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Algebraic Curves in History and School
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Jančařík, Antonín (referee)
TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra
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Taxicab Metric in Teaching-Learning Process at Basic School
Bruna, Jiří ; Zhouf, Jaroslav (advisor) ; Vondrová, Naďa (referee)
This master's thesis explores the possibility of including Taxicab metric as a subject matter into instruction at lower secondary level of education and it does so in several ways. Firstly, it looks into a curricular document of state level (Framework Educational Programme) and discusses instances at which the subject matter and the concept of lower secondary education are in agreement. Secondly, this thesis analyses a selected series of textbooks with respect to exercises that can be seen as linked to non-Euclidean metrics. Furthermore an experiment is described and evaluated, whose purpose, as a part of this thesis, was to find out if selected pupils can successfully solve problems in the context of the Taxicab metric and if related instruction influenced pupils' understanding of the concept of line segment and circle in a desired way. The teaching material which constituted an integral part of the experiment is presented as well.
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Isoperimetric inequalities
Bártlová, Tereza ; Slavík, Antonín (advisor) ; Boček, Leo (referee)
In the present work we study isoperimetric problem and its description by isoperimetric inequality. The legend of Dido, which inspired formulation of the isoperimetric problem, is described in the first chapter. The following chapters are devoted to elementary proofs of isoperimetric inequality for polygons as well as for curves. The last chapter focuses on related problem than isoperimetric that is isodiametric problem. This is described Reuleaux polygon that constitutes a means for proof of isodiametric inequality.
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Length measurement
Pecinová, Iva ; Šarounová, Alena (advisor) ; Surynková, Petra (referee)
My bachelor thesis Length measurement deals with the euclidean length measurement. It deals with the history of the length measurement in the Czech country, the emergence of the basic unit of length - meter and especially the circumference. The work is intended primarily for high school teachers of mathematics and lovers of measurements which are expected to at least high school knowledge of mathematics. This text is good for primary schools teachers of mathematics which is intended Handbook for small meter. The component part of my bachelor thesis is an enclosed CD, where is found the bachelor thesis in an electronic form and the already mentioned Handbook for small meter - a version for printing.
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Circuits and matchings in graphs
Tesař, Karel ; Pangrác, Ondřej (advisor) ; Šámal, Robert (referee)
O grafu řekneme, že je k-linkovaný, pokud pro každých k dvojic jeho vrchol· existují navzájem disjunktní cesty, které dané dvojice spojují. Existuje vztah mezi k-linkovaností a vrcholovou souvislostí grafu. V této práci hledáme vztah mezi vrcholovou souvislostí grafu a vlastností, že každých k jeho disjunktních hran leží na společné kružnici. Tento problém se dá řešit pomocí k-linkovanosti. Naším cílem je dosáhnout lepších odhad· na souvislost, resp. jiných postačujících podmínek než těch, které jsou známe pro k-linkovanost. 1
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Algebraic curves in history and school
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Vondrová, Naďa (referee)
TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra
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Mascheroni Construction
Kaprasová, Monika ; Jančařík, Antonín (advisor) ; Zamboj, Michal (referee)
This Bachelor's thesis presents basic knowledge about constructions with a compass. It's divided into a historical part which indicates how thinking about constructions with a compass evolved. The next part are Mascheroni's constructions. Three Mascheroni's main problems and other two are listed here. Then there is compiled the basic of the proof of Mascheroni's theorem. This thesis includes series of several constructional tasks with compass only. These tasks are solved in GeoGebra program. Each construction contains a proof of its rightness. The proofs are made as simply as possible so that for anyone who shows his interest is the thesis suitable. Because of it this thesis can serve students for their self-study as teachers for an enrichment of teaching geometry.
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Mascheroni Construction
Kaprasová, Monika ; Jančařík, Antonín (advisor) ; Zamboj, Michal (referee)
This Bachelor's thesis presents basic knowledge about constructions with a compass. It's divided into a historical part which indicates how thinking about constructions with a compass evolved. The next part are Mascheroni's constructions. Three Mascheroni's main problems and other two are listed here. Then there is compiled the basic of the proof of Mascheroni's theorem. This thesis includes series of several constructional tasks with compass only. These tasks are solved in GeoGebra program. Each construction contains a proof of its rightness. The proofs are made as simply as possible so that for anyone who shows his interest is the thesis suitable. Because of it this thesis can serve students for their self-study as teachers for an enrichment of teaching geometry.
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Rotation Number on a Circle
Bíma, Jan ; Vejnar, Benjamin (advisor) ; Pražák, Dalibor (referee)
We apply the dynamical method to obtain structural results concerning certain classes of one-dimensional maps. The notion central to the work is that of a rotation number on a circle; we relate the rotation modulus to periodicity of an orientation-preserving circle homeomorphism and generalize the concept to continuous degree-1 circle maps. We investigate the asymptotic orbit behaviour of circle homeomorphisms with irrational rotation number and develop the Poincaré Classification Theorem which establishes topo- logical (semi-)conjugacy of a circle homeomorphism with an irrational rotation number to a rotation with the same rotation number. 1
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Visual inspection of axial bearing
Sýkora, Vojtěch ; Richter, Miloslav (referee) ; Janáková, Ilona (advisor)
This thesis is about visual control and measurement of bearings by using image sensors and it is about providing appropriate conditions for this measurement. It describes the selection of suitable hardware to solve this case. A large part of the thesis is the design and creation of my own light. Furthermore, algorithms for processing the acquired images of bearings are proposed. The result of the processing is the determination of the type of bearing in the image and the finding of possible defects.
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