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master's thesis
Generalizacija Apolonijeva problema
Split: University of Split, University of Split, Faculty of science, 2018. urn:nbn:hr:166:773802
Guberina, Antonija
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Guberina, A. (2018). Generalizacija Apolonijeva problema (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:773802

Guberina, Antonija. "Generalizacija Apolonijeva problema." Master's thesis, University of Split, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:166:773802

Guberina, Antonija. "Generalizacija Apolonijeva problema." Master's thesis, University of Split, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:166:773802

Guberina, A. (2018). 'Generalizacija Apolonijeva problema', Master's thesis, University of Split, Faculty of Science, accessed 19 April 2024, https://urn.nsk.hr/urn:nbn:hr:166:773802

Guberina A. Generalizacija Apolonijeva problema [Master's thesis]. Split: University of Split, Faculty of Science; 2018 [cited 2024 April 19] Available at: https://urn.nsk.hr/urn:nbn:hr:166:773802

A. Guberina, "Generalizacija Apolonijeva problema", Master's thesis, University of Split, Faculty of Science, Split, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:166:773802

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Metadata
TitleGeneralizacija Apolonijeva problema
Title (english)Generalization of Apollonius problem
AuthorAntonija Guberina
MentorNikola Koceić Bilan (mentor)
Committee memberNikola Koceić Bilan (predsjednik povjerenstva)
Committee memberGoran Erceg (član povjerenstva)
Committee memberIvan Jelić (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2018-02-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Apolonijev problem glasi: ”Konstruiraj kružnicu koja dodiruje tri zadane kružnice”. U uvodnom dijelu definiramo Apolonijev problem reda n,n ∈ N i na taj ga način generaliziramo. Detaljno obrađujemo metodu inverzije jer pomoću nje konstruiramo večinu Apolonijevih problema. U glavnom dijelu posebno promatramo sve Apolonijeve probleme reda 1, 2 i 3 te odredujemo GMS rješenja što je posebno interesantno za Apolonijeve probleme reda 2 jer se kao GMS javljaju konike i time dobivamo alternativnu definiciju konika. Važno je istaknuti da se kao GMS rješenja Apolonijevih problema reda 3 javljaju presjeci konika, konika i pravca iako je za očekivati da taj presjek bude prazan. Za Apolonijev problem reda 4 promatramo samo slučaj kada su zadane četiri točke. Apolonijeve probleme reda n ≥ 4 nije interesantno jer rješenja postoje samo u posebnim slučajevima. Također se iznosi ideja za daljne razmatranje stavljajući proizvoljni kut α ∈ [0, 180°〉 umjesto α = 0°, što smo u radu promatrali.
Abstract (english)
Apollonius problem claims ”Construct circles that are tangent to three given circles in a plane.” In introduction we define Apollonius problem order n,n ∈ N and we generalize it on that way. We deal in detail inversion because using that method we construct most of Apollonius problems. In main section, we are observing all Apollonius problems order 1, 2 and 3 and dealing with GCL solutions which are especially interesting for Apollonius problems order 2 because as GCL we have conics and because of that we are getting alternative definition of conics. It is important to say that solutions of Apollonius problems order 3 we get intersections of conics, conics and lines although we can expect that intersection is empty. For Apollonius problem of order 4 we study case with four given points. Apollonius problems of order n ≥ 4 are not so interested for study because solutions exist only in special cases. Also, we represent idea for further consideration putting arbitrary angle α ∈ [0, 180°〉instead α = 0°, which we have been considering in this text.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:773802
Study programmeTitle: Mathematics and Computer Science; specializations in: major in teaching
Course: major in teaching
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of Faculty of Science
Created on2018-06-20 14:51:41