Bicentrički parovi točaka trokuta

master's thesis

• Author: Bernarda Topalović
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Zvonko Čerin (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavani su bicentrički parovi točaka trokuta. Listu, koja trenutno sadrži 119 bicentričkih parova, navodi Clark Kimberling. U prvom dijelu rada definirane su trilinearne i baricentričke koordinate, centar trokuta i bicentrički parovi točaka trokuta. Dana je poveznica između trilinearnih i baricentričkih, kao i trilinearnih i Kartezijevih koordinata. Navedeni su najpoznatiji centri trokuta i njihove trilinearne koordinate te nekoliko bicentričkih parova točaka trokuta. Središnji dio rada čine definicije, teoremi i dokazi vezani uz najpoznatiji bicentrički par točaka trokuta, prvu i drugu Brocardovu točku. Izvedene su trilinearne koordinate Brocardovih točaka i dana neka svojstva Brocardovog kuta. Navedene su definicije i teoremi vezani uz Brocardovu kružnicu te prvi i drugi Brocardov trokut. U završnom dijelu rada obrađen je još jedan poznatiji bicentrički par točaka, Yffove točke i neka njihova svojstva.

Abstract (english)

In this master’s thesis bicentric pairs of triangle points have been analysed. A table which currently contains 119 bicentric pairs is guided by Clark Kimberling. In the first part of the thesis, trilinear and barycentric coordinates, center of triangle, bicentric pairs of points have been defined. Connections between trilinear and barycentric as well as trilinear and Cartesian coordinates have been given. Best known centers of triangle and their trilinear coordinates and some bicentric pairs of triangle points are given. Central part of the thesis contains definitions, theorems, and proofs linked to the best known bicentric pair of triangle points as well as the first and the second Brocard points. Trilinear coordinates of the Brocard points are derived and some characteristics are given to the Brocard angle. Definitions and theorems connected to the Brocard circle as well as the first and the second Brocard triangle are given. In the closing part of this thesis we describe another bicentric pair of points, the socalled Yff’s points and prove some of its properties.

• Keywords: bicentrički parovi točaka trokuta; trilinearne koordinate; baricentričke koordinate; Kartezijeve koordinate; Brocardove točke; Yffove točke
• Keywords (english): bicentric pairs of triangle points; trilinear coordinates; barycentric coordinates; Cartesian coordinates; Brocard points; Yff’s points
• Language: croatian
• URN:NBN: urn:nbn:hr:217:881079
• 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: 2019-02-18 11:07:36