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master's thesis
Konstruktibilnost u planimetriji
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:293491
Filipović, Glorija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Filipović, G. (2022). Konstruktibilnost u planimetriji (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:293491

Filipović, Glorija. "Konstruktibilnost u planimetriji." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:293491

Filipović, Glorija. "Konstruktibilnost u planimetriji." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:293491

Filipović, G. (2022). 'Konstruktibilnost u planimetriji', Master's thesis, University of Zagreb, Faculty of Science, accessed 02 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:293491

Filipović G. Konstruktibilnost u planimetriji [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 December 02] Available at: https://urn.nsk.hr/urn:nbn:hr:217:293491

G. Filipović, "Konstruktibilnost u planimetriji", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:293491

Metadata
TitleKonstruktibilnost u planimetriji
Title (english)Constructability in planimetry
AuthorGlorija Filipović
MentorIgor Ciganović (mentor)
Committee memberVjekoslav Kovač (predsjednik povjerenstva)
Committee memberIgor Ciganović (član povjerenstva)
Committee memberAleksandra Čižmešija (član povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu raspravljali smo o konstruktibilnosti u planimetriji. U prvom poglavlju prikazali smo euklidske konstrukcije jednobridnim ravnalom i šestarom. U drugom poglavlju, bavili smo se algebarskim metodama konstrukcija i proširenjem polja racionalnih brojeva jer se konstrukcije ravnalom i šestarom mogu povezati s tipom proširenja polja racionalnih brojeva, koje sadrži korijene odgovarajućih polinoma. Kroz nekoliko teorema smo pokazali da se ne mogu svi geometrijski objekti dobiti konstrukcijama ravnalom i šestarom. Treće poglavlje bilo je o trima klasičnim problemima, kroz tri podpoglavlja smo opisali kako su oni nastali, naveli smo neke od pokušaja njihovog rješavanja i dokazali nemogu ćnost konstrukcije uporabom samo ravnala i šestara. Na kraju, u četvrtom poglavlju, kroz nekoliko teorema dokazali smo konstruktibilnost pravilnih mnogokuta.
Abstract (english)
In this master’s thesis we shall analyse the issue of constructibility pertaining to planimetry. In the first chapter we will display euclidean constructions using a straight edge ruler and a (regular) divider. In the second chapter we examined the algebraic methods of construction and widening of the field of rational numbers since constructions derived from the utilisation of a ruler and a divider can be associated with the type of expansion of the field of rational numbers that includes the roots of proper polynomials. The employed theorems demonstrate that not all geometric objects can be obtained by constructions using a straight edge ruler and a divider. The third chapter deals with the classical problems whose emergence is discussed in three subheadings, and some attempts at their solution are presented as well, and we demonstrated the impossibility of their construction by using solely a ruler and a divider. Finally, in the fourth chapter we employ certain theorems in order to prove the constructibility of regular polygons.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:293491
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 on2022-10-26 09:45:12