THE COMPLEX PLANE AND TWO-DIMENSIONAL GEOMETRIES

Christian Zakrajšek (2008) THE COMPLEX PLANE AND TWO-DIMENSIONAL GEOMETRIES. EngD thesis.

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.

Item Type:

Thesis (EngD thesis)

Keywords:

Möbius transformation, reflection in a circle, Euclidean geometry, surface curvature, spherical geometry, hyperbolic geometry, ...

Number of Pages:

Language of Content:

Slovenian

Mentor / Comentors:

Name and Surname	ID	Function
izr. prof. dr. Neža Mramor Kosta	242	Mentor

Link to COBISS:

http://www.cobiss.si/scripts/cobiss?command=search&base=50070&select=(ID=6746196)

Institution:

University of Ljubljana

Department:

Faculty of Computer and Information Science

Item ID:

279

Date Deposited:

27 Oct 2008 10:43

Last Modified:

13 Aug 2011 00:32

URI:

http://eprints.fri.uni-lj.si/id/eprint/279

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