Lemoineova točka

master's thesis

• Author: Keti Stepčić
• Mentor: Mea Bombardelli (mentor)
• Committee member: Mea Bombardelli (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu definirali smo pojam simedijane trokuta na dva načina: kao pravac koji prolazi polovištima antiparalela stranica trokuta, te kao pravac koji je izogonalan pravcu kojem pripada težišnica. Zatim smo iskazali i dokazali neka od glavnih svojstava simedijana. U drugom dijelu rada orijentirali smo se više na Lemoineovu točku, koju smo definirali kao sjecište simedijana, te kao izogonalno konjugiranu točku težišta. Zatim smo istraživali neka od svojstava Lemoineove točke. Dokazali smo i povezanost Lemoineove točke s nekim drugim poznatim točkama u ravnini, pa je tako Lemoineova točka trokuta ujedno i težište nožišnog trokuta Lemoineove točke, te je Lemoineova točka Gergonneova točka njemu tangencijalnog trokuta.

Abstract (english)

In this paper we have defined the notion of the symmedian of a triangle in two ways: as the line that goes through the midpoints of the antiparallels to the sides of a triangle, and as the line that is isogonal to the triangle median. We have also presented and provided proof for some of the main properties of the symmedian. In the second part of the paper we have mostly focused on the Lemoine point, which can be defined as the symmedian intersection and as the isogonal conjugate of the triangle centroid. In addition, we have investigated some of the properties of the Lemoine point. We have also proved the connection of the Lemoine point with some other points within the plane, which leads to the conclusion that the Lemoine point of a triangle also serves as the centroid of its pedal triangle and the Lemoine point actually represents the Gergonne point of its tangential triangle.

• Keywords: simedijana; Lemoineova točka; Gergonneova točka
• Keywords (english): symmedian; Lemoine point; Gergonne point
• Language: croatian
• URN:NBN: urn:nbn:hr:217:901125
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-03-15 14:00:40