Haggejeva transformacija

diplomsko delo

Maja Krmpotić (Author), Bojan Hvala (Mentor)

Abstract

Diplomsko delo obravnava Haggejevo transformacijo, in s to transformacijo tesno povezano izogonalno transformacijo. V prvem delu spoznamo izogonalno transformacijo ter definicijo in konstrukcijo Haggejeve transformacije v primeru, ko točka P leži zunaj trikotniku očrtane krožnice, in v primeru, ko P leži na njej. Nato ugotovimo povezavo med izogonalno transformacijo in Haggejevo transformacijo ter dokažemo, da vse Haggejeve krožnice potekajo skozi višinsko točko. Pogledamo, kam Haggejeva transformacija preslika nekaj značilnih točk trikotnika. Sledi obravnava analitične geometrije in vpeljava trilinearnih koordinat. Na koncu pokažemo, da se z izogonalno transformacijo vse premice preslikajo v stožnice. Ker pa je Haggejeva transformacija v tesni zvezi z izogonalno, velja isto tudi zanjo.

Keywords

matematika;trikotniki;očrtane krožnice;Haggejeva krožnica;Haggejeva transformacija;izogonalna transformacija;trilinearne koordinate;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2010
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Krmpotić]
UDC:	51(043.2)
COBISS:	17839368
Views:	2173
Downloads:	271
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	HAGGE TRANSFORMATION
Secondary abstract:	In this diploma Thesis we deal with Hagge transformation and also with isogonal transformation which is closely related to it. In the first part of the thesis we get aquainted with definition and construction of Hagge transformation in the case when point P lies outside of the circumcicle of the triangle and when point P lies on it. Then we make the connection between isogonal transformation and Hagge transformation and prove that all Hagge circles intersect the same orthocentre. We also look at where some characteristic points of the triangle are transformed. After this, we deal with analytical geometry and introduce trilinear coordinates. At the end we show that with isogonal transformation all lines are transformed into conic sections. Consequently, we show that the same holds true for Hagge transformation.
Secondary keywords:	triangle;circumcentre;Hagge circles;Hagge transformation;isogonal transformation;trilinear 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:	X, 72 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18750