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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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Geometry in architecture
BÁRTOVÁ, Michaela
The reader will understand the relationship between geometry and everyday life. Selected curves and bodyes are mathematically described. It is illustrated with photos of architectural elements. 3D models are made in GeoGebra and SketchUp. Blending theory and practice to help understand the geometry. It can be used for teaching math and geometry. This thesis discusses about the conic, selected technical curves and quardics.
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Removal of Anesthesia Tube from Pediatric CT Data
Šejnohová, Marie ; Čmiel, Vratislav (referee) ; Walek, Petr (advisor)
The goal of this semestral thesis is to detect and subsequently to eliminate an anaesthesiological tube from a pediatric CT data using a Hough transform. It describes particular edge detectors based on the first and the second differences. In addition, it explains a principle of the edge detection using to this detectors. Then there is talked about the Hough Transform where is described a parametric space for lines and circles detection. Here follows a description of image to the parametric space. In a practical part there is implementation of the edge detection and the Hough transform. The Hough space must be normalized to better evaluation. At the evaluation there are found a concentric cicrles corresponding with edges of an anaesthesiological tube which is then possible to remove.
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The Municipal Baths
Škůrek, Josef ; Šamalík, Zdeněk (referee) ; Ruller, Ivan (advisor)
Treated area is situated in a part of Stare Brno (between the Voronez hotel and Svratka river). The area is intersected by the delivery tracks (leading to the fair area). This tracks markedly influence the concept of the groundplan design of the project (especially in the southwest part). The volume of the baths respect the streetline of Rybarska street and Porici street and formally finishes the block row of these streets.
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A Collection of Mathematical Problems for the 8th Grade of Basic School
HRANÍČEK, Antonín
This bachelor thesis named A Collection of Mathematical Problems for the 8th Grade of Basic School consists of numerical as well as word problems and it focuses on the topics covered in mathematics in the 8th grade of basic schools. The collection is meant to be used as a practice material. The content is divided into 9 chapters which are further divided into individual subchapters. At the end of each chapter, there are results and solutions for each chapter.
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Kissing Circles
KOTLAS, Miroslav
My thesis deals with various methods of solving the correlation of~the~diametres of four mutually tangent circles. It also deals with the history of~the~derivation of mathematical property. The didactic part contains a book of solved tasks. It involves the topic of Apollony fractals, gothic vaults, examples of~mutually tangent circles and set of exercises for practising different solutions of the various cases.
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Selected topics for teaching mathematics in school with the interactive whiteboard - planimetry
BABKA, Jan
The diploma thesis covers points, line segments, lines and half-lines, angles, circles, triangles and their teaching through computers and interactive whiteboards. It is divided into two parts, theoretical and practical. The first one covers motivation for learning, constructivism, evaluation of teaching materials and interactivity in school environment. The practical part contains worksheets for teaching with an interactive whiteboard created by the author of the thesis and their use in Year Six of primary and lower-secondary schools. In the conclusion the author mentions his observations gained during his own teaching practice.
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