KoG, Vol. 5. No. 5., 2000.
Review article
Notes on Taxicab Geometry
Divjak Blaženka
orcid.org/0000-0003-0649-3267
; Faculty of Organization and Informatics, University of Zagreb, Varaždin, Croatia
Abstract
The taxicab geometry is one of non-Euclidean geometries. Hermann Minkowski (Gesammelte Abhandlungen) introduced this geometry more than 100 years ago. In this hundred years there were the periods of marginalization and the periods of great interest and wide application of this geometry. Today there is a whole specter of application and implementation of the taxicab geometry. There are several reasons for this.
First, the taxicab geometry is similar to Euclidean geometry and easy to understand. It can be observed as such a metric system where the points correspond to the intersections of the streets in the imagined city, streets run only horizontally and \ vertically. There are no one-way streets. From the previous description the name taxicab geometry arises. The taxicab geometry is appropriate to discuss out during the undergraduate study in the form of essays, seminar works and diploma thesis as it is described in [7] and [9].
Second, the taxicab geometry is interesting for theoretical geometry study, too. It can be analyzed by synthetic approach (introduced by David Hilbert), or by metric approach ( described by George David Birkhoff). Mentioned approaches are described and discussed in [6]. There is the third approach in geometry using abstract groups and group theory. This approach was introduced by Felix Klein and Arthur Cayley. They claimed that geometry had to be studied through acting the group of motions on the given set. Further, some propositions about ellipses in the taxicab geometry are proved.
Third, the practical value of the taxicab geometry is its wide application in (urban) transportation problems, city planning and so on. This application has been described in [10].
Keywords
non-Euclidean geometry; taxicab geometry
Hrčak ID:
3980
URI
Publication date:
19.2.2002.
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