Taxicab Geometry Research Paper

In the past few hundred years, many mathematicians have developed and discovered many different forms of geometry. Euclidean geometry is probably considered the most understood and well-known form of geometry and is taught widespread among school systems today. However, many non-Euclidean geometries including Spherical, Hyperbolic, and Fractal geometry also play an important role in the world of mathematics as well. As if four forms of geometry were not enough, there is also another branch of geometry that plays a big role in real world mathematics application: Taxicab geometry. In my opinion, Taxicab geometry is probably the least popular form of geometry. I have to admit, I had never even heard of it until completing this project. However, after researching and understanding the fundamentals of this form of geometry, it is my opinion that Taxicab geometry has the most value in real world application when compared to the other forms of geometry. In this paper, I will discuss many points related to Taxicab geometry including: The background and history of Taxicab geometry The similarities and differences between topics in Taxicab and Euclidean geometry.

Taxicab Geometry stems from the ideas developed over one hundred years ago by the famous German mathematician Hermann Minkowski (1864-1909). Minkowski knew that Euclidean Geometry measured the shortest distance of a straight line between two points. However, Minkowski considered challenges to its real-world situations. What if something was blocking the distance? For example, a large object or building. Minkowski developed a non-Euclidean form of geometry that takes this limitation into account and changed the way to find the distance between two points in a non-Euclidean