|
|
The construction of curves by Descartes
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Zhouf, Jaroslav (referee)
This work studies the construction of algebraic curves by means of mechanical plotting tools designed by René Descartes. The work includes a brief biography of Descartes, an outline of his scientific method and a description of Descartes' views on curves, their construction and use. By means of dynamic geometry several curves established by Descartes are constructed. These include curves constructed by means of a drawing instrument composed of several rulers; a drawing instrument designed for the hyperbola and its different variations, in which the guiding line is replaced by one of conics in a special position. In the final part we present the construction of four ovals, which are usable in catoptric and dioptric that Descartes constructed by a point wise construction. All drawings are made in Cabri Geometry II and are accompanied by a derivation of the equations of the resulting curves. In deriving these equations we used only elementary algebraic methods, which could be used by Descartes himself and which are comprehensible by secondary school students. Keywords: Descartes, ruler device, curve, conchoid, trident, oval
|
|
| |
|
|
Draft of the coach manual for skicross coaches
Malec, Jakub ; Jindra, Matouš (advisor) ; Gnad, Tomáš (referee)
Title: Draft of the coach manual for skicross coaches Objetives: The aim of the diploma thesis is to create draft of the coach manual for skicross. Draft containing a methodological procedure for the acquisition of specific technical aspects in the discipline of skicross, draft of a training concept and introduction to the historical development of the discipline and to its rules. Methods: There was used the method of critical analysis of the documents. Then data from the author's experiences who was the coach in this discipline. And data obtained from interviews with selected respondents. Results: The result of the thesis is the draft of a comprehensive methodology and clarification of specific technical aspects for this discipline. Furthermore, the introduction to the long-term training concept and the periodization of the training process of this discipline. This thesis also presents the characteristics of this discipline, its historical development and rules. Conclusion: The draft of the methodology together with the draft of a long-term training concept will serve as a basis for the creation of a comprehensive coaching manual in the future. As there is no other methodology from abroad we must take into account the fact that this methodological approach and its procedures will change and adjust...
|
|
|
Interpolating and approximating spline curves
Jelínek, Daniel ; Štarha, Pavel (referee) ; Procházková, Jana (advisor)
This bachelor’s thesis deals with properties and algorithms of smooth curves calculation, specifically the calculation of B-spline curves. These curves can be applied in computer graphics. Since their calculation is defined recurrently, it is almost a necessity to use computers with programmed algorithms to obtain these curves. As for the practical part of this work, three programs for the calculation of approximating B-spline curves, interpolating B-spline curves and NURBS curves were created.
|
|
|
Renovation of the railway station in Ústí nad Orlicí
Velešíková, Karolína ; Svoboda, Lukáš (referee) ; Májek, Jan (advisor) ; Daněk, Lukáš (advisor)
The subject of the Bachelor Thesis was the reconstruction of the railway station in Ústí nad Orlicí. The content of the thesis was the Documentation for Building Permits and Documentation for Building Construction, based on the architectural study, which was created in the subject AG34-Atelier of Architectural Design in the winter semester. The building is situated on the outskirts of the town of Ústí nad Orlicí, near the village Kerhatice. Tichá Orlice flows nearby, and on the northern side of the building the terrain rises into a wooded hill. The station was built in 1874. Because of spatial reasons the building was placed between two groups of tracks. At the moment the only access to the building is by underpasses or by access roads for firemen from Nádražní street. Because of the construction of the new railway station, underpasses to platforms and their repairs, the old railway station was decommissioned, but the building was saved and declared as a cultural monument. The main idea was to design an appropriate solution for the using of the old building and preserve its original appearance from the time of construction in 1874. Restore the restaurant in a single-storey building. Create residential areas for the building manager, provide temporary accommodation for travelers, locate interesting historical information about the building and linking the building to the educational trail, possible multifunctional spaces such as workshops, offices and a small shop. Also rental spaces for hairdressers and cosmetics are also available. The assignment was also a space solution next to the object that is not being maintained. Therefore, a park layout was designed which serves passengers as a relaxation zone, for children for fun. The layout is an abstraction of the sound curve of a going train.
|
|
| |
|
|
Curves hidden in differential equations
Žalobínová, Petra ; Pyrih, Pavel (advisor) ; Bárta, Tomáš (referee)
Bachelor thesis Curves hidden in differential equations is engaged in solving and deriving differential equations, leading to the selected curve, which are cycloid curve and curves described by the hyperbolic functions . The core of the work is outlined into four transparent chapters, where the first of them gives a brief insight into the theory of curves and differential equations. In the following chapters, the work is specifically devoted to two historically significant problems, which are brachistochrone and catenary problems, but also deals with eigen, more modern problem of dynamics of symbiotic populations. The text explains the procedure of deriving differential equations from the considered problems and shows their solutions, by multiple methods. The contribution of this work, apart from the formulation and solution of the problem of symbiotic populations, is processing and making additions to solutions of these problems using a variety of methods from cited literature. The most important addition is relatively new and less known proof of the uniqueness of solutions of brachistochrone problem, which is enhanced by eigen intermediate steps and explanations.
|
|
| |
|
|
The construction of curves by Descartes
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Zhouf, Jaroslav (referee)
This work studies the construction of algebraic curves by means of mechanical plotting tools designed by René Descartes. The work includes a brief biography of Descartes, an outline of his scientific method and a description of Descartes' views on curves, their construction and use. By means of dynamic geometry several curves established by Descartes are constructed. These include curves constructed by means of a drawing instrument composed of several rulers; a drawing instrument designed for the hyperbola and its different variations, in which the guiding line is replaced by one of conics in a special position. In the final part we present the construction of four ovals, which are usable in catoptric and dioptric that Descartes constructed by a point wise construction. All drawings are made in Cabri Geometry II and are accompanied by a derivation of the equations of the resulting curves. In deriving these equations we used only elementary algebraic methods, which could be used by Descartes himself and which are comprehensible by secondary school students. Keywords: Descartes, ruler device, curve, conchoid, trident, oval
|
|
|
What is a curve?
Koudela, Libor ; Veselý, Jiří (advisor) ; Pyrih, Pavel (referee) ; Bobok, Jozef (referee)
The notion of a curve played important role in the history of mathematical thought. This dissertation is focused on the conception of a curve in analysis, point set theory and topology. The rectification of curves and the notion of arc length are considered in connection with the history of analysis from antiquity to the beginning of the 20th century. "Measurement of curves" is also discussed from the measure-theoretic viewpoint and various definitions of linear measure and fractional dimension are described. Historically, there are two main approaches to understanding curves. Jordan defined a curve as a continuous image of a closed interval. However, his definition appeared to be too wide, since it was met by objects such as the Peano curve. In the point set theory, a curve is considered to be a one-dimensional continuum. The development of the dimension theory and the continuum theory, starting with the pioneering work of Bolzano, was motivated by the search for rigorous topological definition of a curve, a surface etc. Among "pathological" curves, that were often introduced as counterexamples in the development of modern analysis, we can find early examples of fractals. The fractal theory motivated further study of mathematical properties of these curves in the late 20th century, such as self-similarity and...
|
guest ::
