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1	Mashal rabínico ou parabol? Parábolas dos Evangelhos à luz dos trabalhos de Paul Ricoeur e Yonah Fraenkel / Rabbinical mashal ou parabol? Parables of the Gospel in light of Paul Ricoeurs and Yonah Fraenkels researches Peuzé, Pascal Jean André Roger 08 October 2018 (has links) Nesta tese, as parábolas dos Evangelhos são analisadas segundo o método de Yonah Fraenkel desenvolvido para os meshalim rabínicos. Esse método é baseado na teoria de Paul Ricoeur sobre a metáfora viva, que leva a considerar a parábola como uma narrativa metafórica e hermenêutica. Para a análise das quatro parábolas escolhidas, considera-se primeiro o texto aramaico dos evangelhos na Peshitá, a fim de evidenciar o arraigamento da parábola no seu contexto judaico. A análise prossegue com vários passos metodológicos: modelo de base, trama narrativa, relação mashal-nimshal, torsão da realidade, desvelamentos. Esses passos evidenciam a estrutura literária da parábola e a sua função hermenêutica. Ressonâncias com parábolas rabínicas da literatura talmúdica e midráshica são apontadas. Verifica-se assim a aplicabilidade do método de Fraenkel para as parábolas evangélicas. Percebe-se a necessidade de determinar um corpus de narrativas segundo vários critérios tais como relação à Escritura, narratividade, presença de elementos extravagantes. Um ponto principal diferencia o mashal rabínico da parábola evangélica: a possível presença de traços alegóricos nessa última. Esse dado é devido à diferença de contexto sócioreligioso e do processo na transmissão da parábola até ser posta por escrito. As grandes similitudes superam porém essas diferenças. A parábola hermenêutica dos evangelhos é de fato uma parábola rabínica. / The parables of the Gospel are analyzed in this thesis according to Yonáh Fraenkel\'s method developed for rabbinical meshalim. This method is based on Paul Ricoeur\'s theory on the living metaphor, that considers the parable as a metaphorical and hermeneutical narrative. For the analysis of the four chosen parables, we first take into account the aramaic text of the Gospels, the Peshitta text, in order to evidence the rooting of the parable in its jewish context. The analysis continues with several methodological steps: basic model, narrative plot, correspondences between mashal and nimshal, twisting of the reality, unveilings. These steps evidence the literary structure of the parable and its hermeneutical function. Resonances with rabbinical parables of the talmudic and midrashic literature are pointed out. The applicability of Fraenkels method for parables of the Gospels can be so verified. It is needed to fix a corpus of narratives according to several criterions such as: link to the Scripture, narrativity, extravagant elements. A main issue differentiates the rabbinical mashal from the parable of the Gospels: allegorical marks can be found in the late one. This is due to the difference of social and religious context and the transmission process of the parable until it was put into writing. However, the important similarities overcome those diferencies. The hermeneutical parable of the Gospels is actually a rabbinical parabel. Evangelho Gospels Literatura rabínica Mashal Mashal Parabel Parábola Rabbinical literature
2	The use of technology to motivate, to present and to deepen the comprehension of math Kobal, Damjan 02 May 2012 (has links) (PDF) The aim of the workshop is to present and discuss several ideas which relate to technology as well as to creative teaching. Educational experience, common sense and educational research have all proven how important for comprehensive understanding different cognitive representations are. We will present and discuss several elementary mathematical ideas of which mechanical realisations mean ingenius technological inventions (for example: ‘car differential’ and ‘digital sound technology’). Technological insights can provide deep intuitive understanding of otherwise abstract mathematical concepts and therefore yield also better comprehension of mathematics. Besides that we will use and present the technology in the form of dynamic geometry programs to show, provoke and motivate rethinking and deeper understanding of several elementary mathematical concepts. Motivation Technologie Dynamische Geometrie intuitiv rational Fahrradgetriebe arithmetisches Mittel Differenzialgetriebe im Auto Geodäsie Parabel Dimmen und Flashen der Scheinwerfer Funktion Analog Digital Motivation Technology Dynamic Geometry Intuitive Ratio Bicycle Gears Arithmetic Mean Car Differential Geodesics Parabola Dim and Flash Headlights Function Analog Digital ddc:510 rvk:SD 2009
3	The use of technology to motivate, to present and to deepen the comprehension of math Kobal, Damjan 02 May 2012 (has links) The aim of the workshop is to present and discuss several ideas which relate to technology as well as to creative teaching. Educational experience, common sense and educational research have all proven how important for comprehensive understanding different cognitive representations are. We will present and discuss several elementary mathematical ideas of which mechanical realisations mean ingenius technological inventions (for example: ‘car differential’ and ‘digital sound technology’). Technological insights can provide deep intuitive understanding of otherwise abstract mathematical concepts and therefore yield also better comprehension of mathematics. Besides that we will use and present the technology in the form of dynamic geometry programs to show, provoke and motivate rethinking and deeper understanding of several elementary mathematical concepts. info:eu-repo/classification/ddc/510 ddc:510
4	Metrical Problems in Minkowski Geometry Fankhänel, Andreas 19 October 2012 (has links) (PDF) In this dissertation we study basic metrical properties of 2-dimensional normed linear spaces, so-called (Minkowski or) normed planes. In the first chapter we introduce a notion of angular measure, and we investigate under what conditions certain angular measures in a Minkowski plane exist. We show that only the Euclidean angular measure has the property that in an isosceles triangle the base angles are of equal size. However, angular measures with the property that the angle between orthogonal vectors has a value of pi/2, i.e, a quarter of the full circle, exist in a wider variety of normed planes, depending on the type of orthogonality. Due to this we have a closer look at isosceles and Birkhoff orthogonality. Finally, we present results concerning angular bisectors. In the second chapter we pay attention to convex quadrilaterals. We give definitions of different types of rectangles and rhombi and analyse under what conditions they coincide. Combinations of defining properties of rectangles and rhombi will yield squares, and we will see that any two types of squares are equal if and only if the plane is Euclidean. Additionally, we define a ``new\'\' type of quadrilaterals, the so-called codises. Since codises and rectangles coincide in Radon planes, we will explain why it makes sense to distinguish these two notions. For this purpose we introduce the concept of associated parallelograms. Finally we will deal with metrically defined conics, i.e., with analogues of conic sections in normed planes. We define metric ellipses (hyperbolas) as loci of points that have constant sum (difference) of distances to two given points, the so-called foci. Also we define metric parabolas as loci of points whose distance to a given point equals the distance to a fixed line. We present connections between the shape of the unit ball B and the shape of conics. More precisely, we will see that straight segments and corner points of B cause, under certain conditions, that conics have straight segments and corner points, too. Afterwards we consider intersecting ellipses and hyperbolas with identical foci. We prove that in special Minkowski planes, namely in the subfamily of polygonal planes, confocal ellipses and hyperbolas intersect in a way called Birkhoff orthogonal, whenever the respective ellipse is large enough. Winkelmaß Birkhoff-Orthogonalität Codis Kegelschnitt gleichschenklig-rechtwinklig metrische Ellipse metrische Hyperbel metrische Parabel metrisches Parallelogramm Minkowski-Ebene normierte Ebene Parallelogramm Radon-Ebene Rechteck Rhombus glatte Ebene Quadrat streng konvexe Ebene angular measure Birkhoff orthogonality codis conic section isosceles orthogonality metric ellipse metric hyperbola metric parabola metric parallelogram Minkowski plane normed plane parallelogram Radon plane rectangle rhombus smooth plane square strictly convex plane ddc:516 Minkowski-Geometrie Kegelschnitt Viereck Winkel
5	Metrical Problems in Minkowski Geometry Fankhänel, Andreas 07 June 2012 (has links) In this dissertation we study basic metrical properties of 2-dimensional normed linear spaces, so-called (Minkowski or) normed planes. In the first chapter we introduce a notion of angular measure, and we investigate under what conditions certain angular measures in a Minkowski plane exist. We show that only the Euclidean angular measure has the property that in an isosceles triangle the base angles are of equal size. However, angular measures with the property that the angle between orthogonal vectors has a value of pi/2, i.e, a quarter of the full circle, exist in a wider variety of normed planes, depending on the type of orthogonality. Due to this we have a closer look at isosceles and Birkhoff orthogonality. Finally, we present results concerning angular bisectors. In the second chapter we pay attention to convex quadrilaterals. We give definitions of different types of rectangles and rhombi and analyse under what conditions they coincide. Combinations of defining properties of rectangles and rhombi will yield squares, and we will see that any two types of squares are equal if and only if the plane is Euclidean. Additionally, we define a ``new\'\' type of quadrilaterals, the so-called codises. Since codises and rectangles coincide in Radon planes, we will explain why it makes sense to distinguish these two notions. For this purpose we introduce the concept of associated parallelograms. Finally we will deal with metrically defined conics, i.e., with analogues of conic sections in normed planes. We define metric ellipses (hyperbolas) as loci of points that have constant sum (difference) of distances to two given points, the so-called foci. Also we define metric parabolas as loci of points whose distance to a given point equals the distance to a fixed line. We present connections between the shape of the unit ball B and the shape of conics. More precisely, we will see that straight segments and corner points of B cause, under certain conditions, that conics have straight segments and corner points, too. Afterwards we consider intersecting ellipses and hyperbolas with identical foci. We prove that in special Minkowski planes, namely in the subfamily of polygonal planes, confocal ellipses and hyperbolas intersect in a way called Birkhoff orthogonal, whenever the respective ellipse is large enough.:1 Introduction 2 On angular measures 3 Types of convex quadrilaterals 4 On conic sections info:eu-repo/classification/ddc/516 ddc:516

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