TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and...

This diploma thesis is focused on Selected problems in planimetry. The aim of this diploma thesis is description not only planimetric problems and their verification in a dynamic mathematical program GeoGebra, but also presentation of the author after whom it is called. The thesis is illustrated with pictures, which can help the reader to understand the problem and verification. This thesis can be used as a supplement the curriculum in secondary schools, where using dynamic program GeoGebra and subsequent verification may reach a better understanding of the topic.

In the context of violent crimes and criminal investigations, the effectiveness and proven success of offender or criminal profiling have been well documented. In reference to white-collar crime perpetrators offenders, this is a much less documented topic though. For any organisation to function effectively and be profitable there is huge reliance placed on employees. There is an expectation that the employees will carry out their functions with honesty and integrity while having the employer’s best interests in mind. Recent local and international published fraud surveys reported widely on the growing trend that has become known as the insider threat. This trend relates to the actual occurrence of misconduct by staff members and has increased proportionally over the years, i.e. from 55% in 2010 to a staggering 81% in 2015. The aim of this research was to determine how to profile staff members who commit white-collar crime in the South African short-term insurance industry. In addition, this research also focused on an introduction on the South African short-term insurance industry, as well as the suggested sources to consider when profiling staff as potential white-collar criminal perpetrators and the importance of making use of crime linkage analysis. Results of this research include that the main objective of profiling will at all times be to perform a structured social and psychological assessment of the perpetrator and when conducting the profiling of potential white-collar criminal perpetrators, there are specific offender characteristics to consider, and detailed data will be required pertaining to certain categories. / Police Practice / M. Tech. (Forensic Investigations)

Euclidean Geometry is a challenging topic for most of the learners in the secondary schools. A qualitative case study explores the reasoning skills of ninth graders in the proving of congruent triangles in their natural environment. A class of thirty-two learners was conveniently selected to participate in the classroom observations. Two groups of six learners each were purposefully selected from the same class of thirty-two learners to participate in focus group interviews. The teaching documents were analysed. The Van Hiele’s levels of geometric thinking were used to reflect on the reasoning skills of the learners. The findings show that the majority of the learners operated at level 2 of Van Hiele’s geometric thinking. The use of visual aids in the teaching of geometry is important. About 30% of the learners were still operating at level 1 of Van Hiele theory. The analysed books showed that investigation help learners to discover the intended knowledge on their own. Learners need quality experience in order to move from a lower to a higher level of Van Hiele’s geometry thinking levels. The study brings about unique findings which may not be generalised. The results can only provide an insight into the reasoning skills of ninth graders in proving of congruent triangles. I recommend that future researchers should focus on proving of congruent triangles with a bigger sample of learners from different environmental settings. / Mathematics Education / M. Ed. (Mathematics Education)

Diplomová práce "Strategické rozhodování o investičním projektu Kasárna Slatina" je zaměřena na využití metod rozhodovací analýzy při řešení rozhodovacího problému v rámci revitalizace armádního brownfield Kasárna Slatina. V teoretické části je vysvětlena základní terminologie, metody a postupy, které se vztahují k problematice řešeného rozhodovacího problému. V praktické části je řešeno závažné strategické rozhodnutí spojené s otázkou rozvoje konkrétní brněnské lokality. Na základě použitých postupů je v souladu s rozhodovací metodikou navrženo optimální rozhodnutí.

This thesis deals with the method of distributed ray tracing focusing on optimalization of this method. The method uses simulation of some attributes of light by distributing rays of lights and it produces high quality and partly realistic images. The price for realitic effects is the high computational complexity of the method. The thesis analysis the theory connected with these aspects. A large part describes optimalizations of this method, i.e. searching for the nearest triangle intersection using kd-trees, quasi random sampling with faster convergence, the use of SSE instruction set and fast ray - triangle intersection. These optimalizations brought a noticable speed - up. The thesis includes description of implementation of these techniques. The implementation itself emphasises the practical usability including generating some advanced animations and universal description of objects.

The thesis Higher Cicrcles in Defence Sector and Corruption in Defence Materiel Procurement in the Czech Republic deals with the question of presence of military-industrial complex (MIC) in the Czech society and economy after than more 65 years its constitution in Czechoslovakia by communist defence minister A. Čepička. His effort was initiated by a confidential wish expressed by J. V. Stalin in 1951 within a political meeting with defence ministers newly established people's republics in East Europa. Due to fact that MIC is usually linked with corruption, the thesis deals with the issue of corruption in acquisition of defence materiel; in particular, after 1994 when the first design of building-up the Czech military power was adapted as well as the first acquisition plan of military materiel was introduced for the next 10 years. So, the aim of the thesis is to verify the theory MIC's presence in the Czech Republic and to diagnose the stage of corruption in acquisition of military materiel at the Ministry of Defence. Author scrutinised the validity of two hypotheses: (H1) the MIC is in the Czech Republic omnipresent and (H2) the corruption in acquisition of military materiel at the Ministry of Defence is the stage of systemic corruption. With application of comparative analysis comparing the Czech...

The document describes developing graphical application with limited size. It describes suitable techniques for a polygonal mesh's compression. The second part is focused on practical usage of this techniques for developing scene in 3D modeling environment and also describes how to transfer this model to the executable file. The work attends to optimalizations of source code compilation and executables compression at the final chapters.

This Master's thesis deals with history of Fractal geometry and describes the fractal science development. In the begining there are essential Fractal science terms explained. Then description of fractal types and typical or most known examples of them are mentioned. Fractal knowledge application besides computer graphics area is discussed. Thesis informs about fractal geometry practical usage. Few present software packages or more programs which can be used for making fractal pictures are described in this work. Some of theirs capabilities are described. Thesis' practical part consists of slides, demonstrational program and poster. Electronical slides represents brief scheme usable for fractal geometry realm lectures. Program generates selected fractal types. Thesis results are projected on poster.

<p>This project argues that industrial fires have the capacity to illuminate the complex entanglements (political, ecological, economic, etc.) of life in the era of industrial capitalism. It retells and reframes the stories of five such fires, each off which shines a light on the networks of social, political, technological, economic, and ecological relationships in particular communities at particular moments. It thus contributes to the interdisciplinary fields of American Studies and the environmental humanities, furthering our understanding of the unfolding experience of industrial capitalism in the twentieth and twenty-first century United States. It takes the form of a public humanities project and is produced for a popular audience, using journalistic, literary, historical, and other techniques to tell the stories of these fires. In doing so, I also hope to contribute to the expansion of public humanities scholarship and help foster a thriving and creative future for the humanities both in academia and beyond.</p>