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

PDF
Language: Croatian Download (751kB)  Preview 
Abstract
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 nonparallel points can be joined by a unique cycle. Axiom 2. For any cycle $c$ and any two nonparallel 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 
URI:  http://digre.pmf.unizg.hr/id/eprint/4297 
Actions (login required)
View Item 