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master's thesis
Visine trokuta i konstruktivni problemi
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:846408
Vukoja, Marijana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Vukoja, M. (2014). Visine trokuta i konstruktivni problemi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:846408

Vukoja, Marijana. "Visine trokuta i konstruktivni problemi." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:846408

Vukoja, Marijana. "Visine trokuta i konstruktivni problemi." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:846408

Vukoja, M. (2014). 'Visine trokuta i konstruktivni problemi', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:846408

Vukoja M. Visine trokuta i konstruktivni problemi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:846408

M. Vukoja, "Visine trokuta i konstruktivni problemi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:846408

Metadata
TitleVisine trokuta i konstruktivni problemi
AuthorMarijana Vukoja
MentorSanja Varošanec (mentor)
Committee memberSanja Varošanec (predsjednik povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
Committee memberBoris Širola (član povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-11, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Na početku ovog diplomskog rada definiraju se osnovni pojmovi kao što je visina trokuta i ortocentar. U nastavku se navode i dokazuju neka svojstva ortocentra. U radu je dokazano da su pravci na kojima leže visine Cevaini pravci. Također, bitno je spomenuti i Eulerov pravac i Feuerbachovu kružnicu koji su također opisani. Drugo je poglavlje posvećeno konstruktivnim zadaćama. Navedeno je što sve treba sadržavati konstruktivna zadaća i kakva ona može biti. Dalje prelazimo na konstrukcije trokuta od kojih je barem jedan zadani element visina. Takvih konstrukcija trokuta od kojih je jedna zadana veličina visina ima 47. Od toga je rješivo 36 konstrukcija, 10 konstrukcija nije rješivo i jedna je nemoguća. Prvih nekoliko primjera ima sve potrebne korake koje treba sadržavati konstruktivna zadaća, ostali primjeri imaju samo detaljnu analizu.
Abstract (english)
At the beginning of this thesis basic concepts are defined, such as the height of the triangle and the orthocentre. Some properties of the orthocentre are listed and proven. In this work we demonstrate that the lines in which the heights lie are Ceva lines. The Euler line and the Feuerbach circle are also described. The second chapter is devoted to constructive problems. It is also described what a constructive task should include and what it can be. Next we focus to the construction of a triangle in which at least one given element is height. There are 47 such triangle structures. 36 of them are solvable, 10 structures are not solvable and one has not got a solution. The first few examples have all necessary steps a constructive task has to contain; other examples have only a detailed analysis.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:846408
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 conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2019-02-20 11:19:00