The Taxicab Metric

Topology · Axiom Academy

Understanding the Manhattan Distance Through Worked Examples For two points in , the taxicab distance is: This is the sum of the absolute differences of their coordinates, representing the distance traveled along grid lines. 1 Computing Taxicab Distance in R² 2 Visualizing the Taxicab Open Ball 3 Comparing Taxicab and Euclidean Metrics The taxicab distance between two points is , the sum of absolute differences in each coordinate. It represents the distance traveled along a grid, like navigating city streets. Open balls in the taxicab metric are diamond-shaped (squares rotated 45°). The taxicab distance is always greater than or equal to the Euclidean distance: . Different metrics can define different topologies on the same space, leading to different notions of convergence, continuity, and openness.

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