Izoperimetrijska nejednakost i primjene

master's thesis

• Title (english): Isoperimetric inequality and applications
• Author: Karla Škrnjug
• Mentor: Marija Galić (mentor)
• Committee member: Marija Galić (predsjednik povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Committee member: Josip Tambača (član povjerenstva)
• Committee member: Matej Mihelčić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-12-01, 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: legenda o Didoni; izoperimetrijski problem; izoperimetrijska nejednakost; aktivnosti u nastavi matematike; srednjoškolski zadaci
• Keywords (english): Dido’s legend; isoperimetric problem; isoperimetric inequality; activities in teaching mathematics; high school tasks
• Language: croatian
• URN:NBN: urn:nbn:hr:217:099270
• 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: 2021-12-16 15:56:46