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master's thesis
Laguerreova geometrija
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:252218
Martić, Jelena
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Martić, J. (2015). Laguerreova geometrija (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:252218

Martić, Jelena. "Laguerreova geometrija." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:252218

Martić, Jelena. "Laguerreova geometrija." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:252218

Martić, J. (2015). 'Laguerreova geometrija', Master's thesis, University of Zagreb, Faculty of Science, accessed 29 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:252218

Martić J. Laguerreova geometrija [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 May 29] Available at: https://urn.nsk.hr/urn:nbn:hr:217:252218

J. Martić, "Laguerreova geometrija", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:252218

Metadata
TitleLaguerreova geometrija
AuthorJelena Martić
MentorVedran Krčadinac (mentor)
Committee memberVedran Krčadinac (predsjednik povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
Committee memberJuraj Šiftar (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu bavimo se Laguerreovom geometrijom. Navodimo više modela koji zadovoljavaju aksiome Laguerreove ravnine te ih posebno dokazujemo za svaki od modela. Aksiomi Laguerreove ravnine su: Aksiom 1. Tri u parovima neparalelne točke spojene su jedinstvenim ciklusom. Aksiom 2. Za svaki ciklus \(c\) i za svake dvije neparalelne točke \(PIc\) i \(Q \cancel{I} c\), postoji jedinstveni ciklus \(d\) kroz \(Q\) koji dodiruje ciklus \(c\) u točki \(P\). Aksiom 3. Za svaku točku \(P\) i ciklus \(c\), postoji jedinstvena točka na \(c\) paralelna s \(PIc\). Aksiom 4. Postoji ciklus koji sadrži najmanje tri, ali ne i sve točke. Prikazujemo neke od modela u koordinatnom sustavu. Dokazujemo da postoji izomorfizam među konačnim minimalnim modelima i isto tako među dva beskonačna modela. Na kraju pokazujemo kako možemo definirati Laguerreovu ravninu nad bilo kojim poljem.
Abstract (english)
In this thesis we are dealing with Laguerre’s geometry. We give a several models that satisfy the axioms of Laguerre’s plane. We prove the axioms for each of the given models. The axioms of Laguerre plane: Axiom 1. Three pairwise non-parallel points can be joined by a unique cycle. Axiom 2. For any cycle $c$ and any two non-parallel points \(PIc\) and \(Q \cancel{I} c\), there is exactly one cycle \(d\) through \(Q\) touching \(c\) in \(P\). Axiom 3. For any point \(P\) and any cycle \(c\) there is exactly one point on \(c\) parallel with \(P\). Axiom 4. There is a cycle containing at least three, but not all points. We demonstrate some of the models in coordinate system. We prove that there is an isomorphism between the minimal models and between two of the infinite models. At the end we indicate the way to define Lagurre’s plane over an arbitrary field.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:252218
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 on2019-01-23 10:52:39