Transformacije v evklidski geometriji

diplomsko delo

Viktorija Capuder (Author), Eva Berdajs (Mentor)

Abstract

V diplomskem delu obravnavamo geometrijske transformacije. Geometrijske transformacije so široko področje, zato se bomo omejili na transformacije v evklidski ravnini. Pred samo obravnavo transformacij si pogledamo aksiome v ravninski evklidski geometriji, ki jih je potrebno poznati za obravnavanje transformacij. Posebna vrsta transformacij so izometrije, saj za njih veljajo posebne lastnosti. Poleg izometrij se dotaknemo tudi dveh drugih vrst transformacij in sicer središčnega raztega in inverzije na krožnico. Za konec poiščemo podobnosti med transformacijami z evklidsko geometrijo in možnost menjave temeljev evklidske geometrije s transformacijskim pristopom.

Keywords

evklidske transformacije;izometrija;rotacija;translacija;zrcaljenje;zrcalni zdrs;razteg;transformacijski aksiomi;evklidski izreki;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[V. Capuder]
UDC:	51(043.2)
COBISS:	78599939
Views:	177
Downloads:	13
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Transformations in Euclidean Geometry
Secondary abstract:	In this diploma thesis, we discuss geometric transformations. Being such a broad concept, the focus is only on transformations in Euclidean geometry. Before considering transformations, we look at axioms of planar Euclidean geometry that are the basis for exploring transformations. Isometries represent a special type of transformations that are subject to special properties. Beside isometries, we consider two other types of transformations. These are dilations and inversions in circles. In conclusion, we look at the possibility of changing the foundations of Euclidean geometry with a transformational approach.
Secondary keywords:	Matematika;Geometrija;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak.
Pages:	33 str.
ID:	13410973