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I know that the What is the intersection of two balls in $\mathbb{R}^2$ is either 0,1 or 2 points (since a ball in $\mathbb{R}^2$ is just a circle I can drew this).

What is the intersection of two balls in $\mathbb{R}^3$ ? is it at max 3 points ?

I would also like to know about the more general case of $n>1$

Can someone please help ?

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    A [ball](http://en.wikipedia.org/wiki/Ball_%28mathematics%29) is often taken to mean the interior of a sphere, perhaps including the edge, which would make their intersections a lens2012-04-28

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No it will be a circle or a point (or empty), see this wikimedia image:

enter image description here

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    Thank you both, the picture really help me see that!2012-04-28