Včrtane stožnice

magistrsko delo

Žana Strgar (Author), Aleš Vavpetič (Mentor)

Abstract

V delu obravnavamo stožnice in njihove geometrijske lastnosti. Posebno pozornost namenimo včrtanim stožnicam, to so stožnice, ki se dotikajo nosilk stranic večkotnika. S pomočjo rezultatov evklidske, kot sta izotomična in izogonalna konjugacija, ter projektivne geometrije, kot je polarna zveza, poskušamo raziskati njihove lastnosti ter poiskati točke, ki nam bodo v pomoč pri njihovi konstrukciji. Ogledamo si stožnico včrtano v trikotnik, Steinerjevo in Brocardovo elipso ter parabolo včrtano trikotniku in popolnemu štirikotniku. Omenjene stožnice želimo konstruirati s pomočjo programa GeoGebra. V ta namen želimo poiskati pet točk stožnice, saj je s petimi točkami stožnica natanko določena, ali značilne točke, ki določajo stožnico, na primer gorišča in točko na stožnici.

Keywords

včrtane stožnice;stožnice;projektivna geometrija;preseki stožca;perspektor;izogonalna konjugacija;izotomična konjugacija;polarna zveza;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[Ž. Strgar]
UDC:	514
COBISS:	80572675
Views:	979
Downloads:	251
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Inscribed conics
Secondary abstract:	In this work we study the geometry of conic sections and their geometric properties. We are particularly interested in the inscribed conics, i. e., the conics that are tangent to the sides of the polygon. We study their properties using results of Euclidean, such as isotomic and isogonal conjugation, and projective geometry, such as the polar correspondence. We deal with conics inscribed in a triangle, Steiner and Brocard ellipse, and a parabola inscribed in a triangle and a complete quadrilateral. To construct these conics with GeoGebra program, we need to find five points of the conic, since five points determine a conic, or some characteristic points, for example, foci.
Secondary keywords:	inscribed conics;conics;projective geometry;conic sections;Steiner elipse;perspector;isogonal conjugation;isotomic conjugation;polar correspondence;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Pedagoška matematika
Pages:	IX, 65 str.
ID:	13682543