How Do You Spell MANHATTAN DISTANCE?

1. Manhattan distance, also known as taxicab distance, is a term used in mathematics and computer science to measure the distance between two points in a grid-like system. It is named after the grid-like street layout of Manhattan, a borough in New York City.

   The Manhattan distance is calculated by finding the absolute differences in the x and y coordinates of two points, and then summing up these differences. In other words, it is the sum of the horizontal and vertical distance traveled between two points on a grid, without considering any diagonal movement.

   For example, consider two points in a 2D grid: point A with coordinates (x1, y1) and point B with coordinates (x2, y2). The Manhattan distance between these two points can be calculated as |x2 - x1| + |y2 - y1|.

   Manhattan distance is particularly useful in applications where movement is restricted to only four directions (up, down, left, and right). It has various applications in computer science, including image processing, pathfinding algorithms, and pattern recognition.

   Unlike the Euclidean distance, which measures the straight-line distance between two points, the Manhattan distance provides a more accurate measure of distance in a grid-like system. It is commonly used to find the shortest path between two points in a grid, where each move has a unit cost and can only be made horizontally or vertically.

The term "Manhattan distance" originates from the concept of measuring the shortest distance between two points in a grid-like city layout, such as the Manhattan borough of New York City. It is also known as "taxicab distance" or "city block distance". The name "Manhattan" came about because the grid layout of the streets in Manhattan allows for perpendicular movements (up, down, left, right) between blocks, where the distance is calculated by adding the horizontal and vertical distances traveled. The term was first used in mathematics and computer science to describe such a distance metric.