Mamikonov izrek za ravninska območja

diplomsko delo

Nika Gril (Author), Tatjana Petek (Mentor)

Abstract

V diplomskem delu se ukvarjamo z računanjem ploščin ravninskih območij, ki jih določa Jordanov lok in popišejo tangentni odseki enake ali spremenljive dolžine. Najpreprostejši in motivacijski primer je prevedba kolobarja na ploščinsko enak krog. Posplošitev te ideje je Mamikonov izrek, ki ga formuliramo in dokažemo. Nato izrek uporabimo za ploščine likov, ki jih določajo graf potenčne oziroma eksponentne funkcije. Za konec določimo še ploščino pod enim lokom cikloide.

Keywords

diplomska dela;Mamikonov izrek;tangentni šop;tangentni trak;ploščina;tangenta;podtagenta;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Gril]
UDC:	514.122(043.2)
COBISS:	22191112
Views:	871
Downloads:	98
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Mamikon's theorem for planar regions
Secondary abstract:	In the thesis we consider calculating the areas of planar regions, defined by a Jordan curve and sections of tangents of constant or variable length. The simplest and motivating case is the transition of ring into a circle of equal area. Generalization of this idea is Mamikon's Theorem, which is being formulated and proved. Then we apply the Theorem for calculating the areas, defined by graphs of power and exponential function, respectively. At the end, we determine the area under one arc of cycloid.
Secondary keywords:	Mamikon's theorem;tangent cluster;tangent sweep;the area;tangent;subtangent;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	55 f.
ID:	9127803