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master's thesis
Harmoniteti
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:031538
Jambrošić, Martina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Jambrošić, M. (2021). Harmoniteti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:031538

Jambrošić, Martina. "Harmoniteti." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:031538

Jambrošić, Martina. "Harmoniteti." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:031538

Jambrošić, M. (2021). 'Harmoniteti', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:031538

Jambrošić M. Harmoniteti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:031538

M. Jambrošić, "Harmoniteti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:031538

Metadata
TitleHarmoniteti
Title (english)Harmonies
AuthorMartina Jambrošić
MentorAna Prlić (mentor)
Committee memberAna Prlić (predsjednik povjerenstva)
Committee memberSnježana Lubura Strunjak (član povjerenstva)
Committee memberGoranka Nogo (član povjerenstva)
Committee memberVanja Wagner (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-07-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu objasnili smo povezanost harmoniteta s transformacijama ravnine te iznijeli glavna svojstva i rezultate afine i projektivne transformacije, dvoomjera i inverzije. Zatim smo definirali harmonitete i harmoničke četverokute te naveli i dokazali osnovne teoreme i leme. Nakon toga smo primjenili koncept harmoniteta u rješavanju nekih geometrijkih zadataka s matamatičkih natjecanja. Na kraju smo objasnili na koji način se harmoniteti primjenjuju u glazbi.
Abstract (english)
In this paper we explained the connection between harmonic sets of points and plane transformations. Also we presented the main results and properties of affne and projective transformations, as well as ratios and inversion. We defined harmonic set of points and harmonic quadrilaterals, then we stated and proved the basic theorems and lemmas. We applied the concept of harmonic sets in solving some of the geometric problems which are often found in mathematical competitions. Finally, we explained application of harmonic sets in music.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:031538
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 on2021-09-15 10:13:39