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Loudspeaker System for Laboratory Measurements of Polar Patterns
Morkus, Filip ; Káňa, Ladislav (referee) ; Schimmel, Jiří (advisor)
In the first part the attention is aiming to the choice of suitable loudspeakers. For this choice it was necessary to set required criteria and parameters. The aim of the system was to have as wide reproducibility range of frequency as possible but on the other hand not to be too large. The other criterion was the quality of the loudspeakers and its price. In the second part there was frequency crossover suggested according to the parameters of the chosen loudspeakers. This was suggested for low frequency spectrum as well as for high frequency spectrum. When determining the dividing frequency there were thought over producer’s recommendations and frequency characteristics of the loudspeakers so that the dividing frequency was not set in the place where the loudspeaker does not have “constant” character. The third part concerns the construction of the loudspeaker case. There one can find more details about the construction of the loudspeaker system called D´Appolito and its constructional requirements. This part was kept to the previous parts because integrating “D´Appolito” needs setting the distance between the loudspeakers according to the dividing frequency. It was also necessary to count with their size. According to the loudspeakers parameters it was possible to calculate the capacity of the loudspeaker case, also its shape was said and geometric proportions were calculated. Then everything was simulated in suitable software. In the last part the complete loudspeaker system was measured in an anechoic room. There were the direction characteristics and frequency characteristics measured there. The results of the measuring were compared with the software simulations.
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Introducing the volume of solids using Cavalieri's principle
Fialová, Eliška ; Vondrová, Naďa (advisor) ; Janda, David (referee)
The aim of the thesis is to use a series of pedagogical experiments to introduce the volume of a pyramid, a cone and a sphere using Cavalieri's principle for pupils of the ninth year of primary school. First, the thesis characterizes the theories and approaches on the basis of which the experiment was built, such as the generic model theory and constructivism. The next part deals with the analysis of schoolbooks for the upper primary school and gymnasium, which are devoted to the introduction of the volumes of solids of pyramids, cones and spheres, and especially those schoolbooks which introduce the given volumes using the Cavalieri principle. The pedagogical experiment was preceded by a series of lessons focused on familiarizing pupils with given geometric solids and deriving calculations of their surfaces. This was followed by the introduction of the Cavalieri principle in the plane and also in space. In the practical part of the thesis, the tasks that were used in the pedagogical experiment are presented. The description of the course of the pedagogical experiment is supplemented by copies of the pupils' solutions. The conclusions are illustrated by the pupils' observations and summaries, which they arrived at in the form of a discussion on the tasks. At the end of the thesis, an evaluation of...
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Solving stereometric problems in GeoGebra
HORÁČKOVÁ, Lenka
The aim of the bachelor's thesis on the subject of 'Solving stereometric problems in GeoGebra' was to create a collection of own solved examples from stereometry from the curriculum in the range from primary school, through secondary school to university training of mathematics teachers. The GeoGebra program is a support tool for this bachelor's thesis. The work focuses mainly on the curriculum of primary and secondary schools, partly also on the curriculum at universities. The work focuses mainly on square figures in the scope of the curriculum at primary and secondary schools and partly also at universities.
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Solving of problems dealing with volume and surface in the three-dimensional space by 15-16-year old pupils (9th grade)
Dlouhá, Michaela ; Novotná, Jarmila (advisor) ; Vondrová, Naďa (referee)
The topic of my diploma thesis is the solution to exercises of volume and surface of 3D solids. The aim of the thesis is to make own didactic test and to analyse the methods of solution to math exercises in the 9th grade students of ZŠ Amálská. Also to compare the results of the tests in math and science orientated class to "normal1 " class and to find out the success rate of solutions in both classes. I focused only on pyramid and cone, because they are part of curriculum in 9th grade of basic schools after students are admitted to high schools, and after examination of educational programme of chosen school I realised that both classes had the same outputs of given schoolwork. I divided my thesis into two parts - theoretical and practical part. Theoretical part contains five chapters. In the first chapter I focus on didactic tests and their making. In the next chapter I deal with evaluation in general and school evaluation. In the third part there is the term of word exercise defined. In the fourth chapter there are solutions to the word exercises. And in the last chapter I define the term geometrical solid. In the practical part there are the aims and methods of survey, characteristic of research sample, making of didactic test, content of didactic test and analysis of students' solutions...
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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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Volume of Pyramid
Vaňkát, Milan ; Halas, Zdeněk (advisor) ; Bečvář, Jindřich (referee)
Title: Volume of Pyramid Author: Bc. Milan Vaňkát Department: Department of Mathematics Education Supervisor: Mgr. Zdeněk Halas, DiS., Ph.D. Abstract: The subject of this thesis is Hilbert's third problem. In the first chapter we follow it's roots back to Euclid's Elements. We focus in particular on the theorem that triangular pyramids of equal altitudes are to each other as their bases. We also discuss analogous statements for triangles, parallelograms and parallelepipeds. We point out the way in which the issues of content and volume of geometrical figures were approached in Greek mathematics. In the second chapter we present the historical background of Hilbert's third problem. We outline the development of methods of it's solution - from M. Dehn's first answer in 1901 to the abstract definition of Dehn invariants as a R ⊗Z Rπ- valued functional on the polyhedral group that was introduced by B. Jessen in 1968. Later we construct Dehn invariants and present a thorough solution to the Hilbert's third problem. In the end we sketch out mathematical issues connected to this problem that have been studied in the second half of 20th century. An illustrative high school exercise on derivation of the volume formula for py- ramid by Eudoxus's method of exhaustion is included in the appendix. Keywords: pyramid, volume,...
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On sphere
Ivan, Matúš ; Bečvářová, Martina (advisor) ; Surynková, Petra (referee)
This diploma thesis describes historical evolution of calculation of sphere's volume and surface and provides an analysis of textbooks for secondary and primary schools. It is made with the intention to inspire high school teachers with various approaches of teaching the volume and surface of solid bodies. It can help teachers with motivation of students as well as with selection of textbook and teaching methods for the issue. This thesis is meant to inspire high school students interested in history of mathematics, too. It includes analysis of preserved exercises on the topic from ancient Egypt and Mesopotamia as well as findings from Archimedes' works, which were devoted to this topic. Moreover it describes contribution of enlighteners on the subject and shows exact procedures of derivation of formulas using integral calculus.
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Problems dealing with volume and surface in the three-dimensional space
Dlouhá, Michaela ; Novotná, Jarmila (advisor) ; Dvořák, Petr (referee)
The aim of this bachelor's work is to sort out and comprehensively organize the word problems on volume and surface elements that appear in textbooks and tasks collections for elementary and secondary schools, namely for the needs of pupils and teachers. The introductory part deals with the characteristic of geometric solids. There are the basic concepts related to objects defined and explained. In the following part there is the notion of the word problems defined. The last part deals with the sorting and organizing word problems for volume and surface area. There are a number of specific tasks selected from the textbooks and tasks collections for primary and secondary schools assigned to each type of task. Tasks are presented with their solution. Keywords: volume, surface, geometrical element
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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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