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Japanese sangaku
Javorská, Zdeňka ; Halas, Zdeněk (advisor) ; Slavík, Antonín (referee)
The bachelor thesis familiarize readers with mathematical tablets sangaku which date back to the period of second half of the 17th century to the second half of the 19th century. These tablets are made from the wood with mostly geometrical problems and were hung on the walls in the temples and the shrines. The thesis include a brief history of the period of the origins of the sangaku tablets and the Japanese mathematics of that time. Each problem has its own verbal description and in picture. The solutions have its own pictures for easier orientation too. These problems come from recently publicated book about sangaku tablets. This thesis should be used as source of exercises for geometry lessons in high schools, each exercise is put in section by the main mathematical method used for solving. Powered by TCPDF (www.tcpdf.org)
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History of Kurzweil integral
Berková, Andrea ; Halas, Zdeněk (advisor) ; Slavík, Antonín (referee)
The presented work deals with history of Kurzweil integral. It focuses primarily on its comparison with other important integrals, namely Newton, Rie- mann, Lebesgue, Perron and McShane integral. Each of them is discussed in a separate chapter which acquaints with their authors and theories. Attention is also oriented to Jaroslav Kurzweil and Ralph Henstock. There are also mentioned the circumstances of the discovery of the Kurzweil integral. The aim is to high- light the theory of integration, which has its origins in Bohemia and despite its elementary definition, which is very general and usable in many applications.
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Volume and surface of sphere
Ivan, Matúš ; Bečvářová, Martina (advisor) ; Halas, Zdeněk (referee)
This work presents historical development in methods of calculating volume and surface of a sphere. It's made for high school teachers as a resource for teaching about volume and surface of solids and for high school students who developed interest in historical outlook for this theme. It contains description of particular preserved tasks from ancient Egypt and Mesopotamia. It compares precision of particular approaches taking into account the precision of the constant π. It analyses proofs of facts about volume and surface of sphere from ancient Greece. It describes assets of enlighteners for this theme and shows exact approaches for deducing the formulas for calculating volume and surface of a sphere.
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Volume of solids
Tvrdá, Monika ; Halas, Zdeněk (advisor) ; Staněk, Jakub (referee)
This didactic oriented bachelor project helps to approach an origin of relations for the volumes of solids taught at high school. It is focused on high school and university students. At the beginning the project shows historical meaning of the volumes of solids and the processes which were used to enumerate them in the ancient Egypt and Mesopotamia. Further, the project deals with the definition of volume of solids; it is based on Jordan's measure. The relations for volumes of the sorted solids are derived using the integral calculus. In the end the other ways of deriving of these relations are shown. At first, it is the method that Archimedes from Syracuse invented, furthermore by the visual imaginations and the Cavalieri's principle. 1
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Equations and inequalities in high school mathematics using internet
Gloc, Jaromír ; Halas, Zdeněk (referee) ; Robová, Jarmila (advisor)
This thesis evaluates Czech and English web sites focused on equations and inequations on high school, specially the way of didactics attitude and breadth of content and interactive elements there. On the basic of this comparison author made own web site focused on teaching high school equations and inequations, which is included in this thesis too. It's expected, it will be served as additional material for Czech students.
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Compression of short text messages
Blažek, Jan ; Halas, Zdeněk (referee) ; Dvořák, Tomáš (advisor)
This paper describes implementation of short text message compression algorithm based on PPM. For representation of context model algorithm is used the Optimal Tree Machine data structure built on statistics of training data. Algorithm is optimized for low-level hardware device. This paper summarizes experimental results of this algorithm.
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Stereometrie. E-learning text for pre-service teachers, teachers of secondary schools and their pupils
Jurczyková, Kristýna ; Halas, Zdeněk (referee) ; Robová, Jarmila (advisor)
Stereometry or geometry in space is an important area of geometry, which deals with the study of spatial(stereometric) relations. Basic definitions and theorems concerning properties of axial affinity in an Euklidean space and in a plane are presented in this thesis, as well as basic stereometric theorems and their consequences. Everything is supplemented by illustrations. The thesis attends in more detail to axial affinity between two planes, in a plane and between a circle and an ellipse. A great deal of this thesis is formed by exercises concerning sections of bodies by plane, which are solved by axial affinity, which is unknown to today's students of high schools. Every important chapter contains samples and a pack of exercises for practicing with possibility to display the solution and the procedure step by step. These exercises are also supplemented with applets, which make it possible to look at the solution from different visual angles and they can help students better imagine a stereometric situation of the given exercise. This study material can be used not only by students to extend their knowledge of stereometry, but also to inspire their teachers as well. For them there are prepared exercises, which are not in today's schoolbooks about stereometry, and work sheets, which can be used for teaching.
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Taylor series of the elementary functions
Ibl, Václav ; Halas, Zdeněk (referee) ; Slavík, Antonín (advisor)
In the present work we study the history of power series of the elementary transcendental functions, namely the binomial series, the exponential series, the logarithmic series, sine and cosine series, and the inverse tangent series from early 16th century until 1829. We also describe the history of Taylor's expansion with Lagrange's and Cauchy's form of remainder. Our exposition starts with the works of the Indian mathematicians Madhava and Nilakantha concerning the series for inverse tangent, sine and cosine and proceeds until the publication of Cauchy's textbook, in which he derived and used Taylor's formula with both forms of remainders.
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