Taxicab geometrija

master's thesis

• Title (english): Taxicab geometry
• Author: Vinko Brdarić
• Mentor: Slaven Kožić (mentor)
• Committee member: Slaven Kožić (predsjednik povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Committee member: Vedran Krčadinac (član povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-03-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

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.

Abstract (english)

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.

• Keywords: euklidska geometrija; taxicab geometrija; elipse; hiperbole; parabole; osnovnoškolska nastava matematike
• Keywords (english): Euclidean geometry; taxicab geometry; ellipses; hyperbolas; parabolas; elementary school mathematics
• Language: croatian
• URN:NBN: urn:nbn:hr:217:031684
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-03-23 13:27:07