questionários-sondagem, analisando livros didáticos e comparando-os com os Parâmetros Curriculares Nacionais. Num segundo momento desenvolvemos um efetivo estudo de Matemática: as maneiras mais comuns de se construir números reais e a equivalência entre todas elas. Mostramos também como, a partir de cada uma destas abordagens, chega-se à representação decimal de um número real positivo. Finalizamos com uma proposta pedagógica para o Ensino Fundamental, e uma experiência didática, numa 8ª série, de construção de um número real via medição exata de segmentos de reta. / The first part of this work is an attempt to characterize the problem of learning the concept of real number in Elementary School, making use of questionnaires and analyzing school books as well as the National Parameters for the teaching of Mathematics. The second part deals with the Mathematics involved in the construction of the real numbers, namely, different ways of constructing this set and also the equivalence between all those constructions. We also show how each one of those constructions leads to the decimal representation of a positive real number. The last part of this work consists of a pedagogic proposal for the construction of the real number making use of the (exact) measure of a line segment and the description and conclusions of its implementation in an 8th year of Elementary School.

Este trabalho busca, num primeiro momento, caracterizar a problemática aprendizagem do número real na Escola Básica, aplicando questionários-sondagem, analisando livros didáticos e comparando-os com os Parâmetros Curriculares Nacionais. Num segundo momento desenvolvemos um efetivo estudo de Matemática: as maneiras mais comuns de se construir números reais e a equivalência entre todas elas. Mostramos também como, a partir de cada uma destas abordagens, chega-se à representação decimal de um número real positivo. Finalizamos com uma proposta pedagógica para o Ensino Fundamental, e uma experiência didática, numa 8ª série, de construção de um número real via medição exata de segmentos de reta. / The first part of this work is an attempt to characterize the problem of learning the concept of real number in Elementary School, making use of questionnaires and analyzing school books as well as the National Parameters for the teaching of Mathematics. The second part deals with the Mathematics involved in the construction of the real numbers, namely, different ways of constructing this set and also the equivalence between all those constructions. We also show how each one of those constructions leads to the decimal representation of a positive real number. The last part of this work consists of a pedagogic proposal for the construction of the real number making use of the (exact) measure of a line segment and the description and conclusions of its implementation in an 8th year of Elementary School.

In this thesis entitled ,,Analysis of motion of the bicycle when riding in a straight line”, I deal with the history of the bicycle, classifications and descriptions of the various parts of the bicycle and the analysis of accidents. The main objective is to analyze the movement of cyclists (bicycle) in a straight line in the implementation of tasks, typical for him - pedaling, showing a change in direction, or looking back for him. In conclusion evaluation, which can then be used in the processing of judicial opinions by experts.

In designing devices to produce straight-line motion, the designer has a fundamental choice between selecting sliding devices or selecting pinned linkages. Although they are more complex to design and implement, linkages will often prove a less expensive, more efficient, and generally more satisfactory option than simple sliders. The objective of this thesis is to provide a tool to the designer that serves as an aid in making intelligent decisions in the selection of four-bar linkage type straight-line-mechanisms. This thesis provides research into the selection, evaluation, and implementation of existing straight-line mechanism designs. Twenty-two straight-line mechanisms are compared for both compactness and fidelity of the straight-line path. Also, figures showing position, velocity, and acceleration of each a included. The functional product of to this work is a software program called Straight-line. Straight-line gives the designer a graphical environment from which a wide variety of straight-line mechanisms can be quickly analyzed and evaluated. The software also provides a new type-synthesis technique that allows the designer to generate a straight-line-mechanism by graphically inputting a desired path. / Master of Science

This master’s thesis investigates normative lifelines, time and space in relation to a nonbinary gender identity. My research questions focused on nonbinary aging, orientation in regards to identity and spaces, and views on maturity. I wanted to know how temporality and spatiality can be used as a theoretic framework to better understand nonbinary people’s experiences. This was achieved by interviewing seven Swedish nonbinary subjects aged 30-41 about norms regarding time and place. The results show that the nonbinary informants use gender norms to orient themselves in relation to gender identity. Aging is shown to be a gendered practice and therefore nonbinary aging and what the future will hold is made unclear for the participants. Nonbinary people seek not to be a hindrance or annoyance to the outside world and are aware that their identity often is viewed as childish, made up and illegitimate. Despite fears that they take up too much space I have shown that there is not enough space for nonbinary subjects to comfortably find a place in most rooms.

Diese Arbeit beinhaltet {\it geometrische Algorithmen} zur L\"osung reeller polynomialer Gleichungssysteme mit rationalen Koeffizienten, wobei die Polynome eine reduzierte regul\"are Folge bilden (vgl. Abschnitt \ref{abschgeo}). Unter reellem L\"osen verstehen wir hier die Bestimmung eines Punktes in jeder Zusammenhangskomponente einer kompakten glatten reellen Variet\"at $V:=W \cap \R^n$.\\ Im Mittelpunkt steht die Anwendung des f\"ur den algebraisch abgeschlossenen Fall ver\"offentlichten symbolischen geometrischen Algorithmus nach \cite{gh2} und \cite{gh3}. Die Berechenungsmodelle sind {\em Straight--Line Programme} und {arithmetische Netzwerke} mit Parametern in $\; \Q$. Die Input--Polynome sind durch ein Straight--Line Programm der Gr\"o{\ss}e $L$ gegeben. Eine geometrische L\"osung des Input--Glei\-chungs\-sys\-tems besteht aus einem primitiven Element der Ringerweiterung, welche durch die Nullstellen des Systems beschrieben ist, aus einem mininalen Polynom dieses primitiven Elements, und aus den Parametrisierungen der Koordinaten. Diese Darstellung der L\"osung hat eine lange Geschichte und geht mindestens auf Leopold Kronecker \cite{kron} zur\"uck. Die Komplexit\"at des in dieser Arbeit begr\"undeten Algorithmus erweist sich als linear in $L$ und polynomial bez\"uglich $n, d, \delta$ bzw. $\delta \;'$, wobei $n$ die Anzahl der Variablen und $d$ eine Gradschranke der Polynome im System ist. Die Gr\"o{\ss}en $\delta$ und $\delta \; '$ sind geometrische Invarianten, die das Maximum der {\em Grade des Inputsystems} und geeigneter {\em polarer Variet\"aten} repr\"asentieren (bzgl. des ({\em geometrischen}) Grades vgl. \cite{he}). Die Anwendung eines Algorithmus \"uber den komplexen Zahlen auf das L\"osen von polynomialen Gleichungen im Reellen wird durch die Einf\"urung polarer Variet\"aten m\"oglich (vgl. \cite{bank}). Die polaren Variet\"aten sind das Kernst\"uck und das vorbereitende Werzeug zur effizienten Nutzung des oben erw\"ahnten geometrischen Algorithmus. Es wird ein inkrementelles Verfahren zur Auffindung reeller Punkte in jeder Zusammenhangskomponente der Nullstellenmenge des Inputsystems abgeleitet, welches einen beschr\"ankten glatten (lokalen) vollst\"andigen Durchschnitt in $\R^n$ beschreibt. Das Inkrement des Algorithmus ist die Kodimension der polaren Variet\"aten. Die Haupts\"atze sind Satz $\ref{theorem12}$ auf Seite $\pageref{theorem12}$ f\"ur den Hyperfl\"achenfall, und Satz $\ref{theoresult}$ auf Seite $\pageref{theoresult}$, sowie die Aussage in der Einf\"uhrung dieser Arbeit, Seite $\pageref{vollres}$ f\"ur den vollst\"andigen Durchschnitt. / This dissertation deals with {\em geometric algorithms} for solving real multivariate polynomial equation systems, that define a reduced regular sequence (cf. subsection $\ref{abschgeo}$). Real solving means that one has to find at least one real point in each connected component of a real compact and smooth variety $V := W \cap \R^n$. \\ The main point of this thesis is the use of a complex symbolic geometric algorithm, which is designed for an algebraically closed field and was published in the papers \cite{gh2} and \cite{gh3}. The models of computation are {\em straight--line programms} and {\em arithmetic Networks} with parameters in $\; \Q$. Let the polynomials be given by a division--free straight--line programm of size $L$. A geometric solution for the system of equations given by the regular sequence consists in a {\em primitiv element} of the ring extension associated with the system, a minimal polynomial of this primitive element and a parametrization of the coordinates. This representation has a long history going back to {\em Leopold Kronecker} \cite{kron}. The time--complexity of our algorithms turns out to be linear in $L$ and polynomial with respect to $n, d, \delta$ or $\delta '$, respectively. Here $n$ denotes the number of variables, $d$ is an upper bound of the degrees of the polynomials involved in the system, $\delta$ and $\delta '$ are geometric invariants representing the maximum of the {\em affine (geometric) degree} of the system under consideration and the affine (geometric) degree of suitable {\em polar varieties} (cf. \cite{he} for the ({\em geometric}) degree). The application of an algorithm running in the complex numbers to solve polynomial equations in the real case becomes possible by the introduction of polar varieties (cf. \cite{bank}). The polar varieties introduced for this purpose prove to be the corner--stone and the preliminary tool for the efficient use of the geometric algorithm mentioned above. An incremental algorithm is designed to find at least one real point on each connected component of the zero set defined by the input under the assumption that the given semialgebraic set $V = W \cap \R^n$ is a bounded, smooth (local) complete intersection manifold in $\R^n$. The increment of the new algorithm is the codimension of the polar varieties under consideration. The main theorems are Theorem $\ref{theorem12}$ on page $\pageref{theorem12}$ for the hypersurface case, and Theorem $\ref{theoresult}$ on page $\pageref{theoresult}$ for the complete intersection as well as the statement in the introduction of this thesis on page $\pageref{vollres}$.