TAXICAB GEOMETRY Meaning and
Definition
-
Taxicab geometry, also known as Manhattan geometry, is a form of geometry that measures distances in a way that reflects the behavior of a taxicab navigating through city streets. This concept originated as a thought experiment to understand how distance could be perceived in an urban setting. Unlike the traditional Euclidean geometry, which measures distances as the crow flies, taxicab geometry takes into account the constraints imposed by a grid-like street system.
In taxicab geometry, the distance between two points is determined by the minimum number of perpendicular and parallel "taxi" moves (referring to horizontal and vertical movements) required to travel from one point to the other. Instead of calculating the hypotenuse in a right-angled triangle, as in Euclidean geometry, taxicab geometry focuses on the sum of the absolute differences of the coordinates in each dimension.
This alternative approach to measuring distance in two-dimensional space can often result in substantial differences compared to Euclidean geometry. Specifically, a direct diagonal path may not be the shortest route based on the grid restrictions. Rather, the distance is evaluated based on movement along the streets or grid lines.
Taxicab geometry finds applications in various fields, especially in urban planning, computer graphics, and transportation systems. By considering travel times and distances in a realistic urban environment, taxicab geometry enables more accurate calculations for route planning, navigation algorithms, and optimization of resources in transportation networks.
Etymology of TAXICAB GEOMETRY
The word "taxicab geometry" has its etymology rooted in the concept of taxicabs or taxis, as well as the branch of mathematics known as geometry.
The term "taxicab" refers to a type of transportation, a vehicle typically used to transport passengers. In cities, taxicabs are often associated with the ability to move in any direction on a grid of streets. This freedom of movement without the constraints of specific angles or distances connects to the geometric concept that inspired taxicab geometry.
Taxicab geometry, also known as rectilinear geometry or Manhattan geometry, is a form of Euclidean geometry where the distance between two points is calculated by the sum of the absolute differences of their coordinates. This concept is reminiscent of hailing a taxi in a city, where the taxi can travel along the grid of streets in any direction, but must move along the streets' edges rather than taking direct, diagonal routes.
