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The construction of polygons with the didactic aid
Průšová, Adéla ; Kloboučková, Jaroslava (advisor) ; Havlíčková, Radka (referee)
This thesis deals with construction of polygons with use of a didactic aid a geoboard at primary education. I have done analysis of three series of mathematics books in order to know, if they include possibility of mechanical work during construction of polygons. Based on study of professional literature related to teaching mathematics, mainly geometry at primary education, I have created patterns that can be used altogether with geoboard in mathematics. The patterns had been used in three classes thank to this I could have assess their practical use. Then I have corrected wrong instruction of patterns in order to be clear. Next I described three stages of beginning to work with geoboard that I have personally done and that are written in details in protocol. I have concluded didactic potential work with geoboard and theoretical obstacles while geoboard is using.
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Advanced Topics in Plane Geometry
Hajmová, Kateřina ; Štěpánová, Martina (advisor) ; Moravcová, Vlasta (referee)
The aim of this thesis is to introduce a series of knowledge from advanced planimetry, which can be proved using the knowledge of high school geometry. Selected theorems deal with characteristic of squares with a common vertex (Finsler-Hadwiger theorem, Theorem of Four Squares, Bottema's theorem), significant points of plane entities (Gergonne point theorem, Švrček point theorem, Simson's Theorem, Miquel's theorem), Feuerbach's circle and its relation to the Euler's line. In this thesis, there is also mentioned Reim's theorem, Napoleon's theorem, and Thebault's theorem. This thesis contains a lot of illustrations created in the Geogebra Mathematical Software, which are available online in interactive form.
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Geometric Proofs
Hanusová, Tereza ; Štěpánová, Martina (advisor) ; Halas, Zdeněk (referee)
Title: Geometric Proofs Author: Tereza Hanusová Department: Department of Mathematics Education Supervisor: RNDr. Martina Štěpánová, Ph.D., Department of Mathematics Edu- cation Abstract: This Bachelor's thesis treats such proofs of mathematical theorems in which pictures and secondary school geometry play a significant role. Its aim is to promote an unusual approach to theorem proving which enables to literally see the way they function. The proofs described include three categories: figu- rate numbers, polygons and areas of plane figures with curved boundaries. The thesis can be useful to teachers to liven up their secondary school mathematics lessons or to students of maths-oriented programmes to enrich their knowledge by an unusual approach to theorem proving. Keywords: proof, geometry, figurate number, polygon, area of plane figure 1
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Rectagles inscribed in Jordan curves.
Ye, Tomáš ; Šír, Zbyněk (advisor) ; Vršek, Jan (referee)
We will introduce quotients, which are very special kinds of continuous maps. We are going to study their nice universal properties and use them to for- malize the notion of topological gluing. This concept will allow us to define interesting topological structures and analyze them. Finally, the developed theory will be used for writing down a precise proof of the existence of an inscribed rectangle in any Jordan curve. 1
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Creation of the thematic map in Microstation
Ondová, Natálie ; Berková, Alena (referee) ; Ježek, Jiří (advisor)
This thesis is focused on creating thematic map of settlement urban zone Vinohrady. Based on documents and materials and thanks to suitably chosen measuring methods, was realized mensuration of terrain. Than it was following calculations of the measured data in software environment Groma v.11 and creating list of coordinates of the detailed points and auxiliary measurement points. These points served as the basis for creating a thematic map. The development of this map took place in the software environment MGEO and Microstation V8i. The aim of the work was creation a 1:500 purpose thematic map.
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Introducing the area of polygons, particularly by method of releasing parameter in primary schools
Kovář, Luděk ; Kloboučková, Jaroslava (advisor) ; Tůmová, Veronika (referee)
This thesis deals with the description of constructive approach to teaching mathematics in the third grade of primary school. Teaching mathematics is focused on geometry, specifically on one way of introducing the area of the scalene triangle which describes the relation between a side and its height and corresponding area. In the thesis I describe six particular lessons, their preparation, process of their realization and my own reflections. In these lessons, I analyse some cognitive phenomena as well as social relationships among pupils. Furthermore, I present a detailed examination of tasks from the final diagnostic test, in which I aim towards proving success of this method of teaching mathematics. After four years, I attempt to verify the permanency of the knowledge pupils gained in these particular lessons. I illustrate this by presenting analysis of additional exercises. The whole experimental process was led within the method of releasing parameter. Individual lessons were in accordance with given stages of this method, as described in specialised literature. I verified that the above mentioned method is applicable in teaching mathematics even in the third grade of the primary school. KEYWORDS teachingstyles, perimeter and area, square grid, polygon, method of releasing parameter
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Using Unity for 3D application development
Roček, Jan ; Brožek, Jiří (advisor) ; Junek, Pavel (referee)
This bachelor thesis deals with the development of 3D applications using the Unity 3D multiplatform engine in C# scripting language for the Windows operating system. The theoretical part describes the historical insight into the development of 3D applications and considers the possibilities of modern development tools. There are discussed the pros and cons of available 3D engines. The practical part deals with the development of 3D applications which described in detail the course of development with a final evaluation. The result is a functional 3D game for two players from the isometric view.
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Polygonal Mesh Segmentation
Minařík, Vojtěch ; Havel, Jiří (referee) ; Španěl, Michal (advisor)
Bachelor's thesis deals with 3D model segmentation into particular meaningful segments. Method is based on algorithm described in article Protrusion-oriented 3D mesh segmentation The realized solution is based on assumption, that 3D models consist of a core and core attached protrusions. The segmentation algorithm consists of three main steps: core approximation, selection of salient points which indicate end of protrusion and assignment of points to appropriate segments. Implementation uses library CGAL which is useful for loading and manipulating 3D meshes.
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Polygonal Models Smoothing
Nečas, Ondřej ; Herout, Adam (referee) ; Kršek, Přemysl (advisor)
The result of digitalization 3d surface is affected by many factors. After digitalization can on the surface emerge some unwanted artefacts. The differences from original are caused by resolution of the device or its limited precision. For elimination of this artefact exists many smoothing algorithms, but we want to choose that which best suits this purpose. So it is useful to know their limits and characteristics.
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3D Triangles Polygonal Mesh Conversion on 3D Spline Surfaces
Jahn, Zdeněk ; Španěl, Michal (referee) ; Kršek, Přemysl (advisor)
This bachelor's thesis deals with the problem of the remeshing of unstructured triangular 3D meshes to more suitable representations ( quadrilateral meshes or spline surfaces ). It explains the basic problems related with the unstructured meshes and the reasons for its solution. It classifies the usable methods, describes the most suitable candidates briefly. It follows the chosen method in detail - both the theoretical matter and the specific implementation.
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