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Building Model Generator for Open Street Maps
Galacz, Roman ; Poulíček, Zbyněk (referee) ; Polok, Lukáš (advisor)
This work concerns obtaining data from the maps provided by the project OpenStreetMap. The data are converted from the format of geographical latitude and longitude to the Cartesian coordinate system. This work also concerns building type recognition in build-up area which are situated on the downloaded map. Part of the work is a demonstration application which is able to model 3D geometry of the buildings, based on the results of the recognition algorithms and also creates a terrain in which these buildings are situated. Generated model is displayed using the OpenGL graphics library.
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Angles, areas, volumes: dot product and determinant
Ondič, Milan ; Beran, Filip (advisor) ; Zamboj, Michal (referee)
This bachelor thesis deals with the introduction of scalar product and determinant, which are important tools of analytic geometry. The purpose of the thesis is to provide a parallel interpretation of these two key concepts of advanced algebra - the dot product and the determinant - primarily from a geometric, not an algebraic, point of view. The aim of the thesis is to show how both representations can be derived just by solving geometric problems in two-dimensional space and then how to transfer them to three-dimensional space. The first part of the work is devoted to finding the angle between two vectors in the plane and to calculating the area of a triangle. Both of problems are solved in several ways and then the scalar product and determinant are derived. The second part of the work is devoted to three-dimensional space, in particular the angle between two vectors, lines and planes and the volume of a tetrahedron and parallelogram. This is then supplemented by the introduction of some notions of linear algebra, an investigation of the algebraic properties of the dot product and determinant, and a generalization of the notions to the n-dimensional space. The last part of the thesis is devoted to the analysis of selected czech high school mathematics textbooks in terms of the occurrence and...
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Elementary mathematics of imaging methods for radiology assistants
JELÍNKOVÁ, Barbora
The topic of the bachelor's thesis responded to the finding that there is currently no suitable educational text containing mathematical foundations for the education of radiological assistants and other related fields. The bachelor thesis contains selected areas of mathematics that are necessary to know to understand the physical foundations of imaging methods. The formulation of these areas is appropriate to the needs of future graduates of these fields of study. The goals of the bachelor thesis were the following: G1 Creation of an educational text and examples containing elementary mathematics that are essential to fully understand physical principles of imaging methods. G2 Compilation of a test that will be used to verify the knowledge of mathematics of radiological assistance field students and its graduates, followed by a statistical expression of knowledge level. Based on the goals, the following hypotheses were made: H1 By application of a curricular process a structure of elementary mathematics of imaging methods for radiological assistants can be described. H2a By comparing mathematical structures with components of a radiological assistant´s profile, individual structural levels of elementary mathematics for radiological assistants can be described. H2b According to needs and abilities of radiological assistants, examples of functions, differentiation, integration, and vectors can be chosen. H3 Knowledge of respondents in radiology mathematics will be distributed close to a normal distribution. With regard to the curricular process, a teaching text was compiled together with example illustrations. This step led to the fulfillment of goal G1. Then, a single-choice test of 20 questions was compiled to determine the level of mathematics knowledge across the field of radiological assistance. This step led to the achievement of goal G2. This test was subsequently extended using an online form among radiological assistants and students in this field. Given the above objectives, hypotheses H1, H2a and H2b could be confirmed. The test results were statistically expressed in the practical part of the bachelor thesis. It was confirmed that the empirical distribution of test responses is close to the normal distribution. Hypothesis H3 was also confirmed by this step. The benefits of the bachelor's thesis can be seen in the practical level (construction of an educational text verified by a test survey) and in the theoretical level (verification of the application of the theory of the curricular process).
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Practical didactic tests for preparation for the math matriculation examination
PIVOŇKA, Jiří
This bachelor thesis deals with the practical didactic tests for the math matriculation examination. It is divided into two parts. The first part is divided into 7 chapters. Each chapter deals with a specific thematic subjects for the math matriculation examination. The second part includes 3 didactic tests. For each didactic test is assigned solution. The aim of this bachelor thesis is to help students perform math matriculation examination.
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Analytic geometry textbooks used in The first Czechoslovak Republic
Melčová, Babeta ; Hromadová, Jana (advisor) ; Šarounová, Alena (referee)
My thesis is intended not only for high school teachers and students, but also for the public to deepen their understanding of analytical geometry and to compare the knowledge of today's students with the knowledge of students from the 1920s and 1930s. The thesis includes analysis of textbooks of analytical geometry originated in the era of the First Republic and their further comparison in terms of content, used language and whole elaboration. Furthermore, it includes selected examples of calculations using both historical and contemporary methods, accompanied by pictures from Geogebra programme. The thesis contains testing of current students when solving historical excercises .
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Analytical representation of congruent transformations at high schools
Ptáčková, Tereza ; Robová, Jarmila (advisor) ; Hromadová, Jana (referee)
This work deals with analytical representation of congruent transforma- tion in a plane at high schools. The work is a web page, it contains several interactive components which help student to understand the problem like hyperlinks, stepping of the construction, applets, etc. The work contains several solved problems. Main emphasis is placed on the connection of the synthetic and the analytic approach to congruent transformation. The work uses knowledge of analytic geometry students learn at high school. The web page is aimed at talented students of high school and for teaching at mathematical class. 1
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Building Model Generator for Open Street Maps
Galacz, Roman ; Poulíček, Zbyněk (referee) ; Polok, Lukáš (advisor)
This work concerns obtaining data from the maps provided by the project OpenStreetMap. The data are converted from the format of geographical latitude and longitude to the Cartesian coordinate system. This work also concerns building type recognition in build-up area which are situated on the downloaded map. Part of the work is a demonstration application which is able to model 3D geometry of the buildings, based on the results of the recognition algorithms and also creates a terrain in which these buildings are situated. Generated model is displayed using the OpenGL graphics library.
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