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Teaching geometric series through CLIL method with using of German language
Korcová, Aneta ; Moravcová, Vlasta (advisor) ; Hromadová, Jana (referee)
The core of the thesis is the realization of three lessons of mathematics conducted in accordance with the CLIL method, which integrates the teaching a non-linguistic subject with foreign language teaching. The topic of the lessons was non-finite geometric series and the chosen foreign language was German. The first part of the thesis introduces key definitions and theorems concerning sequences and geometric series. Comparisons are drawn between approaches of the Czech Republic and two German-speaking countries, Austria and Germany, in relationship to the teaching non-finite geometric series. Furthermore, available teaching materials of the selected countries are compared and applied visualized problems which appear in them are analysed. In the second part, the CLIL teaching method is presented together with the methodology according to which the lessons were prepared, realized and subsequently assessed. To conclude, the thesis presents a detailed analysis of the preparation and progress of the lessons, including the reflection. The appendix comprises of the utilized teaching materials as well as a range of the solved problems.
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Selected Fractal Algorithms and Their Use
Michálek, Bedřich ; Španěl, Michal (referee) ; Herout, Adam (advisor)
To read up on the problems of fractal algorithms, to program a simple demo application of this algorithms and propose alternatives of a further study was the goal of my project. Since the subject of fractals and fractal algorithms is very extensive, I concentrated on three specific types of them - the Mandelbrot set and the Julia sets related to it, iterated function systems with application of different algorithms for generating, and the stochastic fractals and their utilization for grass, shrub and plasma modelling. I tried out for a certain rate of their optimalization, acceleration and the comparison of time and memory requirements in my study and application although it is not ever possible due to the characteristic of the given fractal type. I also theoretically present some utilization options of the SSE technology for the acceleration of fractal algorithm calculations. The demo application is proposed in the very easy way because there was not the goal to programme a new carefully worked-out software, but rather to try to implement the read up algorithms. For this reason I focused on the clear implementation of these algorithms to be their utilization easily possible. The application is written in C/C++ language with SDL library used to handle the graphics output.
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Fractals in Computer Graphics
Šelepa, Jan ; Venera, Jiří (referee) ; Sumec, Stanislav (advisor)
The goal of this work is to give introduction and specification of fractals. The first chapter presents the basics of fractal geometry. The second chapter maps the history of fractals and points out the most important people of fractal science. The third chapter presents fractal classification based on several criteria and gives basic examples. The fourth chapter is a summary of widely used applications for fractal creation. The last chapter describes the application that was made to demonstrate given algorithms and fractals mentioned in this thesis.
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Fractal Dimension Analysis And Fractal Properties of Financial Markets
Jedličková, Marie
Financial markets are a subject of many studies and research purposes. The ability to correctly observe and describe the dynamics of financial markets would mean the possibility to predict its future behaviour. Many approaches and methods have been used to achieve this objective. In recent history it has come to light that many natural phenomena could be described using fractal geometry. Alongside with the fractals can be often found the application of fuzzy logic and also the theory of chaos. These three concepts are recently very powerful in describing complex system and getting closer to understanding them. This paper deals with the basic concepts of fractal analysis and also fuzzy logic and the possibility to use those to observe financial markets and analyze their behaviour. The purpose of this is to present the reader with introduction to the problematics and propose starting concepts to begin the research into the matter.
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LEGO Mindstorms: Didactic utilization in mathematics with a focus on fractals
Čadek, Jan ; Jančařík, Antonín (advisor) ; Pilous, Derek (referee)
TITLE: LEGO Mindstorms: Didactic utilization in mathematics with a focus on fractals ABSTRACT: The objective of this thesis is to determine whether the teaching of fractal geometry supported by computer and robotic LEGO Mindstorms NXT has its place in the education of primary and secondary schools pupils in the Czech Republic. The theoretical part focuses on key topics and personalities closely connected to fractal geometry problematics. It provides a brief historical overview of the fractal geometry development, its potential use in teaching mathematics (with reference to Turkish curriculum documents), and a description of LEGO Mindstorms NXT which can well serve as a manual for teachers and pupils. The practical part contains instructions for building a robotic turtle as well as a proposal of teaching block aimed to support pupils' algorithmic and geometric thinking including key competencies. Quantitative comparison of the results taken from Turkish studies and evaluation of the project by the author and pupils are a part of the experiment as well. KEYWORDS: LEGO Mindstorms NXT, fractal, programming, Logo, learning by doing, turtle, Papert, L-system, microworlds
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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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Fractal pattern patch antenna
Prouza, Jakub ; Pítra, Kamil (referee) ; Raida, Zbyněk (advisor)
This bachelor thesis deals with the application of fractal layouts in the design of microstrip antennas. Attention is turned to assessing their impact on properties of a conventional patch antenna. The first part of thesis is focused on theoretical knowledge of fractal geometry and planar antennas. In the next part of this thesis, first antenna is describer together with ways of its design. In the final section, next fractal antenna design is given. Proposed antenna is made, the results obtained are compared and benefits of the fractal design are evaluated.
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Transcendental aspects of architectural design as factors of sustainability
Volnohradský, Radan ; Peřinková, Martina (referee) ; Loutocká, Vlasta (referee) ; Uřídilová, Marcela (referee) ; Urbášková, Hana (advisor)
This thesis deals with complex processes, relationships and phenomena which go beyond the assumed and accepted materialistic perception of the world in general and the process of architectural design specifically. It clarifies and actually redefine the sustainability from a point of higher universal principles forming our environment. At the beginning this thesis presents an extensive knowledge base of existing holistic design systems including Feng-shui, sacred geometry, geomancy or numerology. The purpose is to build and establish a solid foundation for understanding and further research as well as objectively interpreting lesser known topics as a whole. On the basis of intersecting information through the above mentioned topics we specify the hypothesis which proposes the pre-existence of one unifying design matrix of harmonic structures in architecture. The structure of its verification takes us from an analysis of the science of human perception to systems of self-similar contextual references of animated and inanimated forms. These systems of emergent form and flow are basically known as fractals, and could be expressed in both mathematical and geometrical languages. The thesis research then consists of analysing chosen examples of urban and architectural scale in sense of fractality, symbolism and geometrical matrices. We include and integrate the research of associated and relevant phenomena in pedagogical practice, and a case study of the application of fractals in development of a chosen town. From the results of this thesis we abstract five non-dogmatic guidelines or tenets for architectural design; which are supported by experimental verification on some of the author´s buildings. These tenets stand as pillars of implosive architecture. This kind of architecture in context of transcendental overlaps means a possibility of how to bring our anthropogenic environment closer to the natural and harmonic code of the Universe.
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