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Surfaces with constant Gauss curvature
Zemanová, Silvie ; Kureš, Miroslav (referee) ; Doupovec, Miroslav (advisor)
This bachelor thesis deals with description of surfaces with constant Gaussian curvature and its main goal is to classify these surfaces. The first part is devoted to the classification of surfaces of revolution with constant Gaussian curvature. The next part consists of description of selected surfaces with zero Gaussian curvature, on which is shown that the same shape of the first fundamental form can be achieved. The last part deals with the classification of all surfaces with zero Gaussian curvature. For easier understanding of the text, the thesis includes images of selected surfaces.
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Hyperbolic geometries
Brdečková, Johanka ; Tomáš, Jiří (referee) ; Doupovec, Miroslav (advisor)
The present thesis deals with hyperbolic geometry. We derive parametric equations of the curve tractrix and the surface pseudosphere. Then we discuss two models of hyperbolic geometry, which are derived from the parametrization of pseudosphere.
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Surfaces with constant Gauss curvature
Zemanová, Silvie ; Kureš, Miroslav (referee) ; Doupovec, Miroslav (advisor)
This bachelor thesis deals with description of surfaces with constant Gaussian curvature and its main goal is to classify these surfaces. The first part is devoted to the classification of surfaces of revolution with constant Gaussian curvature. The next part consists of description of selected surfaces with zero Gaussian curvature, on which is shown that the same shape of the first fundamental form can be achieved. The last part deals with the classification of all surfaces with zero Gaussian curvature. For easier understanding of the text, the thesis includes images of selected surfaces.
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Hyperbolic geometries
Brdečková, Johanka ; Tomáš, Jiří (referee) ; Doupovec, Miroslav (advisor)
The present thesis deals with hyperbolic geometry. We derive parametric equations of the curve tractrix and the surface pseudosphere. Then we discuss two models of hyperbolic geometry, which are derived from the parametrization of pseudosphere.
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Geometry in real life
ZOUBEK, Tomáš
The aim of this diploma thesis is a set of methodical materials for geometry education on primary, secondary schools and possibly during the basic courses on a university. This materials will be based on real geometry phenomenon which we meet every day. The knowledge and understanding of this phenomenon might play an important part during studies of mathematics and geometry. It also shows mathematics and geometry in their close relationship with the real world. The part of the description this phenomenon presented will be solved examples, examples for demonstration and also examples for practise. They are prepared a task, solution and a methodical reviews for each exercise. When preparing this work, it was used his current knowledge of methodology of mathematics and it was selected such forms, means and didactics procedures, which will go together with requirements on a visual solution (mathematical and geometrical software, an interactive whiteboard, worksheets, ) and with the purpose of the example presented (it´s interpretation, practise, testing, ). The part of this diploma thesis are worksheets. This worksheets can help get to know with geometrical phenomena in this work. The worksheets have primary and secondary school level.
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