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The Golden Section
Moravcová, Vlasta ; Šarounová, Alena (advisor)
Title of the master's thesis: The Golden Section Author: Bc. Vlasta Chmelíková Abstract: This text has been written especially as an educational material for secondary school teachers of mathematics and descriptive geometry, however it can be interesting also for students of secondary schools and universities and for another persons interes- ted in problems of the golden section. The thesis includes a calculation and properties of the golden number, several construction methods of the golden section, its occurence and use in plane and solid geometry, history of the golden section and its connections with art, architecture, nature, psychology, etc. In addition, there are added examples from older textbooks and proposals of the jobsheets for improvement of the mathematics lessons.
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Mirroring in a linear perspective.
Marková, Kateřina ; Hromadová, Jana (advisor) ; Šarounová, Alena (referee)
Title: Mirroring in a linear perspective Author: Kateřina Marková Department: Department of Mathematics Education Supervisor: RNDr. Jana Hromadová, Ph.D., Department of Mathematics Edu- cation Abstract: This text is intended especially for teachers and students of high schools and colleges who are interested in descriptive geometry. The thesis on the topic of mirroring in linear perspective presupposes basic knowledge of linear perspective. It includes short introduction into the topic of linear perspective and its basic terms, explanation of the principle of mirroring and clarification of constructions that are needed to solve tasks. Main part of the thesis is a problem book with solution. It contains examples on the topic of mirroring in linear perspective for all the basic mirror positions. Every task is supplied with step-by-step solution in the GeoGebra software and a PDF file. Another part of the thesis are photographs of different mirror positions in real life situations. Keywords: Linear perspective, mirroring, vertical, horizontal, sloping mirror
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Spatial Geometry in Secondary School Education
Smetana, Adam ; Surynková, Petra (advisor) ; Šarounová, Alena (referee)
1 Title: Curriculum of solid geometry at czech high schools Author: Adam Smetana Department: Department of Mathematics Education Supervisor: RNDr. Petra Surynková, Ph.D Abstract: The topic of the bachelor thesis is Curriculum of solid geometry at Czech high schools. All of the basic and advanced terms are explained and shown in simple illustrations. The thesis contains a number of solved examples and exercises that are being taught at Czech high schools. All the examples are supported by 2D and 3D applets in GeoGebra software. Keywords: curriculum, solid geometry, cross sections, GeoGebra
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Intersection of solids
Otrubová, Anna ; Hromadová, Jana (advisor) ; Šarounová, Alena (referee)
The four chapters of this diploma thesis introduce a survey of the basic intersection types of solids, the focus being placed on the intersection of two pyramid and prisma solids, acting as a counterweight to most textbooks' interest in intersection of curved surfaces. The first chapter provides a detailed, wide-ranging insight into the issue of the solid and line intersection. The conclusion part of the thesis provides the reader with a brief commentary on the used literature. The work is supplemented with figures and example solutions. In the appendix part are found pre-drawn assignments. The enclosed CD contains complementary materials such as step by step solutions and 3D models created in the GeoGebra software along with drawn problems found especially in upper secondary school geometry textbooks and curriculum.
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Geometric Constructions of Linear Perspective and its Application in Practice
Pecinová, Iva ; Surynková, Petra (advisor) ; Šarounová, Alena (referee)
Title: Geometric Constructions of Linear Perspective and its Application in Practice Author: Bc. Iva Pecinová Department: Department of Mathematics Education Supervisor: RNDr. Petra Surynková, Ph.D., Department of Mathematics Education Abstract: The content of the diploma thesis is primarily one-point and two-point perspective. The aim is to familiarize the reader with the basic constructions of the linear perspective. Another part was a plan of project days, testing it in practice and using the theory described in the thesis. During the project days, I received filled in questionnaires from my students in which I tested spatial imagination, knowledge of optical illusions and basic principles of a linear perspective. The results of the questionnaires are presented at the end of the thesis. I also created a set of my own original and solved exercises, and I present here instructions on how to create perspective optical illusions - on the enclosed DVD is a template to build the Ames room. The reader will also get acquainted with a brief history of imaging in a linear perspective. Part of the thesis is also a chapter about application of the principles of linear perspective in art lessons at primary and secondary schools. One of the main benefits of the work is a set of coloured spatial images that make it...
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Cuts of polyhedrons
Borzíková, Žofia ; Bečvář, Jindřich (advisor) ; Šarounová, Alena (referee)
Title: Cuts of polyhedrons Author: Žofia Borzíková Department: Department of Mathematics Education Supervisor: doc. RNDr. Jindřich Bečvář, CSc., Department of Mathematics Education Abstract: The topic of the bachelor thesis is Cross Sections of Polyhedra. The basic principles of constructing such cross sections are shown and explained through illustrative examples of cross sections of solids together with the detailed description of the construction process. Especially, the cross sections of some "common" polyhedra like prism, tetrahedron, pyramid or octahedron are further discussed. The reader should use them to take up with the main issue of constructing cross sections. As an application of the acquired knowledge, the cross sections of other solids like Platonic or Archimedean solids are introduced here. The goal of these examples is to cultivate spatial intelligence for the purpose of constructing cross sections or better understanding of polyhedral in general. The bachelor thesis is a commented set of examples, which can be used as an additional material in the education of mathematics, not only in grammar schools. Keywords: cross sections, cube, cuboid, prism, pyramid, tetrahedron, regular polyhedra, semi-regular polyhedra
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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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Circumferences and areas of plane figures
Šrámek, Martin ; Robová, Jarmila (advisor) ; Šarounová, Alena (referee)
Title: Circumferences and areas of plane figures Author: Martin Šrámek Department: Department of Mathematics Education Supervisor: doc. RNDr. Jarmila Robová, CSc. Abstract: This diploma thesis Circumferences and areas of plane figures is designed for teachers and high school students. Teachers might find some interesting tasks including various metric problems from the field of synthetic geometry as well as inference of mathematic equations for calculation circumferences and areas of plane figures which are taught at elementary schools and high schools. Pupils can appreciate solved tasks and their knowledge can be applied to other similar tasks. The ninth chapter includes more difficult tasks. There are many drawings exported from GeoGebra which can help students to understand the task better. Keywords: circumference, area, length, teaching of mathematics
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Length measurement
Pecinová, Iva ; Šarounová, Alena (advisor) ; Surynková, Petra (referee)
My bachelor thesis Length measurement deals with the euclidean length measurement. It deals with the history of the length measurement in the Czech country, the emergence of the basic unit of length - meter and especially the circumference. The work is intended primarily for high school teachers of mathematics and lovers of measurements which are expected to at least high school knowledge of mathematics. This text is good for primary schools teachers of mathematics which is intended Handbook for small meter. The component part of my bachelor thesis is an enclosed CD, where is found the bachelor thesis in an electronic form and the already mentioned Handbook for small meter - a version for printing.
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Polyhedra and their nets
Martínková, Jana ; Šarounová, Alena (advisor) ; Bečvář, Jindřich (referee)
This text is especially intended as an educational material and didactic help for primary and secondary-school teachers. The thesis can be divided into four parts. In the first one there are summerized facts about polyhedra. There is said something about prisms, pyramids, regular, semiregular and Kepler-Poinsot polyhedra. Other part consists of worksheets especially for secondary-school students. It could be helpfull for improving their skills. In the third part we can find solutions of worksheets made by students. In the last part of thesis there are some examples of models as didactic help.
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