"The writhing number made easy"

Date:
1975
Reference:
PP/CRI/H/6/12/1
Catalogue details

Licence: In copyright

Credit: "The writhing number made easy". Source: Wellcome Collection.

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    20th October 1975 Professor F Brock Fuller CalifDonia Institute of Technology Alfred P Sloan Laboratory of Mathematics and Physics Pasadena California 91125 USA Dear Professor Fuller This is a very belated reply to your letter of September 2nd. We enjoyed your remarks about inversion and the very neat proof that the writhing number is zero for any closed curve lying on a sphere. We do apologise about the question on joining two elements of ribbon. I unthinkingly posed this question to Klug when I was in hospital. The question should be stated Given two elements of ribbon an arbitrary distance apart and in arbitrary orienta tions. Joan these by a continuous ribbon. This stretch of ribbon will have a twist. Can one say whether one can draw this continuous ribbon so that the twist along it has a minimußi? The answer appears to be that one can always find a joining ribbon for which not only the total twist along it is zero but that its twist is everywhere zero. This must be very obvious to yojt but I only noticed xt when I came to reply to your letter. ,< A related question would be to join the two ribbon elements by/ a ribbon having as its axis the straight line between the two ribbon elements (the shortest ribbon). Then the twist along the connecting ribbon is fixed Ïapart from adding or subtrating integer amounts of twist). One is tacitly assuming that the axis of the ribbon can be kinked but that the twist must not be discontinuous. I have expressed this badly but I hope you can see what I'm trying to say. We have, as yet s no evidence for kinks but suspect they will turn up somewhere. Notice that our kink imparts a small twist at the kink. We look forward to your thoughts on polygons in space. Yours sincerely F H C Crick
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