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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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Restaurant and facilities for ČRS Lačnov
Štěpánová, Martina ; Pobořil, Lukáš (referee) ; Petříček, Tomáš (advisor)
The subject of this thesis is the process of building technical part of the design documentation for the realization of a newly-built restaurant and facilities for Czech fishing union in the village Lačnov. The building consists of two objects interconnected by a connecting neck. The ground floor of the building with a flat roof is used as a restaurant. The restaurant is wheelchair accessible. Public entrance is from the southern side. The entrance for the staff and the supply will be from the east side. Facilities for staff and technical facilities there is in the northern part of the building. On the second floor there is an office, a meeting room and a training room for the Czech fishing union. In the second object with a gabled roof is an apartment for a fishing man and a shop with small fishing equipment. There is also a showers and toilets for the disabled. The technical background is situated in the attic. The house is based on strips foudations. Vertical loadbearing structures above ground are made of Porotherm system, external walls of the basement are made of prefabricated concrete shuttering blocks. Horizontal structures are designed as a monolithic reinforced concrete slab. Building is insulated. Part of the external wall finish are made of silicone plaster and part of it consists of ventilated facade with timber cladding.
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Cavalieri's principle
Kreslová, Iva ; Halas, Zdeněk (advisor) ; Štěpánová, Martina (referee)
The Bachelor thesis deals with the development of key ideas important for formal formulating of Cavalieri's principle, its proof in general form and using Cavalieri's principle in determining the area of plane figures and volumes of solids. Determining of area and volumes using Cavalieri's principle is associated with the derivation of the well-known formulae for calculating area and volume.
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Aids for Teaching Geometry
Smutná, Anežka ; Štěpánová, Martina (advisor) ; Hromadová, Jana (referee)
This thesis deals with aids for teaching Geometry at primary and secondary schools. The aim of the thesis is creating several visual aids for substantiation of statements or constructions. Specifically, there is a tool for explaining validity of the Pythagorean theorem, a tool for showing formation of conic sections as sections of circular cone, a tool for demonstrating the definition of an ellipse and its Gardener's construction and a tool for showing and simulating both stereometric relations and problems. A part of the thesis deals with the current curriculum of Geometry on Czech primary schools and selected types of secondary schools. Further, the thesis lists and describes some aids that are used in general public schools and in selected types of schools using alternative methods of teaching Mathematics (The Hejný method, Waldorf and Montessori schools). The thesis is also intended to be used by teachers for inspiration of developing their own tools or to orient themselves in the tools already produced.
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Workbook of Monge projection
Pajerová, Nikola ; Hromadová, Jana (advisor) ; Štěpánová, Martina (referee)
In this thesis there can be found various examples from Monge projection. The theory is summarized in the beginning, which is important of understanding the projection and for solving the examples. There are also examples of solving axial affinity and central collineation. Then there is a chapter about the projection of all types of angular and rotational solids, which are solved at the secondary schools. Then follows a chapter, where the sections of these solids are constructed. In the last chapter, there are solved intersection of solids from each type. Powered by TCPDF (www.tcpdf.org)
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Secondary school chapters from an orthogonal axonometry
Janišová, Lenka ; Moravcová, Vlasta (advisor) ; Štěpánová, Martina (referee)
Title: Secondary school chapters from an orthogonal axonometry Author: Lenka Janišová Department: Department of Mathematics Education Supervisor: RNDr. Vlasta Moravcová, Department of Mathematics Education Abstract: The work describes the process displaying the situation in orthogonal axonometry from getting distorted the units on the axes through the constructi- ons of elementary objects up to the theoretical solution of objects sections and displaying more complex objects. It includes tasks for practicing. Some of these tasks are available in presentations, which are adapted for projection by a projec- tor and contain step by step solutions of excercise. Auxiliary models are attached to the tasks at the beginning, which consist of the distorted axes problem, so the tasks can be illustratively visualized. The work is intended for secondary school pupils as a material for self-study, presentations and models can also be used for teaching in the school. Keywords: orthogonal axonometry, orthogonal projection, projection, intersection method, construction tasks 1
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Geometric transformation in secondary school mathematics with the support of internet
Ptáčková, Tereza ; Robová, Jarmila (advisor) ; Štěpánová, Martina (referee)
This work deals with geometric transformation in a plane in high school mathematics. The work is a web page, it contains several interactive components which help student to understand the problem like hyperlinks or stepping of the construction. The work contains several solved problems. Main emphasis is placed on illustration of problems in the form of drawings and construction. The illustration is better by using of applets. The applets show the steps of the construction one after another as the students proceed with the con- struction on a sheet of paper. Together with each step of construction its symbolic description is showed. Created web page could be used by high-school students as well as tea- chers to demonstrate the problem.
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On Employing Persons with Health Impairment: Law, Possibilities, Difficulties
Štěpánová, Martina ; Cimrmannová, Tereza (advisor) ; Stretti, Sylvie (referee)
I want to achieve several goals in this Master Thesis. The first one is a brief description of the nowadays understanding of the phenomenon of unemployment, health disability and their common interaction. Another aim of the thesis is to summarize the social effects which are caused by unemployment. Possibilities of finding a position for the invalid people in the employment market are discussed as well. I will mention certain disadvantages of employing invalid persons. The disadvantages are mainly caused by the health status of invalids and eventually by a long period of being unemployed. The substantial part of the thesis consists of case studies of persons with health impairment. These case studies contain proposals of solving the current situation of these person along with the confrontation of their real situation with the theory. Powered by TCPDF (www.tcpdf.org)
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Origins of Matrix Theory in Czech Lands (and the responses to them)
Štěpánová, Martina ; Bečvář, Jindřich (advisor) ; Slavík, Antonín (referee) ; Hora, Jaroslav (referee)
In the 1880s and early 1890s, the Prague mathematician Eduard Weyr published his important results in matrix theory. His works represented the only significant contribution to matrix theory by Czech mathematicians in many decades that followed. Although Eduard Weyr was one of the few European mathematicians acquainted with matrix theory and working in it at that time, his results did not gain recognition for about a century. Eduard Weyr discovered the Weyr characteristic, which is a dual sequence to the better known Segre characteristic, and also the so-called typical form. This canonical form of a matrix is nowadays called the Weyr canonical form. It is permutationally similar to the commonly used Jordan canonical form of the same matrix and it outperforms the Jordan canonical form in some mathematical situations. The Weyr canonical form has become much better known in the last few years and even a monograph dedicated to this topic was published in 2011.
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