Laguerreova geometrija

Martić, Jelena (2015) Laguerreova geometrija. Diploma thesis, Faculty of Science > Department of Mathematics.

Language: Croatian

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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.

Item Type: Thesis (Diploma thesis)
Supervisor: Krčadinac, Vedran
Date: 2015
Number of Pages: 29
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 22 Oct 2015 11:50
Last Modified: 22 Oct 2015 11:50

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