| Popis: |
Ukratko, cilj ovog rada je proučavanje taxicab geometrije odnosno, preciznije, analiziranje kako razni geometrijski pojmovi izgledaju u taxicab geometriji. Glavni fokus je na razlikama između euklidske i taxicab geometrije. Započinjemo uvođenjem taxicab udaljenosti i uspoređivanjem s euklidskom udaljenosti. Zatim, obrađujemo različite slučajeve simetrale dužine u taxicab geometriji. Pokazujemo i razliku kruga i kružnice u euklidskoj i taxicab geometriji. Nakon toga prelazimo na elipse, hiperbole i parabole u euklidskoj i taxicab geometriji te na opisanu i upisanu kružnicu trokuta u taxicab geometriji. Konačno, bavimo se problemom prezentacije koncepta taxicab geometrije u okviru osnovnoškolske nastave matematike. In short, the goal of this thesis is to study taxicab geometry, i.e., to analyze how various geometric objects look in taxicab geometry. The main focus is on the differences between Euclidean and taxicab geometry. We start by introducing the taxicab distance and comparing it with the Euclidean distance. Next, we consider various cases of segment bisectors in taxicab geometry. We also show the differences between circles in Euclidean and taxicab geometry. Next, we shift to ellipses, hyperbolas and parabolas in Euclidean and taxicab geometry and to the incircle and circumcircle of a triangle. Finally, we deal with the problem of presenting the concept of taxicab geometry in elementary school mathematics. |
