master's thesis
Euklid

Marina Matić (2016)
Sveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Zavod za teorijsku matematiku
Katedra za algebru i matematičku analizu
Metadata
TitleEuklid
AuthorMarina Matić
Mentor(s)Ivan Matić (thesis advisor)
Abstract
Cilj ovog rada je upoznati se s nekim rezultatima iz Euklidovog djela Elementi. U prvom dijelu rada predstavili smo njegove aksiome i postulate te smo proučili njegovu verziju Pitagorinog poučka, kao i neke tvrdnje potrebne za dokaz tog teorema. To je bio sadržaj prve knjige Elemenata. Zatim smo pisali o drugoj knjizi i geometrijskoj algebri, te vidjeli bitne rezultate vezane uz rješavanje kvadratnih jednadžbi pomoću geometrije. Nakon toga smo, kroz treću i četvrtu knjigu, proučili propozicije koje govore o svojstvima kružnica i konstrukciji pravilnog peterokuta, čime je rad i završen.
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
Lower level organizational unitsZavod za teorijsku matematiku
Katedra za algebru i matematičku analizu
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Geometry and Topology
Study programme typeuniversity
Study levelintegrated undergraduate and graduate
Study programmeMathematics and Computer Science
Academic title abbreviationmag. educ. math. et inf.
Genremaster's thesis
Language Croatian
Defense date2016-09
Parallel abstract (English)
The aim of this paper is to familiarize with some results from Euclid’s Elements. In the first part of the paper we presented his axioms and postulates and have studied his version of the Pythagorean theorem, as well as some things that are necessary to prove this theorem. This was the content of the first book Elements. Then we wrote about the second book and geometric algebra, and we saw significant results related to solving quadratic equations by using geometry. After that, through the third and fourth book, we studied propositions that speak of the properties of circles and construction of regular pentagon, and we completed work with this.
Parallel keywords (Croatian)Euklid Euklidovi elementi
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:508975
CommitterMirna Šušak Lukačević