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Dot product in school mathematics
Krejčí, Veronika ; Halas, Zdeněk (advisor) ; Škorpilová, Martina (referee)
Title: Dot product in school mathematics Author: Veronika Krejčí Department: Department of Mathematics Education Supervisor: Mgr. Halas Zdeněk, DiS., Ph.D., Department of Mathematics Edu- cation Abstract: The theme of the bachelor thesis is the dot product in school mathe- matics. The bachelor thesis is adressed to the teachers, who teach at the secondary school. The first part consist of an analysis of the textbooks, the result of the ana- lysis is the reason to write this bachelor thesis and to build a new introduction to the theme of the dot product. In the second part we build the new introduction. The third and the fourth part consist of application of the dot product. Keywords: dot product, hyperplane, distance, angle 1
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Angle in Geometry
Michálková, Iveta ; Holíková, Marie (advisor) ; Pilous, Derek (referee)
This thesis examines the role of angle in the course of history of mankind. The introductory part of this thesis presents the historically first mentions of angles. The second and the third part pay attention to the development of tools and devices allowing practical measurement of angles. The fourth part follows the issue of introducing angle in textbooks of primary and secondary schools in the Czech Republic. It observes whether the topic of angle is imported in individual textbooks correspondingly or if the process in a textbook or textbooks differs considerably. The following parts of this thesis concentrate on various types of angles and pairs of angles and operations with them. Both arithmetic and graphic operations with angles are inspected. A substantial part of this thesis deals with trigonometric functions. This work comprises different manners of implementation and defining of trigonometric functions. Based on examples, this thesis demonstrates usage and significance of trigonometric functions and their properties in practical tasks. The penultimate chapter studies complex numbers. In this chapter, this thesis focuses primarily on complex numbers in trigonometric format and calculations with them. The final chapter holds a collection of exercises. This thesis is concluded by solutions...
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Stanovení potřebného výkonu motoru v závislosti na úhlu řezu při řezání motorovou řetězovou pilou
KOUBA, Štěpán
This bachelor thesis deals with the measurement of the power of the electric chainsaw depending on the cutting angle. The engine power is influenced by number of factors which ultimately affect the work process and its economy. The main goal of this bachelor thesis was to make measurements which are needed to determine the cutting power of the electric chainsaw engine and to determine the factors which may affect this cutting power. The main factors include the power and the cubic capacity of the chainsaw engine, the type of clutch, the type and sharpness of used chain, the age of the chainsaw, the operator's experiences, the type and condition of the sawn wood and the angle of cutting angle.
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Relations among elements of a triangle
Machovcová, Lucie ; Zhouf, Jaroslav (advisor) ; Dvořák, Petr (referee)
This thesis summarizes not only most of the basic components and qualities of a triangle but it also brings pieces of information about triangles which are not usually taught at elementary and high schools. The aim of the thesis is to make readers acquainted with those components and to show differences between them. There are solved constructional and arithmetical problems in the last chapter. These problems utilize relations described in the thesis. The topic of these relations goes beyond mathematical curriculum of high schools. A part of the thesis is made of pictures to imagine better the terms described and the relations of components. All of the pictures are designed in a geometrical program called GeoGebra. Key words: triangle, side, angle, altitude, median, area, perimeter.
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Geometric Measurement of 3D Models
Svoboda, Pavel ; Švub, Miroslav (referee) ; Šiler, Ondřej (advisor)
Work is discussing questions about measuring essential geometric property on model using OpenSceneGraph library. Program contains simple distance and angle measurement on model and distance and angle measurement on projection plane, which is defined by user. There is not missing usefull theory for measuring in Euclidean space, neither explanation of used methods and constructs for implementation by Open Scene Graph. For better understandig of work with OpenSceneGraph here is simply described use of OpenSceneGraph library. Manual and technical documentation is part of this work too.
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Design of self-balancing mobile robot
Bartončík, Michal ; Hrabec, Jakub (referee) ; Šolc, František (advisor)
This thesis treatise about design self-balancing wheelframe type of segway. Introduces the principle of segway, the original models and solutions other people. The simulation uses a mathematical model to determinate the characteristics of senzors. Selection the method of measuring the angle and implementation with the help of sensors. Furthermore, deal with engines for moving of model, multifunction I/O card and desktop board for processing signal from sensors. Their connections and attechments on the construction.
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Stereometric ultrasonic distance sensor
Nguyen, Thuc Tuyen ; Marada, Tomáš (referee) ; Zuth, Daniel (advisor)
This bachelor thesis deals with designing and realizing a sensory system for detecting the presence of targets and its location. Target is located by two parameters: the distance and the view angle from sensory system. This system is set up by two ultrasonic distance sensors SRF02, driven by microcontroller Atmega128, using I2C communication protocol. The placement of the two ultrasonic distance sensors is optimized by using mathematical model, it enables the system to perform optimum accuracy and be able to observe the largest area possible. The measurement results then will be shown on LCD display module or they can be saved and used as input parameters for other tasks.
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