Manhattanetäisyyttä

Manhattanetäisyyttä, also known as taxicab geometry or L1 distance, is a metric defined in a grid-like space. It represents the distance between two points if you can only travel along horizontal and vertical lines, similar to how a taxi would navigate the streets of Manhattan. Unlike the familiar Euclidean distance, which measures the straight-line path, Manhattanetäisyyttä sums the absolute differences of their Cartesian coordinates.

For two points p = (x1, y1) and q = (x2, y2) in a two-dimensional plane, the Manhattanetäisyyttä is calculated as |x1 - x2| + |y1 - y2|. This concept can be extended to any number of dimensions. In three dimensions, for points p = (x1, y1, z1) and q = (x2, y2, z2), the distance would be |x1 - x2| + |y1 - y2| + |z1 - z2|.

This metric has applications in various fields, including computer science, image processing, and operations research. For example, in robotics, it can be used to plan paths for robots operating in environments with restricted movement. In machine learning, it's employed in algorithms like k-nearest neighbors and clustering. The geometric shape formed by all points equidistant from a central point in Manhattanetäisyyttä is a diamond or square rotated by 45 degrees, contrasting with the circle formed by Euclidean distance.