  For a given family of similar shapes, what we call a "unit shape" strongly
analogizes the role of the unit circle within the family of all circles. Within
many such families of similar shapes, we present what we believe is naturally
and intrinsically unital about their unit shapes. We present a number of
calculus problems related to extremal questions about collections of unit
shapes, and we recapitulate some isoperimetric problems in terms of unit
shapes. We close by presenting some problems (some of which are open) and by
proffering perhaps a new perspective on the $\pi$ vs. $\tau$ debate.
