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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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Context of economic cycles and economic policy in the Czech Republic since the early 21st CENTURY
Vaňkát, Milan ; Czesaný, Slavoj (advisor) ; Řežábek, Pavel (referee)
The aim of the diploma thesis is to analyze the economic cycle in the Czech republic since 2000. Theoretical-methododological part of this thesis is consist of the theories of economic cycle, kinds of economic policy and indicators of external and internal policy, which will be used later in the analysis. In the practical part I focuse on the cause of the crisis, its expansion to the Europe and as well on Germany as the economics which influences the cycle of Czech republic, which is the fact I prove statisticaly in my thesis. The analysis of indicators of czech economics is carried out trend indicators included. The conclusion and the aim which have been fulfilled is identification and evaluation of business policy of Czech republic and the suggestion of next steps leading to the improvement of the state of the economics.
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Development of German economy in 1936-1939.
Vaňkát, Milan ; Stellner, František (advisor) ; Soběhart, Radek (referee)
After the Great Depression, Germany was hit by massive unemployment and a general decline in production. Under the Nazi administration, public investments served as a solution to reduce unemployment to a minimum level and in 1936 were fully diverted to the defense industry. In relation to the rearmament of the German army the country was supposed to be ready for a short war in four years. In order to quickly equip the army, Germany faced a lack of raw materials and especially the lack of funds for acquiring them. Despite these problems, the German economy recorded a great economic growth in that period. This situation leads to the question, what economic conditions were in Germany and what contributed to such an economic outcome.
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