Taxicab geometrija

Tkalčec, Ivana (2015) Taxicab geometrija. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this graduate thesis we study Taxicab geometry as one of non-Euclidean geometry. In the first chapter we expose short history of this geometry along with few solved problems which indicate its simplicity and possible applications. In next chapters we remind a reader on definition of metric of this geometry and we introduce the basic objects like circle, ellipse, hyperbola and parabola. We analyse their shapes in taxicab geometry and we obtain their equations. But definition of parabola impose the question how to measure the distance from a point to a line. The answer to this question is given in proved theorem that tells us about two different cases for the shortest path. Then we study bisector t-analogue which in taxicab geometry has even four forms. Afterwards we continue with studying t-angles and their measures which depend on position of angle. We also analyse sectioning of an angle using only taxicab constructs. Before the end we look back to get some more information about t-conics giving their general equations as well as detailed classification. Considering that this thesis was created for the purpose of finishing graduate program in mathematics education, last chapter is dedicated to implementing the basics of taxicab geometry for the students in high school.

Item Type: Thesis (Diploma thesis)
Supervisor: Milin-Šipuš, Željka
Date: 2015
Number of Pages: 86
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 29 Oct 2015 10:59
Last Modified: 16 Feb 2016 13:49
URI: http://digre.pmf.unizg.hr/id/eprint/4332

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