The Manhattan norm, also known as the L1 norm or taxicab norm, is a mathematical concept used to measure the distance between two points in a grid-like system. It calculates the distance by summing the absolute differences of their coordinates. For example, in a two-dimensional space, the distance between points (x_1, y_1) and (x_2, y_2) is given by |x_1 - x_2| + |y_1 - y_2|. This method is particularly useful in urban settings, where movement often resembles a grid layout, similar to the streets of Manhattan. The Manhattan norm is widely used in various fields, including statistics, machine learning, and computer science. It helps in tasks such as clustering and optimization, where understanding the distance between data points is crucial. Unlike the Euclidean norm, which measures straight-line distance, the Manhattan norm emphasizes movement along