Trikotniki z danima ploščino in obsegom

diplomsko delo

Klara Štravs (Author), Bojan Hvala (Mentor)

Abstract

V diplomskem delu obravnavamo trikotnike z obsegom P in ploščino A. Dokažemo izoperimetrično neenakost, iz katere izhaja, da pri določenih začetnih podatkih A in P (ki tej neenakosti ne ustrezata) takih trikotnikov sploh ni. Pri začetnih podatkih, ki pa neenakosti ustrezata, raziskujemo število ustreznih trikotnikov, njihove lastnosti ter se osredotočimo na kote. Podamo interval, na katerem ležijo koti trikotnika z danima obsegom in ploščino. Ugotovitve ponazorimo na izbranem primeru trikotnika, določenega z A = 2 in P = 7. Slednje je kot animacija prikazano s pomočjo računalniškega programa Geogebra.

Keywords

matematika;trikotniki;ploščina;obseg;kot;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2009
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[K. Štravs]
UDC:	51(043.2)
COBISS:	16848648
Views:	3152
Downloads:	253
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Triangles sharing area and perimeter
Secondary abstract:	In diploma paper we explore triangles with perimeter P and area A. We prove the isoperimetric inequality from which results that by certain initial data A and P (that do not correspond with inequality) triangles do not exist. With initial data that correspond with inequality we explore the number of proper triangles, their characteristics and we focus on the angles. We offer the interval on which we find the angles of all the triangles with perimeter P and area A. Findings are illustrated on the chosen model of the triangle with A = 2 and P = 7. The latter is presented as an animation using the computer program Geogebra.
Secondary keywords:	triangle;perimeter;area;angle;isoperimetric inequality;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	40 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	17755