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The new synagogue in Frýdek-Místek
Hanousek, Ondřej ; Baranyai, René (referee) ; Dulenčín, Juraj (advisor)
The thesis deals with a hypothetical project of a new building complex of a synagogue, a kosher restaurant and a community centre at the location of the former synagogue in Frýdek. The proposal includes a memorial of the destroyed synagogue and Jewish community, as well as the incorporation of the complex into the urban structure of the city. The project proposes a building distributed into three volumes. The restaurant and community centre are connected by an underground garage within a U-shaped floor plan. The buildings are axially symmetrical, white, with expressive rhythmical perforations of the facade. They surround the building of the synagogue in the shape of a seven-sided pyramid, which is clad with blue tempered steel and creates a strong contrast with the associated buildings. The whole complex is oriented towards the park and the chateau in Frýdek, from which it is clearly visible and thanks to its distinct volumetric and material expression and axially symmetrical composition creates a new landmark for the city.
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Introducing the volume of solids using Cavalieri's principle
Fialová, Eliška ; Vondrová, Naďa (advisor) ; Janda, David (referee)
The aim of the thesis is to use a series of pedagogical experiments to introduce the volume of a pyramid, a cone and a sphere using Cavalieri's principle for pupils of the ninth year of primary school. First, the thesis characterizes the theories and approaches on the basis of which the experiment was built, such as the generic model theory and constructivism. The next part deals with the analysis of schoolbooks for the upper primary school and gymnasium, which are devoted to the introduction of the volumes of solids of pyramids, cones and spheres, and especially those schoolbooks which introduce the given volumes using the Cavalieri principle. The pedagogical experiment was preceded by a series of lessons focused on familiarizing pupils with given geometric solids and deriving calculations of their surfaces. This was followed by the introduction of the Cavalieri principle in the plane and also in space. In the practical part of the thesis, the tasks that were used in the pedagogical experiment are presented. The description of the course of the pedagogical experiment is supplemented by copies of the pupils' solutions. The conclusions are illustrated by the pupils' observations and summaries, which they arrived at in the form of a discussion on the tasks. At the end of the thesis, an evaluation of...
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Solving stereometric problems in GeoGebra
HORÁČKOVÁ, Lenka
The aim of the bachelor's thesis on the subject of 'Solving stereometric problems in GeoGebra' was to create a collection of own solved examples from stereometry from the curriculum in the range from primary school, through secondary school to university training of mathematics teachers. The GeoGebra program is a support tool for this bachelor's thesis. The work focuses mainly on the curriculum of primary and secondary schools, partly also on the curriculum at universities. The work focuses mainly on square figures in the scope of the curriculum at primary and secondary schools and partly also at universities.
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Volume of Pyramid
Vaňkát, Milan ; Halas, Zdeněk (advisor) ; Bečvář, Jindřich (referee)
Title: Volume of Pyramid Author: Bc. Milan Vaňkát Department: Department of Mathematics Education Supervisor: Mgr. Zdeněk Halas, DiS., Ph.D. Abstract: The subject of this thesis is Hilbert's third problem. In the first chapter we follow it's roots back to Euclid's Elements. We focus in particular on the theorem that triangular pyramids of equal altitudes are to each other as their bases. We also discuss analogous statements for triangles, parallelograms and parallelepipeds. We point out the way in which the issues of content and volume of geometrical figures were approached in Greek mathematics. In the second chapter we present the historical background of Hilbert's third problem. We outline the development of methods of it's solution - from M. Dehn's first answer in 1901 to the abstract definition of Dehn invariants as a R ⊗Z Rπ- valued functional on the polyhedral group that was introduced by B. Jessen in 1968. Later we construct Dehn invariants and present a thorough solution to the Hilbert's third problem. In the end we sketch out mathematical issues connected to this problem that have been studied in the second half of 20th century. An illustrative high school exercise on derivation of the volume formula for py- ramid by Eudoxus's method of exhaustion is included in the appendix. Keywords: pyramid, volume,...
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The new synagogue in Frýdek-Místek
Hanousek, Ondřej ; Baranyai, René (referee) ; Dulenčín, Juraj (advisor)
The thesis deals with a hypothetical project of a new building complex of a synagogue, a kosher restaurant and a community centre at the location of the former synagogue in Frýdek. The proposal includes a memorial of the destroyed synagogue and Jewish community, as well as the incorporation of the complex into the urban structure of the city. The project proposes a building distributed into three volumes. The restaurant and community centre are connected by an underground garage within a U-shaped floor plan. The buildings are axially symmetrical, white, with expressive rhythmical perforations of the facade. They surround the building of the synagogue in the shape of a seven-sided pyramid, which is clad with blue tempered steel and creates a strong contrast with the associated buildings. The whole complex is oriented towards the park and the chateau in Frýdek, from which it is clearly visible and thanks to its distinct volumetric and material expression and axially symmetrical composition creates a new landmark for the city.
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Understanding of formulas for areas and volumes of geometric figures in the history of mathematics and in pupils
Tavačová, Adela ; Kvasz, Ladislav (advisor) ; Vondrová, Naďa (referee)
Title: Understanding Area and Volume Formulae of Geometric Figures in the History of Mathematics and by Pupils Author: Bc. Adela Tavačová Supervisor: prof. RNDr. Ladislav Kvasz, DSc. The aim of this thesis is to describe the nature and possible causes of problematic areas in pupils' understanding of area and volume of geometric shapes and solids and treat this issue from the point of view of its ontogeny and phylogeny. Modern theories of gradual formation of the concepts of area and volume in pupils' minds will be characterized, together with the historical development of these concepts (from ancient Egypt and Greece to modern day). Complex analysis of the current Mathematics course books for primary and lower-secondary level is offered in the second part of the thesis. The analysis is based on the criteria following from the study of academic literature and on the historic research in this area. The aim of the analysis is to describe the way in which the course books treat geometric formulae and to what extent they respect their gradual development. In the final discussion, general aspects leading from the analysis will be summarized and offered as possible inspiration for pupils, teachers and future teachers of Mathematics. Key Words: formula, area, volume, algebraic language, hypothetical...
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Intersection of solids
Otrubová, Anna ; Hromadová, Jana (advisor) ; Šarounová, Alena (referee)
The four chapters of this diploma thesis introduce a survey of the basic intersection types of solids, the focus being placed on the intersection of two pyramid and prisma solids, acting as a counterweight to most textbooks' interest in intersection of curved surfaces. The first chapter provides a detailed, wide-ranging insight into the issue of the solid and line intersection. The conclusion part of the thesis provides the reader with a brief commentary on the used literature. The work is supplemented with figures and example solutions. In the appendix part are found pre-drawn assignments. The enclosed CD contains complementary materials such as step by step solutions and 3D models created in the GeoGebra software along with drawn problems found especially in upper secondary school geometry textbooks and curriculum.
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Cuts of polyhedrons
Borzíková, Žofia ; Bečvář, Jindřich (advisor) ; Šarounová, Alena (referee)
Title: Cuts of polyhedrons Author: Žofia Borzíková Department: Department of Mathematics Education Supervisor: doc. RNDr. Jindřich Bečvář, CSc., Department of Mathematics Education Abstract: The topic of the bachelor thesis is Cross Sections of Polyhedra. The basic principles of constructing such cross sections are shown and explained through illustrative examples of cross sections of solids together with the detailed description of the construction process. Especially, the cross sections of some "common" polyhedra like prism, tetrahedron, pyramid or octahedron are further discussed. The reader should use them to take up with the main issue of constructing cross sections. As an application of the acquired knowledge, the cross sections of other solids like Platonic or Archimedean solids are introduced here. The goal of these examples is to cultivate spatial intelligence for the purpose of constructing cross sections or better understanding of polyhedral in general. The bachelor thesis is a commented set of examples, which can be used as an additional material in the education of mathematics, not only in grammar schools. Keywords: cross sections, cube, cuboid, prism, pyramid, tetrahedron, regular polyhedra, semi-regular polyhedra
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Volume of Pyramid
Vaňkát, Milan ; Halas, Zdeněk (advisor) ; Bečvář, Jindřich (referee)
Title: Volume of Pyramid Author: Bc. Milan Vaňkát Department: Department of Mathematics Education Supervisor: Mgr. Zdeněk Halas, DiS., Ph.D. Abstract: The subject of this thesis is Hilbert's third problem. In the first chapter we follow it's roots back to Euclid's Elements. We focus in particular on the theorem that triangular pyramids of equal altitudes are to each other as their bases. We also discuss analogous statements for triangles, parallelograms and parallelepipeds. We point out the way in which the issues of content and volume of geometrical figures were approached in Greek mathematics. In the second chapter we present the historical background of Hilbert's third problem. We outline the development of methods of it's solution - from M. Dehn's first answer in 1901 to the abstract definition of Dehn invariants as a R ⊗Z Rπ- valued functional on the polyhedral group that was introduced by B. Jessen in 1968. Later we construct Dehn invariants and present a thorough solution to the Hilbert's third problem. In the end we sketch out mathematical issues connected to this problem that have been studied in the second half of 20th century. An illustrative high school exercise on derivation of the volume formula for py- ramid by Eudoxus's method of exhaustion is included in the appendix. Keywords: pyramid, volume,...
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