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Rauš, Jaroslav ; Slavík, Antonín (advisor) ; Boček, Leo (referee)
anglicky Mercator projection, loxodromes, and related topics This bachelor thesis deals with the Mercator projection from both today's and historical point of view. Special emphasis is placed on the formal derivation of the projection, and on the studying of its properties. The projection for the surface of revolution is also considered. Then the thesis deals with the loxodromes, their properties, and their relation to the Mercator projection. The loxodromes on the surface of revolution are also considered, again. And the thesis ends with some relations between the Mercator projection, the stereographic projection, and the complex exponential function. 1


Inequalities for talented pupils of high schools
Šalom, Pavel ; Robová, Jarmila (advisor) ; Boček, Leo (referee)
The thesis contains a textbook for high school pupils. The aim of the textbook is to teach the reader how to solve problems concerning inequalities proposed at czech or international mathematical competitions for high school pupils. In the first part we present some basic ineqaulities (AG, Cauchy's inequality) and we show how to understand them and how to use them. In the second part we broaden reader's horizon by presenting rearrangement and Jensen's inequality. In the third part we present widely applicable methods such as "Abstract Concreteness Method" or "Sum of Squares Method". Some techniques concerning the Sum of Squares Method were written by Phan Kim Hung in 2006. We are trying to significantly involve the reader. We prefer just hints to many of the proposed problems rather than complete solutions and we give some harder problems to solve at the end of each part. 1


Web application for teaching basic knowledge of mathematics at secondary school
Pavlicová, Vladimíra ; Robová, Jarmila (advisor) ; Boček, Leo (referee)
Title: Web application for teaching basic knowledge of mathematics at secondary school Author: Vladimíra Pavlicová Department: Department of Mathematics Education Supervisor: RNDr. Jarmila Robová, CSc. Supervisor's email address: robova@karlin.mff.cuni.cz Abstract: The presented work is intended to serve as a teaching material for pupils of the first year of secondary school, focusing on the basic knowledge of mathematics. Specifically, it deals with the subject matter of powers and polynomials. It is composed of two subsections  an educational text, in which the subject matter is clearly explained and illustrated through solved examples, and exercises to practice, which allow pupils to check, eventually improve, their knowledge. Owing to the fact that the work has a form of a web application, the emphasis is placed on interactive elements (for example, stepbystep solutions, multiple choice tests), which increase the attractiveness of the presented curriculum for pupils. Pupils are therefore able to learn and practice the curriculum by enjoyable way. The fact that the application is freely available on the Internet can also increase pupils' interest in it. Keywords: basic knowledge of mathematics, powers, polynomials


Web application for planimetry teaching
Kurka, Štěpán ; Robová, Jarmila (advisor) ; Boček, Leo (referee)
This thesis was created as a web site for planimetry teaching. It is addressed mainly to high school students and high school teachers. The web site is divided into two main parts. At first it summaries high school planimetry, mostly triangles, quadrangles, sets of points of certain attribute, and then it contains forty construction exercises. Those exercises involve applets of dynamic geometry, which interactively depend on changeable measures of the exercise. One of the parts of the thesis is an overview through present web sites in Czech, in Slovak, in English and in German language. This thesis is an extension of a bachelor thesis from the same author.


Properties and applications of low degree surfaces
Mirová, Aneta ; Šír, Zbyněk (advisor) ; Boček, Leo (referee)
My thesis "Properties and applications of low degree surfaces" deals mainly with properties of two quadrics. We introduce so called canonical forms of two quadrics and classification of intersection curve of two quadrics. There are used index and signature sequence to obtain classification of intersection curve of two quadrics. These sequence can determine the number of component of the intersection curve, their algebraic degrees and singularities. Our work also contains many examples with pictures. One part of the thesis also presents possible application of intersection curve of two quadrics in practice. This thesis also contains an enclosed CD, with the thesis in an electronic form and the source files of all pictures in the thesis.

 

Isoperimetric inequalities
Bártlová, Tereza ; Slavík, Antonín (advisor) ; Boček, Leo (referee)
In the present work we study isoperimetric problem and its description by isoperimetric inequality. The legend of Dido, which inspired formulation of the isoperimetric problem, is described in the first chapter. The following chapters are devoted to elementary proofs of isoperimetric inequality for polygons as well as for curves. The last chapter focuses on related problem than isoperimetric that is isodiametric problem. This is described Reuleaux polygon that constitutes a means for proof of isodiametric inequality.


Modern approach to teaching spatial geometry
Bartošová, Eliška ; Surynková, Petra (advisor) ; Boček, Leo (referee)
This work is a collection of solved problems in descriptive geometry, supplemented by elementary theory needed for their solution. The theory includes definitions and elementary properties of polygons and their constructions. Theory about solids, mostly prisms and pyramids, is also included. The second chapter introduces theory of projection, including definitions of projection methods (Monge, center, etc.) and corresponding terms. The second part contains a collection of problems, where each problem is solved in four projection methods (there are problems of construction of a point, line, plane, prism and pyramid). For each problem there is an animation for Lisa Viewer program attached, which makes an integral part of the work. These animations allow to look at figures of the problems interactively and even in three dimensions. There is also a PDF document with problem assignment and solution for each problem, suitable for print. Powered by TCPDF (www.tcpdf.org)
