OK, for metric spaces there are apparantly 3 different possibilities for the distance function in M where M is the usual Euclidean Plane:(adsbygoogle = window.adsbygoogle || []).push({});

(A) D(u,v) = sqrt((x_{1}-x_{2})^{2 }+ (y_{1}-y_{2})^{2})

(B) D(u,v) = max(|x_{1}-x_{2}|,|y_{1}-y_{2}|)

(C) D(u,v) = |x_{1}-x_{2}| + |y_{1}-y_{2}|

which somehow correspond to the picture I have attached.

A corresponds to the circle, B to the square and C to the diamond(this is supposed to be a square diamond but i created the image in paint, sorry)

Now, I understand (A) but I cannot seem to understand why (B) and (C) end up looking this way. and to be honest, I dont understand B and C at all.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Metric Spaces-BASIC DISTANCE

**Physics Forums | Science Articles, Homework Help, Discussion**