Geometry of Calugareanu's theorem

Details Geometry of Calugareanu's theorem Geometry of Calugareanu's theorem

2005-03-07

arxiv.org/abs/math-ph/0503012v2

Proc R Soc Lond A 461 (2005) 3245-54

Physics

Mathematical Physics

10 pages, 3 figures, Royal Society style; revised

Scientific paper

10.1098/rspa.2005.1527

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.

Affiliated with

Also associated with

No associations

Rating

Geometry of Calugareanu's theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometry of Calugareanu's theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry of Calugareanu's theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-557486