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master's thesis
Simsonov pravac i poopćenja
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:667060
Vrančić, Katarina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Vrančić, K. (2014). Simsonov pravac i poopćenja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:667060

Vrančić, Katarina. "Simsonov pravac i poopćenja." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:667060

Vrančić, Katarina. "Simsonov pravac i poopćenja." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:667060

Vrančić, K. (2014). 'Simsonov pravac i poopćenja', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:667060

Vrančić K. Simsonov pravac i poopćenja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 November 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:667060

K. Vrančić, "Simsonov pravac i poopćenja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:667060

Metadata
TitleSimsonov pravac i poopćenja
AuthorKatarina Vrančić
MentorMea Bombardelli (mentor)
Committee memberMea Bombardelli (predsjednik povjerenstva)
Committee memberSanja Varošanec (član povjerenstva)
Committee memberVlado Volenec (član povjerenstva)
Committee memberMladen Jurak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-09-24, 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
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:667060
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-19 15:44:14