Enakostranični trikotniki in Jordanove krivulje

delo diplomskega seminarja

Nejc Zajc (Author), Aleš Vavpetič (Mentor)

Abstract

V diplomski nalogi odgovorimo na vprašanji obstoja in števila enakostraničnih trikotnikov na Jordanovih krivuljah. Osrednji del naloge je namenjen analizi te tematike v ravnini. V nalogi definiramo pojem presečnega števila krivulj in si ogledamo kaj so triode. Z uporabo teh pojmov uspemo pokazati, da kvečjemu dve točki na Jordanovi krivulji nista oglišči nekega enakostraničnega trikotnika, ki ima vsa oglišča na tej krivulji. V drugem delu naloge posplošimo rezultate iz ravnine v prostore višjih dimenzij. Ob koncu si pogledamo še nekatere rezultate glede obstoja kvadrata na ravninski Jordanovi krivulji in pokažemo, da na njej vselej obstaja pravokotnik.

Keywords

matematika;enakostranični trikotniki;Jordanove krivulje;presečno število;ravnina;triode;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[N. Zajc]
UDC:	514.7
COBISS:	122283011
Views:	618
Downloads:	63
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Equilateral triangles and continuous curves
Secondary abstract:	In this work, we give answers to questions regarding the existence and the number of equilateral triangles on Jordan curves. The main part of the work gives these results in the plane. We define the intersection number of two functions and take a look at triods. Using these concepts we show that all but two points on a Jordan curve are vertices of some equilateral triangle on this curve. In the second part we generalize the results from the plane to spaces of higher dimensions. At the end we take a look at some of the results on the topic of squares on Jordan curves. We also show that there always exists a rectangle on a Jordan curve.
Secondary keywords:	mathematics;equilateral triangles;Jordan curves;intersection number;plane;triod;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	22 str.
ID:	16487815