File:Taxicab vs euclidean.png

Summary
Taxicab distance is the distance a taxi would have to travel on streets in a city with square blocks. Euclidean distance is the actual "as the crow flies" distance from the starting point to the destination. In this figure, the destination is 3 blocks north and 4 blocks east of the starting point, a total of 7 blocks by taxicab by any route, although the actual Euclidean distance is 5 blocks. A taxi traveling 5 blocks by any route could not reach the destination.

Created by me in PowerPoint and screen-captured as a bitmap.