Geometry of Calugareanu's theorem

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dc.creatorDennis, M. R.
dc.creatorHannay, J. H.
dc.date2005-03-07
dc.date2005-06-10
dc.date.accessioned2026-07-07T06:18:19Z
dc.date.available2026-07-07T06:18:19Z
dc.descriptionA 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.
dc.description10 pages, 3 figures, Royal Society style; revised
dc.identifierhttps://arxiv.org/abs/math-ph/0503012
dc.identifierhttp://arxiv.org/abs/math-ph/0503012
dc.identifierProc R Soc Lond A 461 (2005) 3245-54
dc.identifierdoi:10.1098/rspa.2005.1527
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94695
dc.subjectMathematical Physics
dc.subjectSoft Condensed Matter
dc.subjectBiological Physics
dc.titleGeometry of Calugareanu's theorem
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