Globalni izreki o sklenjenosti krivulj

diplomsko delo

Tina Špringer (Author), Marko Slapar (Mentor)

Abstract

V prvem delu diplomske naloge najprej predstavimo osnovne definicije in lastnosti krivulj v prostoru, to je krivulj, ki ležijo v R3. Definiramo ločno dolžino in ukrivljenost. V nadaljevanju dokažemo nekaj globalnih izrekov o ukrivljenosti krivulj. Prvi izrek poveže ukrivljenost in skladnost krivulj. Fenchelov izrek nam pove, koliko se mora prostorska krivulja ukrivljati, da postane sklenjena, medtem ko nam Fary-Milnorjev izrek pove, koliko se mora prostorska krivulja vsaj še dodatno ukrivljati, da postane zavozlana. V zadnjem delu diplomske naloge pa zaključimo z ukrivljenostjo ravninskih krivulj, to je krivulj, ki ležijo v R2.

Keywords

ukrivljenost krivulj v R3;skladnost krivulj;Fenchelov izrek;Fary-Milnorjev izrek;

Data

Language:	Slovenian
Year of publishing:	2017
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[T. Špringer]
UDC:	51(043.2)
COBISS:	11699785
Views:	595
Downloads:	192
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Global theorems of closed curves
Secondary abstract:	In this diploma thesis we first present basic definitions and properties of space curves, that is curves in R3. We define the length and local curvatures of space curves. Next we prove some global theorems concerning the curvatures. The first theorem connects congruence and curvatures of a space curves. Fenchel's theorem shows the lower estimate on total curvature of a closed curve while Frey-Milnor's theorem shows that a knotted curve must have an even larger total curvature. We conclude by discussing total curvature of plane curves.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Dvopredmetni učitelj, fizika-matematika
Pages:	IV, 22 str.
ID:	10864178