Çuhadar, Yağız (2014) A FIELD TRIP IN A NON‐EUCLIDIAN GEOMETRY. Other thesis, TED ANKARA KOLEJİ.
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Abstract
From elementary school to high school we have been learning different types of geometry. Taxicab geometry is an example of non‐euclidean geometry. Although it has similar points with Euclidian geometry, it differs from Euclidian geometry in an area; in distance functions. I have decided to try a new geometry. So, I have found taxicab geometry. When I researched about taxicab geometry, I have asked myself that “Could I turn this geometry into three dimensions?” My research subject is “Taxicab Geometry in Three Dimensions”. In the first part of the essay, my reasons of choosing this subject and an explanation of taxicab geometry are briefly given. After this quick information in the second part I will be proving Taxicab geometry is a metric*. Third part involves Euclidian geometry’s theorems for distance and theorems that are highly related to distance functions in three dimensions are given. Also formulas for distance in two dimensional taxicab geometry are given a. Furthermore, these theorems are taken as reference points for converting taxicab geometry to three dimensions. Distance function in two dimensions is converted to third dimension in this part. In the fourth part, sphere and cylinder which belongs to Euclidian geometry are recreated by me in taxicab geometry using the formulas that are found in the third part. The last part of the essay is about applications of taxicab geometry “Taxicab Geometry in Three Dimensions”. The taxicab space’s part in daily life, city planning and in buildings is explained by an example. To conclude, I will try to find answer to the question “Is it possible to convert sphere and cylinder from three dimensional Euclidian geometry to three dimensional taxicab geometry?”
| Item Type: | Thesis (Other) |
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| Additional Information: | Supervisor: Ali Oktay Koç, IB Notu: C |
| Uncontrolled Keywords: | Taxicab geometry, non‐euclidean geometry, Three Dimensions, mathematical model |
| Subjects: | Q Science > QA Mathematics |
| Depositing User: | Kamil Çömlekçi |
| Date Deposited: | 14 Sep 2014 11:44 |
| Last Modified: | 14 Sep 2014 11:44 |
| URI: | http://tedprints.tedankara.k12.tr/id/eprint/559 |
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