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Models of Lobachevskij's geometry and possibilities of their use at secondary school
Kosina, Jan ; Kvasz, Ladislav (advisor) ; Jančařík, Antonín (referee)
This thesis Models of Lobachevskij's geometry and the possibilities of their use at secondary school focuses on one kind of non-Euclidean geometries, the Bolyai - Lobachevskij's geometry. The first chapter describes the history of non-Euclidean geometry, shows difficulties of understanding of one publication dedicated to these problems by current students of secondary schools and shows some chosen methods in the didactics of mathematics, especialy the constructivist method. The second chapter is dedicated to elemental concepts of projective geometry, Bolyai - Lobachevskij's geometry and it shows its basic models. It further analyses the specific features of this kind of geometry in Beltrami - Klein's model, especially mutual positions of straight lines. This theses further contains a set of gradual tasks. The third chapter is dedicated to the description of a didactical experiment. In this experiment were students of secondary school acquainted with this theory and tasks, which they solved. Student's solution were writen down and than analysed in the constructivist methodology term in the didactics of mathematics.
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Mathematics in Ancient India
Sýkorová, Irena ; Bečvář, Jindřich (advisor) ; Veselý, Jiří (referee) ; Hykšová, Magdalena (referee)
The thesis is devoted to ancient Indian mathematics; it describes the mathe- matical knowledge, computational techniques and methods for solving various ari- thmetic, algebraic and geometric problems that the Indians knew and used. The thesis follows the development of Indian mathematics from the oldest knowledge contained in ancient Vedic texts to the knowledge originated from the classic me- dieval arithmetic and algebraic works. This is the first comprehensive text written in Czech which contains the translation of original problems and analysis of their solutions in the current mathematical formulation and symbolism. The sources are mainly English translations of ancient Sanskrit texts and their commentaries.
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On geometry in fundamental ontology
Kovář, Vojtěch ; Kouba, Petr (advisor) ; Nitsche, Martin (referee)
The following text attempts to rethink the challenge of Edmund Husserl in his text On the Origin of Geometry. Interpretation of fundamental ontology developed by Martin Heidegger in Being and Time provides field on which it is possible to try to answer the question of the origin of geometry. It is conceived as a completely unique ontological possibility that nature is able to vouch for an explanation of the geometry.
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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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Pathfinding within a Hierarchical Navmesh Based on Geometry Analysis
Chomut, Miroslav ; Plch, Tomáš (advisor) ; Bída, Michal (referee)
Title: Pathfinding within a Hierarchical Navmesh Based on Geometry Analysis Author: Miroslav Chomut Department / Institute: Department of Software and Computer Science Education Supervisor of the master thesis: Mgr. Tomáš Plch, Media and Communications Office Abstract: Pathfinding is a common problem in the computer science dealing with navigation from a starting point to a destination point. Common algorithms today are mostly based on A* search on a graph representation of navigated world. Another common approach is creation of navigation structure of convex navigation meshes and navigating on them. Our goal is to propose pathfinding algorithm on hierarchical navigation meshes, based on the terrain geometry, which benefits from complexity of hierarchical search yet provides paths comparable in length to reference ones. This thesis analyses and describes our proposed approach of navigation including generation of the navigation structure. Keywords: navmesh, pathfinding, A*, hierarchy, terrain analysis, geometry
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Financial mathematics in selected problems from comprehensive school geometry curriculum
Kocourková, Zuzana ; Novotná, Jarmila (advisor) ; Tůmová, Veronika (referee)
Title: Financial mathematics in selected problems from comprehensive school geometry curriculum Author: Zuzana Kocourková Department: Department of Mathematics and Mathematical Education Supervisor: Prof. RNDr. Jarmila Novotná, CSc. The core of the bachelor thesis is a selection of problems that combine geo- metry and financial mathematics and can be used at comprehensive school. In the first part the author defines and describes financial literacy and its inclusion into primary and secondary school education. It also presents foundations of finan- cial mathematics. The second part of the thesis focuses on problems that combine geometry and financial matematics and on their introduction at comprehensive school level. When possible, several suitable solving strategies are demonstrated. Each of the problems is supplemented by a list of knowledge and skills prerequi- site to their solution. Keywords: financial literacy, financial mathematics, problems, geometry, comprehensive school
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Project Teaching in Geometry in the Primary School
Faltinová, Magdaléna
The diploma thesis Project teaching in Geometry in the primary school concerns with the theory of the project teaching and its further realization in practise. He points out today how teachers use teaching project and whether it properly understand The theoretical part characterizes the historical development of the project teaching, defines the terms connected with this teaching. The theoretical part is based on studied literature and is complemented by practical experience. In the practical part are three projects focused on geometry. Projects were realized with the students of the fifth class in the primary school in Nymburk. In the diploma thesis are also records their implementation, the final self-reflection and evaluation of project benefits for students.
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On geometry in fundamental ontology
Kovář, Vojtěch ; Kouba, Petr (advisor) ; Ritter, Martin (referee)
The following text attempts to rethink the challenge of Edmund Husserl in his text On the Origin of Geometry. Interpretation of fundamental ontology developed by Martin Heidegger in Being and Time provides field on which it is possible to try to answer the question of the origin of geometry. It is conceived as a completely unique ontological possibility that nature is able to vouch for an explanation of the geometry.
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