  We give several new positive finite presentations for the pure braid group
that are easy to remember and simple in form. All of our presentations involve
a metric on the punctured disc so that the punctures are arranged "convexly",
which is why we describe them as geometric presentaitons. Motivated by a
presentation for the full braid group that we call the "rotation presentation",
we introduce presentations for the pure braid group that we call the "twist
presentation" and the "swing presentation". From the point of view of mapping
class groups, the swing presentation can be interpreted as stating that the
pure braid group is generated by a finite number of Dehn twists and that the
only relations needed are the disjointness relation and the lantern relation.
