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Mascheroni constructions
Hatschbachová, Jana ; Hromadová, Jana (advisor) ; Škorpilová, Martina (referee)
This bachelor's thesis concerns with the topic of Mascheroni constructions. These are constructions done with compass alone. The thesis contains three chapters, the first is devoted to a brief summary of the history of Mascheroni constructions. The second chapter presents Mohr-Mascheroni theorem and its proof. The third chapter contains a description of several basic Mascheroni constructions including proofs. Part of this work is also a GeoGebra book - Mascheroni constructions, which is divided into two parts. In the first part, there are stepped solutions for all constructions mentioned in the third chapter. The second part contains interactive exercises for each construction.
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Matrices with Entries -1, 1, 0
Píšová, Vendula ; Škorpilová, Martina (advisor) ; Bečvář, Jindřich (referee)
In this thesis we introduce selected classes of matrices, whose entries are only numbers −1, 1, 0. We combine existing results from various fields of Mathematics and enrich them with specific examples and explanations, with the aim of making the understanding of the text easier. Thanks to that, the reader can comprehend the theory and look under the hood of non-trivial applications. We will start with introducing adjacency matrices and covering of complete graphs with complete bipartite graphs. Then we follow with Hadamard matrices and will show the conditions for their constructions. Incidence matrices of the set systems will help us solve the combinatorial problem of the Odd-town clubs. Finally, we will prove the Cayley formula about the spanning trees of the complete graph, using incidence matrices.
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Assortment of perennials used on rural gardens and their application
Škorpilová, Martina ; Matiska, Pavel (advisor) ; Adam, Adam (referee)
This thesis collects and assesses data on the assortment of perrenials grown in rural areas in the Kolín, Nymburk and Prague - East districts in the Central Bohemian Region. The aim of this work was to ascertain which varieties of perennials are used in public greenery in rural areas and their application in individual districts.
The collected data assesses on the assortment of perennials grown in the selected areas, and presents tables and charts summarising the occurrence of individual plant varieteies.
Options for using perennials to brighten up public areas in rural municipalities are proposed in the final part of the thesis.
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