Produkti in konjugacije v geometriji trikotnika

diplomsko delo

Maja Šket (Author), Bojan Hvala (Mentor)

Abstract

V diplomskem delu definiramo Yiujev produkt točk P in Q. Na podoben način uvedemo t. i. Parryjev produkt. Opišemo tudi geometrijsko konstrukcijo, s katero pri danih točkah P in Q konstruiramo ustrezni produkt. V nadaljevanju pri dani točki P v ravnini definiramo transformacijo ravnine, ki jo imenujemo konjugacija s polom P. Nato opišemo tri konstrukcije: konstrukcijo P-konjugacije poljubne točke pri danem paru konjugiranih točk, konstrukcijo pola P-konjugacije pri danem paru konjugiranih točk in konstrukcijo P-konjugacije poljubne točke pri danem polu. Za izpeljavo rezultatov uporabljamo trilinearne in baricentrične koordinate, ki so predstavljene v začetnih poglavjih.

Keywords

matematika;geometrija;trikotniki;produkti;konjugacije;koordinate;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Šket]
UDC:	51(043.2)
COBISS:	18236936
Views:	2243
Downloads:	301
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	PRODUCTS AND CONJUGATIONS IN TRIANGLE GEOMETRY
Secondary abstract:	In this graduate thesis we define the Yiu product of points P and Q. In a similar way we introduce the so-called Parry product. We also present a construction of both products. At the given point P in the plane we define a transformation of the plane called conjugation with pole P. Later we give three constructions: the construction of P-conjugation of an arbitrary point by a given pair of conjugated points, the construction of pole P by a given pair of conjugated points and the construction of P-conjugation of an arbitrary point by a given pole P. For the derivation of results we use trilinear and barycentric coordinates that are presented in the initial chapters.
Secondary keywords:	Yiu product;Parry product;conjugations;trilinear coordinates;barycentric coordinates;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	74 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19145