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master's thesis
Izoperimetrijska nejednakost i primjene
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:099270
Škrnjug, Karla
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Škrnjug, K. (2021). Izoperimetrijska nejednakost i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:099270

Škrnjug, Karla. "Izoperimetrijska nejednakost i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:099270

Škrnjug, Karla. "Izoperimetrijska nejednakost i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:099270

Škrnjug, K. (2021). 'Izoperimetrijska nejednakost i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:099270

Škrnjug K. Izoperimetrijska nejednakost i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:099270

K. Škrnjug, "Izoperimetrijska nejednakost i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:099270

Metadata
TitleIzoperimetrijska nejednakost i primjene
Title (english)Isoperimetric inequality and applications
AuthorKarla Škrnjug
MentorMarija Galić (mentor)
Committee memberMarija Galić (predsjednik povjerenstva)
Committee memberBoris Muha (član povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberMatej Mihelčić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-12-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu opisana je prva pojava izoperimetrijskog problema u matematici te otkriće tog problema (legenda o Didoni) i važnost u svakidašnjem životu. Rezultat izoperimetrijskog problema jest izoperimetrijska nejednakost. Izoperimetrijska nejednakosti dokazana je uporabom tehnike diferencijalnog računa te primjenom Fourierovih redova. Prikazana je konkretna primjena izoperimetrijske nejednakosti na geometrijskim likovima u ravnini (trokut i četverokut). Naposljetku, rezultati izoperimetrijske nejednakosti primjenjeni su na srednjoškolskim zadacima, pri čemu su prikazane različite aktivnosti u nastavi matematike koje potiču učenike na logičko razmišljanjem i zaključivanje. Izoperimetrijska nejednakost skriva se u pozadini rješenih zadataka srednjoškolskih učenika u različitim područjima matematike.
Abstract (english)
This thesis describes the first appearance of the isoperimetric problem in mathematics and the discovery of this problem (Dido’s legend) and its importance in everyday life. The result of the isoperimetric problem is isoperimetric inequality. Isoperimetric inequalities are proved using the technique of differential calculus and the application of the Fourier series. The concrete application of isoperimetric inequality on geometric figures in a plane (triangle and quadrilateral) is presented. Finally, the results of isoperimetric inequality were applied to high school assignments, showing different activities in mathematics teaching. Isoperimetric inequality is hidden in the background of solved problems of high school students in different areas of mathematics.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:099270
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 on2021-12-16 15:56:46