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Special Surfaces
Ochodnický, Erik ; Vašík, Petr (referee) ; Doupovec, Miroslav (advisor)
The aim of this thesis is to create an overview of special surfaces and to define their characteristics. Categories of surfaces that I found the most important are surfaces of revolution, minimal, with constant Gaussian curvature, and finally Clairaut surfaces. For every category I'll introduce, in my opinion, the most important examples of surfaces along with their parametrizations and I'll describe them. Surfaces will be accompanied by images, created in MATLAB. In the last part I'm going to focus on Clairot patches, on finding geodesics on these surfaces and their description. I'll show numerous original images of geodesics on diverse surfaces.
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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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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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|
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Special Surfaces
Ochodnický, Erik ; Vašík, Petr (referee) ; Doupovec, Miroslav (advisor)
The aim of this thesis is to create an overview of special surfaces and to define their characteristics. Categories of surfaces that I found the most important are surfaces of revolution, minimal, with constant Gaussian curvature, and finally Clairaut surfaces. For every category I'll introduce, in my opinion, the most important examples of surfaces along with their parametrizations and I'll describe them. Surfaces will be accompanied by images, created in MATLAB. In the last part I'm going to focus on Clairot patches, on finding geodesics on these surfaces and their description. I'll show numerous original images of geodesics on diverse surfaces.
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