Simedianska točka trikotnika in tetraedra

Jeglič, Anja (author), Cencelj, Matija (mentor), Gabrovšek, Boštjan (comentor)

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.

• Language: Slovenian
• Keywords: trikotnik
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Year: 2020
• PID: 20.500.12556/RUL-117525
• COBISS.SI-ID: 22456323
• Publication date in RUL: 15.07.2020

Secondary language

• Language: English
• Title: Symmedian point of a triangle and a tetrahedron

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.

• Keywords: triangle