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Comparison of lightning detection networks over Czechia
Pacovská, Lucie ; Popová, Jana (advisor) ; Müller, Miloslav (referee)
This thesis focuses on ground-based lightning detection which is important since lightning discharges still cause casualties yearly worldwide. The thesis provides description of several ground-based lightning detection networks and an analysis of lightning data of three lightning detection networks covering the Czech Republic during 2015 - 2021. Specifically, the data of the World Wide Lightning Location Network (WWLLN), the amateur network Blitzortung and the European network EUropean Cooperation for LIghtning Detection (EUCLID) are investigated. The thesis examines the spatial and temporal characteristics of lightning discharges from the three detection networks, the relationship between lightning discharges and land cover from CORINE Land Cover data, and the relationship of lightning discharges with types of weather situations based on the Czech Hydrometeorological Institute (CHMI) data. The results show that there is not much difference in the temporal and spatial characteristics of lightning discharges among the three detection networks. The relationship between lightning activity and land cover is the same for the three networks. Unlike the relationship between lightning activity and land cover, the relationship between lightning activity and weather types is in good agreement among the...
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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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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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Comparison of Euclid's and Hilbert's Axiomatic Systems of Geometry from the Didactic Viewpoint
Tavačová, Adela ; Kvasz, Ladislav (advisor) ; Holíková, Marie (referee)
Title: Comparison of Euclid's and Hilbert's Axiomatic Systems of Geometry from the Didactic Viewpoint Author: Adela Tavačová Supervisor: prof. RNDr. Ladislav Kvasz, Dr. The aim of this thesis is to describe the development of axiomatic systems of geometry and its applicability in didactics of mathematics. The thesis is composed of two parts, the first of which is focused on Euclid and his work The Elements, the second being aimed at David Hilbert and his work Grundlagen der Geometrie. The thesis contains a short historical context describing the gradual development of geometry and geometrical thinking, from the ancient times up to now. It will further cover the influence of The Elements upon mathematics as such, its teaching, and a spread across the countries of the world and the Czech Republic in particular. A detailed view is given to the characteristics of Euclid's axiomatic system and its possible difficulties caused predominantly by a vast temporal span and translations from Greek to other languages. I will continue with the analysis of the most considerable logical gaps in The Elements, thus paving the way for the introduction of a modern axiomatic system of geometry, represented by David Hilbert. Apart from the main features and the structure of David Hilbert's axiomatic system, the second...
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