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master's thesis
Apolonijeve kružnice
2019. urn:nbn:hr:126:112149
Semkiv, Marija
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Semkiv, M. (2019). Apolonijeve kružnice (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:112149

Semkiv, Marija. "Apolonijeve kružnice." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:112149

Semkiv, Marija. "Apolonijeve kružnice." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:112149

Semkiv, M. (2019). 'Apolonijeve kružnice', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 09 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:112149

Semkiv M. Apolonijeve kružnice [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 November 09] Available at: https://urn.nsk.hr/urn:nbn:hr:126:112149

M. Semkiv, "Apolonijeve kružnice", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:112149

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Metadata
TitleApolonijeve kružnice
Title (english)Apollonius Circles
AuthorMarija Semkiv
MentorIvica Martinjak (mentor)
Committee memberMihaela Ribičić Penava (predsjednik povjerenstva)
Committee memberIvica Martinjak (član povjerenstva)
Committee memberSuzana Miodragović (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2019-10-04, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
U ovome radu proučavati ćemo Apolonijeve kružnice. Na početku ćemo proći kroz osnove konstruktivne geometrije i metodu inverzije kako bi mogli konstruirati neke od slučajeva Apolonijevog problema. Zatim ćemo se upoznati s Apolonijevim skupom. Proći ćemo kroz neka svojstva koja vrijede za četiri kružnice koje se diraju te vidjeti kako saznati broj kružnica u Apolonijevom skupu. Zatim ćemo se upoznati s Apolonijevom grupom i vidjeti analogon hipoteze o blizancima za Apolonijev skup. Na kraju ćemo navesti neke primjene Apolonijevog problema u drugim područjima.
Abstract (english)
In this paper we study Apollonian circles. At the beginnig, we touched the basics of constructions in geometry and inversion method so that we could construct some cases of the Apollonian problem. Then, we meet the Apollonian packing. We go through some characteristics that are valid for four circles that are touching each other and see how to find out the number of circles in an Apollonian packing. Then we meet then the Apollonian group and see the analog of the hypothesis about twins for the Apollonian packing. Finally, we adduce some applications of the Apollonian problem in other areas.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:112149
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-10-29 07:46:36