- A singly encircled band with two half-twists is topologically equivalent to a doubly-encircled untwisted band.
- The
**Linking number**describes both forms, and comprises;

**Lk = T**_{w}+ W_{r}

*W*_{r}or**Writhe**measures the extent to which coiling of the central curve has**relieved**local twisting**T**of the ribbon (T_{w}is ∫T) - Writhe connects the manifold of a single doubly-twisted band in 2D space (T=2, W=0) with
that of a
doubly-encircled untwisted band in 2D space (T=0, W=2) by projection
into
**3D space**(T + W = 2) - Positive values of W
_{r}are termed**overtwisting**by supercoiling - Negative values of W
_{r}are termed**undertwisting**by supercoiling - Both T
_{w}and W_{r}are signed**Chiral**indices.

**The White, Cãlugãreanu, Fuller Theorem;** J. H. White, *Am. J. Math.*, **1969**,
*91*, 693-728; G. Cãlugãreanu,
*Czech Mathematics J.*, **1961**, *11*, 588-625;
F. Fuller, *Proc. Natl. Acad. Sci.*,
**1971**, *68*, 815-819.

© H. S. Rzepa, 2007.