Posledici Carnotovega izreka

delo diplomskega seminarja

Ada Šadl Praprotnik (Author), Aleš Vavpetič (Mentor)

Abstract

Carnotov izrek nam pove, kdaj šest točk, po dve na vsaki stranici poljubnega trikotnika, leži na isti stožnici. Predstavili in dokazali bomo Carnotov izrek v evklidski in projektivni ravnini ter dve njegovi posledici. Prva posledica je definirana v evklidski ravnini in nam predstavi, kako s pomočjo danega trikotnika in izbrane točke konstruiramo šest točk na nosilkah stranic trikotnika, ki ležijo na isti stožnici. To stožnico imenujemo Cevova stožnica. Druga posledica je definirana v projektivni ravnini in nam pove, da točke na stranicah poljubnega trikotnika - ki jih dobimo tako, da iz vsakega oglišča tega trikotnika narišemo dve tangenti na dano stožnico, nato pa tangenti sekamo z nasprotno stranico - ležijo na isti stožnici.

Keywords

matematika;Carnotov izrek;Pascalov izrek;projektivna ravnina;Cevova stožnica;Gergonnova točka;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[A. Šadl Praprotnik]
UDC:	514
COBISS:	18690137
Views:	1311
Downloads:	2135
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Two applications of the theorem of Carnot
Secondary abstract:	The theorem of Carnot gives us a necessary and sufficient condition for six points, two on each side of a given triangle, to be on a conic. We will explain the theorem in both Evclidean and projective plane and then explain two of its applications. The first one is called the construction of the Cevian conic. It tells us how to construct six points on the sides or the carriers of the sides of a triangle so that they will form a conic, a Cevian conic. The second application is defined in the projective plane and tells us that the tangent lines from the vertices of a given triangle to an arbitrary conic intersect the carriers of the opposite sides of the triangle in six points that are on a conic.
Secondary keywords:	mathematics;Carnot theorem;Pascal theorem;projective plane;Cevian conic;Gergonne point;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	37 str.
ID:	11192190