Simedianska točka trikotnika in tetraedra

magistrsko delo

Anja Jeglič (Author), Matija Cencelj (Mentor), Boštjan Gabrovšek (Co-mentor)

Abstract

Predstavili smo simediansko točko trikotnika, ki je ena od več tisoč znamenitih točk povezanih s trikotnikom. Na začetku smo definirali izogonalno konjugiranko premice skozi oglišče trikotnika, s pomočjo katere smo nato definirali simediansko točko trikotnika. Pogledali smo si nekaj zanimivih lastnosti simedianske točke trikotnika in v kakšnem odnosu je simedianska točka trikotnika z nekaterimi drugimi značilnimi točkami trikotnika. V nadaljevanju smo predstavili tetraeder in definirali izogonalno konjugiranko ravnine skozi rob tetraedra. S pomočjo tega smo lahko definirali simedianske ravnine katerega koli tetraedra. Na koncu smo predstavili dokaz, da se vseh šest simedianskih ravnin tetraedra seka v skupni točki in da se ta točka imenuje simedianska točka tetraedra.

Keywords

trikotnik;izogonalna konjugiranost;simedianska točka;tetraeder;diedrski kot;simedianska ravnina;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.09 - Master's Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[A. Jeglič]
UDC:	514(043.2)
COBISS:	22456323
Views:	393
Downloads:	44
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Symmedian point of a triangle and a tetrahedron
Secondary abstract:	We present the symmedian point of a triangle which is one of several thousand particular points associated to a triangle. First the isogonal conjugate of a line through a vertex of the triangle is defined in order to define the symmedian point. We take a closer look at some of the interesting properties of the symmedian point of a triangle and the relationship of the symmedian point with some other particular points of the triangle. Next we consider a tetrahedron and define the isogonal conjugate of a plane through a side of the tetrahedron. This enables us to define the symmedian planes of any tetrahedron. A proof that all six symmedian planes of a tetrahedron intersect in a common point is presented and this point is called the symmedian point of the tetrahedron.
Secondary keywords:	mathematics;geometry;matematika;geometrija;
File type:	application/pdf
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak, Poučevanje, Predmetno poučevanje
Pages:	52 str.
ID:	11899670