Simsonov pravac i poopćenja

master's thesis

• Author: Katarina Vrančić
• Mentor: Mea Bombardelli (mentor)
• Committee member: Mea Bombardelli (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Vlado Volenec (član povjerenstva)
• Committee member: Mladen Jurak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Na početku ovog diplomskog rada definiramo Simsonov pravac kao pravac kojemu pripadaju ortogonalne projekcije točke P kružnice opisane trokutu ABC na pravce kojima pripadaju stranice tog trokuta. Upoznamo se i s nekim njegovim svojstvima. Nakon toga definiramo još jedan skup kolinearnih točaka koje pripadaju Steinerovom pravcu. U nastavku poglavlja o Steinerovom pravcu navode se i dokazuju svojstva Steinerovog pravca, zatim veza Simsonovog pravca i Steinerovog pravca te još neka posebna svojstva Simsonovog pravca. Treće poglavlje posvećeno je međusobnom odnosu dvaju Simsonovih pravaca, dok se u četvrtome poglavlju susrećemo s poopćenim Simsonovim pravcem te njegovim odnosom sa Simsonovim pravcem. Na samom kraju rada promatramo Simsonove pravce svakog od vrhova tetivnog četverokuta.

Abstract (english)

At the beginning of this thesis Simson’s line with its properties is defined. It’s a line that encompasses the orthogonal projection of a point P of a circle of a triangle ABC on the line’s that belong to the sides of the triangle. Furthermore, a set of colinear points belonging to Steiner’s line is defined. In the following chapter the properties of the Steiner’s line are listed and proved. Additionally we introduce the link between Steiner’s line and Simson’s line. Third chapter is dedicated to the relationship between the two Simson’s lines, while in the fourth we meet generalized Simson’s line and its relationship to Simson’s line. At the very end we observe Simson’s line of each of the vertices of a cyclic quadrilateral.

• Keywords: Simsonov pravac; Steinerov pravac
• Keywords (english): Simson’s line; Steiner’s line
• Language: croatian
• URN:NBN: urn:nbn:hr:217:667060
• 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: 2019-02-19 15:44:14