How Math Changes in a City

In Manhattan geometry, a straight line is not the shortest path between two points. Because you must follow a grid of streets like a taxi, the diagonal distance is equal to traveling around the block.

Standard geometry assumes you can move in any direction, but taxicab geometry accounts for restricted paths like city streets. In this system, you add the horizontal and vertical distances instead of using a direct diagonal line. Interestingly, this means multiple paths between two points can be the same shortest length. It is a fascinating way to model navigation in modern urban environments.