  A central result in the space geometry of closed twisted ribbons is
Calugareanu's theorem (also known as White's formula, or the
Calugareanu-White-Fuller theorem). This enables the integer linking number of
the two edges of the ribbon to be written as the sum of the ribbon twist (the
rate of rotation of the ribbon about its axis) and its writhe. We show that
twice the twist is the average, over all projection directions, of the number
of places where the ribbon appears edge-on (signed appropriately) - the `local'
crossing number of the ribbon edges. This complements the common interpretation
of writhe as the average number of signed self-crossings of the ribbon axis
curve. Using the formalism we develop, we also construct a geometrically
natural ribbon on any closed space curve - the `writhe framing' ribbon. By
definition, the twist of this ribbon compensates its writhe, so its linking
number is always zero.
