  The curvatures of the circles in integral Apollonian circle packings, named
for Apollonius of Perga (262-190 BC), form an infinite collection of integers
whose Diophantine properties have recently seen a surge in interest. Here, we
give a new description of Apollonian circle packings built upon the study of
the collection of bases of Z[i]^2, inspired by, and intimately related to, the
`sensual quadratic form' of Conway.
