Kompleksna ravnina in dvodimenzionalne geometrije

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Language:	Slovenian
Year of publishing:	2008
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[C. Zakrajšek]
UDC:	004(043.2)
COBISS:	6746196
Views:	1051
Downloads:	225
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Secondary language:	English
Secondary title:	[ǂThe ǂcomplex plane and two-dimensional geometries]
Secondary abstract:	This work comprises description of applications of complex numbers in two-dimensional geometry and demonstration development with programming tool Mathematica. In the first part, consisting of chapters two to six, I interpreted complex functions as transformations of the plain and developed theory, necessary for defining and understanding geometry. I interpreted spherical and hyperbolic geometry as geometry of the sphere and the pseudosphere. Transformation groups of Euclidean, spherical and hyperbolic geometries are formed using the three reflections theorem. I developed isometric mappings from the sphere and the pseudosphere to the plain and interpreted transformation groups of the three geometries as transformations of the plain and consequently as Möbius transformations. In the second part, consisting of chapter seven, I described applications which demonstrate two-dimensional geometries.
Secondary keywords:	Möbius transformation;reflection in a circle;Euclidean geometry;surface curvature;spherical geometry;hyperbolic geometry;computer science;diploma;
File type:	application/pdf
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univerza v Ljubljani, Fakulteta za računalništvo in informatiko
Pages:	VII, 85 str.
ID:	23829089