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Computer-aided Teaching of Spherical Geometry
Bémová, Kristýna ; Surynek, Pavel (advisor) ; Voráčová, Šárka (referee)
Basically we distinguish two types of geometry: Euclidean and Non-Euclidean. Everyone meets Euclidean geometry at basic school, but hardly ever a student hear about Non-Euclidean geometry. In this thesis, we are dealing with spherical geometry, which is a special part of Non-Euclidean geometry. We introduce basic concepts of spherical geometry in the thesis. A more detailed description is devoted to spherical trigonometry, which studies characteristics of spherical triangle and solves the corresponding problems. We also discuss differences between Euclidean and Non-Euclidean geometry. As a part of the thesis we developed an educational software for drawing on the spherical surface. The software is intended as an educational instrument for teaching spherical geometry. The program allows a student to draw shapes like a point, an abscissa, a circle and triangle. Further, the student can measure a length or an angle, which characterizes the differences between Euclidean and Non-Euclidean geometry in the best way. Our educational program improves user's stereometric imagination since the drawn shapes can be displayed from different visual angles.
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Surfaces Used in Architecture
Surynková, Petra ; Šarounová, Alena (advisor) ; Voráčová, Šárka (referee)
Nazev prace: Plochy stavcbni praxe Anfor: Pelra Surynkova Katedra (ustav): Katcdra didaktiky matematiky Yedouci diplomove prace: PhDr. Alena Sarounova, C'Sc. e-mail vcdouciho: Alena.Sarounovafajmff.cuni.cz Abstrakt: Bakalafska prace Plochy stavcbni praxe sc zabyva zakladnimi vlastnostmi ploch a jcjich vyuzitim v tcchnicke praxi. Specialne se venuje rozvinutelnym plocham. Prace je koncipovana jako ucebni text pro ucilele a studenty deskriptivni geometric a zajemcc o architekturu. Prace strucnc popisuje nektcre druhy ploch a ukazuje navrhy jejich vyuziti. Podrobnc pak studuje rozvinulelne plochy, jcjich vytvofcni, zakladni vlastnosti a uvadi i nekolik pfikladii rozvijeni rozvimitelnyeh ploch do roviny. Cast prace tcz pi'edklada inozna vyuziti ro/.vimitelnyeh ploch v praxi. K vctsine ploch jc pripojen take obrazek. K praci je pfidana obrazova pfiloha, ktera obsahuje fotografie staveb 7 eeleho svcta, na kteryeh sc /.minenc plochy vyskytuji. Soucasti bakalafske prace je rovnez pfilozcnc CD, na ncmz sc nachdzi dalsi obrazova pfiloha a bakalafska prace v clektronicke podobc. Kroine toho jsou na C'D zdrojove soubory vsech obrazku z bakalafske prace. Klicovci slova: plocha, rozvinutelna plocha, stfccha, klenba Title: Surfaces of Building Practice Author: Petra Surynkova Department: Department of Mathematics...
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A Plane Perspectivity
Plichtová, Petra ; Voráčová, Šárka (advisor) ; Boček, Leo (referee)
This thesis is intended for high school and university students and their teachers, who want to expand their knowledges about plane geometry. In the introduction of the text we let the reader know ideal point, dividing ratio and cross ratio. Thesis shows the dividing mappings in plane according to their characteristics which they maintaining. With some simple examples it shows their use in practice, their characteristics and main types. Main part of the thesis is projective transformations and affine transformations, derivation of their characteristics, searching for other points and their use. The work is added with illuminating pictures and photos. Pictures were drawn in QCAD software and GeoGebra software.
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Analysis of Point Clouds Representing Surfaces of Engineering Practice
Surynková, Petra ; Voráčová, Šárka (advisor) ; Pokorný, Milan (referee) ; Lávička, Miroslav (referee)
Title: Analysis of Point Clouds Representing Surfaces of Engineering Practice Author: Petra Surynková Department: Department of Mathematics Education Supervisor: Mgr. Šárka Voráčová, Ph.D., Faculty of Transportation Sciences, Czech Technical University in Prague Abstract: The doctoral dissertation Analysis of Point Clouds Representing Surfaces of Engineering Practice addresses the development and application of methods of digital reconstruction of surfaces of engineering and construction practice from point clouds. The main outcome of the dissertation is a presentation of new procedures and methods that contribute to each of the stages of the reconstruction process from the input point clouds. The work is mainly focused on the analysis of input clouds that describe special types of surfaces. Several completely new algorithms and improvements of existing algorithms that contribute to individual steps of surface reconstruction are presented. New procedures are based on geometrical characteristics of the reconstructed object. An important result of the dissertation is an analysis of not only synthetically generated point clouds but above all an analysis of real point clouds that have been obtained from measurements of real objects. The significant contribution of the dissertation is also an...
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A Plane Perspectivity
Plichtová, Petra ; Voráčová, Šárka (advisor) ; Boček, Leo (referee)
This thesis is intended for high school and university students and their teachers, who want to expand their knowledges about plane geometry. In the introduction of the text we let the reader know ideal point, dividing ratio and cross ratio. Thesis shows the dividing mappings in plane according to their characteristics which they maintaining. With some simple examples it shows their use in practice, their characteristics and main types. Main part of the thesis is projective transformations and affine transformations, derivation of their characteristics, searching for other points and their use. The work is added with illuminating pictures and photos. Pictures were drawn in QCAD software and GeoGebra software.
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Surfaces of Building Practice
Surynková, Petra ; Voráčová, Šárka (referee) ; Šarounová, Alena (advisor)
My diploma thesis Surfaces of Building Practice deals with the basic properties of surfaces, their mathematical description, categorization, and application in technical practice. Each studied surface is defined and its process of construction and parametrical description is listed. The thesis studies selected types of surfaces in details - these surfaces include surfaces of revolution, ruled surfaces, screw surfaces, and translational surfaces. An application of each studied surfaces is shown and each surface is accompanied with a picture. The thesis also contains a picture attachment with photographs of buildings from all over the world on that the studied surfaces visibly appear. The diploma thesis has an attached DVD that contains studied surfaces as models created in the Maple program, presentation with animations showing creation of selected surfaces, and the diploma thesis in the electronic format. Apart from these, the DVD contains source files of all pictures in the thesis. The thesis is outlined as an educational text for the teachers and the students of descriptive and differential geometry, and for those interested in architecture as well.
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Geometry in Architecture of Santini-Aichl
Štíchová, Růžena ; Šarounová, Alena (advisor) ; Voráčová, Šárka (referee)
This text is meant for all people from general public with interest in mathematics and geometry. Primarily it is meant to be study material for teachers of mathematics and descriptive geometry at secondary schools. In the thesis there is included summary and properties of surfaces used in building constructions and their parametric and implicit expression. Thereinafter it deals with particular use of these rectilinear planes and also other ones in construction of arches, specifically in arches of some Santini's buildings. There is also mentioned a list of Santini's buildings and an in-depth analyse of geometry in plans of some of them. The text is supplemented with illustrative pictures made in Cabri Geometry II Plus (version 1.3.1), Maple 7, Rhino 3.0 and AutoCAD 2005, digital photographs and pictures from quoted literature.
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