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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
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Length measurement
Pecinová, Iva ; Šarounová, Alena (advisor) ; Surynková, Petra (referee)
My bachelor thesis Length measurement deals with the euclidean length measurement. It deals with the history of the length measurement in the Czech country, the emergence of the basic unit of length - meter and especially the circumference. The work is intended primarily for high school teachers of mathematics and lovers of measurements which are expected to at least high school knowledge of mathematics. This text is good for primary schools teachers of mathematics which is intended Handbook for small meter. The component part of my bachelor thesis is an enclosed CD, where is found the bachelor thesis in an electronic form and the already mentioned Handbook for small meter - a version for printing.
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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.
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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.
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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.
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Length measurement
Pecinová, Iva ; Šarounová, Alena (advisor) ; Surynková, Petra (referee)
My bachelor thesis Length measurement deals with the euclidean length measurement. It deals with the history of the length measurement in the Czech country, the emergence of the basic unit of length - meter and especially the circumference. The work is intended primarily for high school teachers of mathematics and lovers of measurements which are expected to at least high school knowledge of mathematics. This text is good for primary schools teachers of mathematics which is intended Handbook for small meter. The component part of my bachelor thesis is an enclosed CD, where is found the bachelor thesis in an electronic form and the already mentioned Handbook for small meter - a version for printing.
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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
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