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A guide to fractal geometry
Hajmová, Kateřina ; Pokorný, Dušan (advisor) ; Boček, Leo (referee)
This text is intended for the general public. The aim of this work is acquaint readers with foundations of the fractal geometry. The thesis explains important terminology, such as the coastline paradox or the fractal dimension. A great emphasis is placed on explaining the concept of the box-counting dimension. The thesis includes the construction methods of the L-systems, IFS, TEA and random fractals. In addition, it shows the use of fractal geometry in practice. The text is completed with illuminating figures drawn in most cases in Geogebra software and Wolfram Mathematica.
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Advanced Topics in Plane Geometry
Hajmová, Kateřina ; Štěpánová, Martina (advisor) ; Moravcová, Vlasta (referee)
The aim of this thesis is to introduce a series of knowledge from advanced planimetry, which can be proved using the knowledge of high school geometry. Selected theorems deal with characteristic of squares with a common vertex (Finsler-Hadwiger theorem, Theorem of Four Squares, Bottema's theorem), significant points of plane entities (Gergonne point theorem, Švrček point theorem, Simson's Theorem, Miquel's theorem), Feuerbach's circle and its relation to the Euler's line. In this thesis, there is also mentioned Reim's theorem, Napoleon's theorem, and Thebault's theorem. This thesis contains a lot of illustrations created in the Geogebra Mathematical Software, which are available online in interactive form.
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A guide to fractal geometry
Hajmová, Kateřina ; Pokorný, Dušan (advisor) ; Boček, Leo (referee)
This text is intended for the general public. The aim of this work is acquaint readers with foundations of the fractal geometry. The thesis explains important terminology, such as the coastline paradox or the fractal dimension. A great emphasis is placed on explaining the concept of the box-counting dimension. The thesis includes the construction methods of the L-systems, IFS, TEA and random fractals. In addition, it shows the use of fractal geometry in practice. The text is completed with illuminating figures drawn in most cases in Geogebra software and Wolfram Mathematica.
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