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master's thesis
Starogrčka geometrijska algebra
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:112452
Smrk, Ines
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Smrk, I. (2019). Starogrčka geometrijska algebra (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:112452

Smrk, Ines. "Starogrčka geometrijska algebra." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:112452

Smrk, Ines. "Starogrčka geometrijska algebra." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:112452

Smrk, I. (2019). 'Starogrčka geometrijska algebra', Master's thesis, University of Zagreb, Faculty of Science, accessed 18 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:112452

Smrk I. Starogrčka geometrijska algebra [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 May 18] Available at: https://urn.nsk.hr/urn:nbn:hr:217:112452

I. Smrk, "Starogrčka geometrijska algebra", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:112452

Metadata
TitleStarogrčka geometrijska algebra
AuthorInes Smrk
MentorFranka Miriam Bruckler (mentor)
Committee memberFranka Miriam Bruckler (predsjednik povjerenstva)
Committee memberDamir Bakić (član povjerenstva)
Committee memberAna Prlić (član povjerenstva)
Committee memberZlatko Drmač (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-11-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U radu opisujemo probleme vezane uz geometriju kojima su se bavili starogrčki matematičari, a koji se moderno mogu interpretirati algebarski. U pokušajima rješavanja koristili su razne metode, no valjana geometrijska konstrukcija dopuštala je samo korištenje konstrukcija ravnalom i šestarom. U prvom poglavlju navodimo neke klasične konstrukcije ravnalom i šestarom koje su bile poznate među grčkim matematičarima. Drugo poglavlje opisuje neke pokušaje rješavanja tri klasična problema. U trećem poglavlju naglasak je na drugoj knjizi Euklidovih Elemenata. Četvrto poglavlje sadrži dokaz nesumjerljivosti stranice i dijagonale kvadrata te način na koji je Apolonije opisivao konike. Rad završava opisom Descartesovog povezivanja geometrije i algebre, dokazom ekvivalencije konstrukcija ravnalom i šestarom s rješavanjem algebarskih kvadratnih jednadžbi te dokazom da tri klasična problema nisu rješivi konstrukcijama ravnalom i šestarom.
Abstract (english)
This thesis describes geometric problems that ancient Greek mathematicians were trying to solve and which can be interpreted geometrically. In their attempts they used different methods, but only solutions that used straightedge and compass were considered valid. In the first chapter we describe some of the classical straightedge and compass constructions that were known to Greek mathematicians. The second chapter describes some attempts to solve three classical problems. In the third chapter the emphasis is on the second book of Euclid’s Elements. The fourth chapter contains a proof of the incommensurability of the side and diagonal of a square and Appolonius’ approach to conics. The thesis concludes with Descartes’ connection of geometry and algebra, with proof that straightedge and compass constructions are equivalent to solving algebraic quadratic equations and with proofs of the impossibility of solving the three classical problems with ruler and compass constructions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:112452
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 on2020-07-15 12:57:28