Geometry, often described as the mathematics of shape and space, explores the properties of objects, such as their angles and surfaces (Kunwar, 2018). The study of geometry is central in school mathematics curriculum, playing a pivotal role in the development of spatial awareness and geometric thinking in students (Kemp, 2018 as cited in Oladasu, 2014). Moreover, the profound impact of geometry and it’s practical application can be recognized by the idea that “all geometry is a product of our thinking and represents just one of the ways in which we try to communicate about our surroundings and understand certain aspects of reality” (Kemp, 2018, as cited in Grunbaum, 1981).
Krause (1987) suggests that to truly grasp the intricacies of Euclidean geometry, one should explore non-Euclidean geometries. Specifically, these non-Euclidean geometries should meet three key criteria: (1) they should closely resemble Euclidean geometry in their axiomatic structure, (2) they should have practical applications, and (3) they should be comprehensible to individuals who have completed introductory courses in Euclidean geometry (Krause, 1987). While other geometries like elliptical or hyperbolic geometry fulfill some aspects listed, Taxicab geometry emerges as a prime example that satisfies all three conditions (Krause, 1987) that is not only useful in the world but can facilitate a deeper understanding of Euclidean geometry.
Some practical problems that require the use of Taxicab metric are:
- A police department receives a report of a motorcycle accident at X=(-1,4). There are two police cars located in the area. Car A is at (2,1) and car B is at (-1,1). Which car should be sent?
- How to find the apartment for four people in a town working in four different offices staying in the same apartment in the shortest distance?
- There are three high schools in the city. School A is at (2,1), student B is at (-3,3) and C is at (-6,-1). How to make the school boundaries so that each student in the City attends the school closest to them?
- The telephone company wants to set up pay phone booths so that everyone living within 12 blocks of the center of town are within four blocks of a payphone booth. Money is tight so how should the telephone company set up the booths so that they have the least amount of booths possible.
As Professor Krause points out "while Euclidean geometry appears to be a good model of the 'natural' world, taxicab geometry is a better model of the artificial urban world that man has built” (Kunwar, 2018). Thus, Taxicab geometry should be emphasized in schools and learned by all due to its applicabilty and relevance.