A need for a distance-between-two-points function arises frequently enough to warrant consideration for inclusion in the math module.   It shows-up throughout mathematics -- everywhere from simple homework problems for kids to machine learning and computer vision.

In the latter cases, the function is called frequently and would benefit from a fast C implementation that includes good error checking and is algorithmically smart about numerical issues such as overflow and loss-of-precision.

A simple implementation would be something like this:

    def dist(p, q):
        'Multi-dimensional Euclidean distance'
        # XXX needs error checking:  len(p) == len(q)
        return sqrt(sum((x0 - x1) ** 2 for x0, x1 in zip(p, q)))

The implementation could also include value added features such as hypot() style scaling to mitigate overflow during the squaring step:

    def dist2(p, q):
        # https://en.wikipedia.org/wiki/Hypot#Implementation
        diffs = [x0 - x1 for x0, x1 in zip(p, q)]
        scale = max(diffs, key=abs)
        return abs(scale) * sqrt(fsum((d/scale) ** 2 for d in diffs))