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System for support of conic sections teaching
Hejlová, Eliška ; Surynková, Petra (advisor) ; Karger, Adolf (referee)
The work presents own software for geometric drawing aimed to construction of conic sections. It's designed for high school students and their teachers, to use in lessons of descriptive geometry and mathematics. It contains a number of exercises with solutions which are prepared to solve in the program. Next part of this work is a theory about conic sections. We show various definitions, constructions and some basic properties. We also show a construction and properties of tangent in the point of conic section. Theory is supplemented by animations and pictures made in program GeoGebra. There are also proofs of equivalence of presented definitions. 1
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The mathematical theory of juggling
Búzik, Michal ; Slavík, Antonín (advisor) ; Karger, Adolf (referee)
Title: The mathematical theory of juggling Author: Michal Búzik Department: Department of Mathematics Education Supervisor: RNDr. Antonín Slavík, Ph.D. Abstract: This bachelor thesis is concerned with methods of mathematical descrip- tion of juggling. The main part deals with notation of simulation of throwing balls using integer sequences, so-called siteswaps. It indicates generating, mutual relations and ways of graphic interpretation of these sequences in diagrams. Summarized re- sults with generalization of all possible calculations of juggling sequences according to restrictive aspects are provided in this thesis. Beside usage of combinatorics and graph theory, there are also relations between juggling and braid theory, and change ringing interpreted. Keywords: juggling, sequence, siteswap
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Graph theory at high school teaching
Jirovský, Lukáš ; Pavlíková, Pavla (advisor) ; Karger, Adolf (referee)
The task of this thesis is to create an interactive website focusing on some problems of graph theory and the possibility to use them to model a variety of situations (for example as a motivation in the lessons of mathematics and computer science). The created instructional material will be applicable for high school teaching as good as for self-study. The thesis is mostly focused on a wide range of tasks, problems and fully-worked solutions and the basic terms and ideas from graph theory.
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Web application: Basic knowledge of mathematics at secondary school
Pavlicová, Vladimíra ; Robová, Jarmila (advisor) ; Karger, Adolf (referee)
The presented work is intended to serve as a teaching material in particular for pupils of the first year of secondary school, focusing on the basic knowledge of mathematics. The first part of the thesis is devoted to an analysis of existing web page, which corresponds to the theme of the diploma thesis. The evaluation takes into account the expertise as well as the scope of use of interactive elements. In the next part, the created teaching material in a form of web page is presented. It deals with the subject matter of powers, roots, polynomials and rational expressions. In accordance with current trend, the emphasis is put on both visualisation of curriculum (charts, use of graphics) and interactivity. All exercises to practise involve solution, therefore users are allowed to gain immediate feedback and thus to study individually. Web page is free available.
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Spatial generalizations of the properties of the triangle
Šrubař, Jiří ; Karger, Adolf (advisor) ; Boček, Leo (referee) ; Lávička, Miroslav (referee)
TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and...
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Teaching a Spatial Geometry and Developing Spatial Abilities Using a Computer
Gergelitsová, Šárka ; Holan, Tomáš (advisor) ; Karger, Adolf (referee) ; Pech, Pavel (referee)
of doctoral thesis Title: Teaching a Spatial Geometry and Developing Spatial Abilities Using a Computer Author: Šárka Gergelitsová Department: Department of Software and Computer Science Education Supervisor: RNDr. Tomáš Holan, Ph.D., Department of Software and Computer Science Education Abstract: In this thesis we present a contemporary overview of current possibilities of using computer support for teaching geometry and the development of spatial imagination. The materials are aimed at the secondary school curriculum (for students 15-19 years old), many of them, however, could be used for younger or older students. The work is outlined as a tool and a set of teaching materials for teachers. The basic part of this thesis is a set of commented examples and tasks that can be solved by the use of dynamic geometry systems including the 3D models for these tasks. The set consists of more than 100 problems and examples with hints or answers and includes a CD with more than 300 supportive models including models-templates for creating tests. Materials include some prepared spatial imagination tests and quizzes. Some of the mo- dels serve as a tool for their design and offer automatic solution checking. We present also our own set of educational applications and games created to support the im- provement...
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Reconstruction of photographs
Frühbauer, František ; Surynková, Petra (advisor) ; Karger, Adolf (referee)
Bachelor thesis Reconstruction of Photographs is engaged in constructive pho- togrammetry, reconstruction of horizontal image and 3D visualization of recon- structed objects . It can be used as a teaching supplement in the studying descrip- tive geometry. The work contains a section about linear perspective, which shows several used constructions. Then it deals with photogrammetry. Shortly describes the history, classification and use of photogrammetry. It continues with detailed described examples about the reconstruction of the horizontal image and exam- ples of using constructive photogrammetry in practice. The text is supplemented with number of own images, that were created in the modeling program Rhino- ceros. The work contains a CD with an electronic version of the thesis, images and source files of most images. 1
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