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Fibonacci numbers with applications
Váňa, Viktor ; Kureš, Miroslav (referee) ; Klaška, Jiří (advisor)
This bachelor thesis deals with golden ratio, its appearance and possible use in technical practice. It is divided into two main parts. First part deals with golden ratio appearance in chemistry. Specificly inquire into distance between centers of atoms in a halide salts compounds, asymmetric features of chemical processes, stability of transuranic elements, energy levels of gas electrons and spin number of subatomic elements. Another part takes an interest in simulation of electrical power lines supplied by two sides and calculatinon of its parameters. Last section is included in order to present variety of Fibonacci numbers appearence. It shows us relations between insects and flower, where insect live.
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Applications of Fibonacci numbers in economy - Elliott Wave Principle
Rusyniak, Martin ; Karásek, Jiří (referee) ; Klaška, Jiří (advisor)
The Elliott wave principle, as a technique for prediction of price movements, combines knowledge of Fibonacci numbers, golden ratio and crowd psychology. This method replaces price fluctuations with waves, amongst which it is finding relation to the golden ratio. In the introduction of this bachelor thesis, we are going to have a look at Fibonacci, his integer sequence and theoretical description of the Elliott wave principle. The core of this thesis is explanation of basic strategy on five-wave pattern and later, swing breakout strategy and 3-swing pattern. All of these strategies are presented on real-world examples with explanation of analogy and nuances. These strategies were explained as factual usable algorithms with clarification of all properties. Concept of algorithm for the application of breakout strategy and its flowchart is included in matching chapter. After that follows insight into problematic of spirals as a method uncovering another options for use of the golden ratio for analysing price movements.
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Quaternion algebras
Bečka, Pavel ; Klaška, Jiří (referee) ; Kureš, Miroslav (advisor)
This thesis deals with quaternion algebras. A quaternion algebra is a four dimensional vector space with basis 1, i, j, k and multiplication defined as i2 = a, j2 = b, ij = -ji = k. The thesis deals with the basic attributes of quaternion algebras, quaternion orders and maximal orders. Lastly the thesis deals with the concept of discriminant of algebras and connected terms like Hilbert symbol and Legendre symbol. Throughout the thesis we show solved problems using mathematical software SAGE.
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Quaternion algebras
Bečka, Pavel ; Klaška, Jiří (referee) ; Kureš, Miroslav (advisor)
This thesis deals with quaternion algebras. A quaternion algebra is a four dimensional vector space with basis 1, i, j, k and multiplication defined as i2 = a, j2 = b, ij = -ji = k. The thesis deals with the basic attributes of quaternion algebras, quaternion orders and maximal orders. Lastly the thesis deals with the concept of discriminant of algebras and connected terms like Hilbert symbol and Legendre symbol. Throughout the thesis we show solved problems using mathematical software SAGE.
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Applications of Fibonacci numbers in economy - Elliott Wave Principle
Rusyniak, Martin ; Karásek, Jiří (referee) ; Klaška, Jiří (advisor)
The Elliott wave principle, as a technique for prediction of price movements, combines knowledge of Fibonacci numbers, golden ratio and crowd psychology. This method replaces price fluctuations with waves, amongst which it is finding relation to the golden ratio. In the introduction of this bachelor thesis, we are going to have a look at Fibonacci, his integer sequence and theoretical description of the Elliott wave principle. The core of this thesis is explanation of basic strategy on five-wave pattern and later, swing breakout strategy and 3-swing pattern. All of these strategies are presented on real-world examples with explanation of analogy and nuances. These strategies were explained as factual usable algorithms with clarification of all properties. Concept of algorithm for the application of breakout strategy and its flowchart is included in matching chapter. After that follows insight into problematic of spirals as a method uncovering another options for use of the golden ratio for analysing price movements.
|
|
|
Fibonacci numbers with applications
Váňa, Viktor ; Kureš, Miroslav (referee) ; Klaška, Jiří (advisor)
This bachelor thesis deals with golden ratio, its appearance and possible use in technical practice. It is divided into two main parts. First part deals with golden ratio appearance in chemistry. Specificly inquire into distance between centers of atoms in a halide salts compounds, asymmetric features of chemical processes, stability of transuranic elements, energy levels of gas electrons and spin number of subatomic elements. Another part takes an interest in simulation of electrical power lines supplied by two sides and calculatinon of its parameters. Last section is included in order to present variety of Fibonacci numbers appearence. It shows us relations between insects and flower, where insect live.
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