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Using mathematical calculations to solve problems in sciences
Gáborová, Andrea ; Novotná, Jarmila (advisor) ; Jančařík, Antonín (referee)
This work deals with word problems from natural sciences whose main mathematical apparatus are circle, sphere and their parts. The work is divided into three main parts - part about word problems, part about used mathematical apparatus in word problems and part containing verbal tasks from sciences. The first part defines the word problems and describes how to solve the problems. The second part contains the mathematical apparatus used in the word problems in part three. The third part is a collection of verbal tasks from the sciences, divided into the taskes solved at primary and secondary schools. The individual vocabulary is presented as a necessary theoretical basis of sciences. In the third part, I created most of the vocabulary myself.
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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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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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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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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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Plane geometry teaching at secondary schools
Machovcová, Lucie ; Zhouf, Jaroslav (advisor) ; Dvořák, Petr (referee)
This work compares and evaluates several math's textbooks for secondary school where we can find schoolwork from plane geometry. The aim of this work is drawing the main advantages and disadvantages of those textbooks, evaluating whether all textbooks contain themes which are required by School Curriculum and interpretation of a questionnaire survey among teachers of mathematics. In the last chapter, it is described how a new ideal textbook of plane geometry wouldlook like. Those were taken on the grounds of gained information from my questionnaire survey. Themes which cannot be found in compared textbooks for secondary schools are a part of recently made textbook since it is not necessary to know any new terms for their understanding. Key words: geometry, teaching geometry, textbooks, polygon, circle
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Nekonečné matroidy
Böhm, Martin ; Pangrác, Ondřej (advisor) ; Loebl, Martin (referee)
We summarize and present recent results in the field of infinite matroid theory. We define and prove basic properties of infinite matroids and we discuss known classes of examples of these structures. We focus on the topic of connectivity of infinite matroids and we link some matroid properties to connectivity. The main result of this work is the proof of existence of infinite matroids with arbitrary finite connectivity, but without finite circuits or cocircuits. Powered by TCPDF (www.tcpdf.org)
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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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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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S335
Dostál, Jan ; Rais, Lukáš (referee) ; Gabriel, Michal (advisor)
The Bachelor thesis named S355 takes the form of a large-format metal object. The default material for the sculpture is the construction steel S355, and the sculpture consists of individual interconnected segments that form the resulting shape of a rising circle. The determining principle of the sculpture is the shape and the size of the circle, the motif of which occurs not only in the resulting form, but also in individual segments.
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