SCIPRESS FORMA
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Forma, Vol. 18 (No. 4), pp. 263-293, 2003
Original Paper

A Constructive Approach to Modelling the Tight Shapes of Some Linked Structures

E. L. Starostin*

Bernoulli Institute for Mathematics, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland
E-mail address: star@mpipks-dresden.mpg.de

(Received December 12, 2002; Accepted November 27, 2003)

Keywords: Ideal Knot and Link, Borromean Rings, Tight Clasp

Abstract. A variational approach is used to find the shortest curves connecting two pairs of points. The curves are to be separated by a constant distance and they are confined to lie in two orthogonal planes. The method is applicable to constructing tight shapes of linked structures each component of which is known to be planar. Two particular examples are considered and explicit solutions are presented for the Borromean rings, and for two clasped pieces of a rope that provide the minimum of the centreline length for a fixed diameter of the cross-section. A concept of tight periodic structures is introduced and discussed.


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