8f6b33d0-3d52-4679-a228-60277e1704fb
prompter
How do I find the distance between two points?
9d0dc5ef-93a5-4129-ae14-d2d22f8b3b32
8f6b33d0-3d52-4679-a228-60277e1704fb
assistant
You need to provide more context.
But if you are talking about two points in the plane you can use the Pythagoras theorem. d = ( ( x_2 - x_1 )^2 + ( y_2 - y_1 )^2 )^½
If you are talking about two points in a 3 dimensional space you will need a generalization of Pythagoras. d = ( ( x_2 - x_1 )^2 + ( y_2 - y_1)^2 + (z_2 - z_1)^2  )^½
dc667cd5-e8fd-4115-b3d9-3d7a2d471a8c
9d0dc5ef-93a5-4129-ae14-d2d22f8b3b32
prompter
Thanks, but I was interested in the Manhattan distance. How can I compute it?
07e0a8e6-6225-468d-a812-2c058868398a
dc667cd5-e8fd-4115-b3d9-3d7a2d471a8c
assistant
The Manhattan distance, also known as the L1 distance, is a measure of the absolute differences between two points in a grid-based space, such as a city grid. To calculate the Manhattan distance between two points (x1, y1) and (x2, y2), you simply add the absolute differences of their coordinates:

d = |x1 - x2| + |y1 - y2|

In a 3-dimensional space, you would extend the formula to:

d = |x1 - x2| + |y1 - y2| + |z1 - z2|