Download Braiding : new and automatic methods for constructing knots by A G Schaake; J C Turner; D A Sedgwick PDF

By A G Schaake; J C Turner; D A Sedgwick

ISBN-10: 0908830009

ISBN-13: 9780908830008

ISBN-10: 0908830025

ISBN-13: 9780908830022

ISBN-10: 0908830076

ISBN-13: 9780908830077

ISBN-10: 0908830149

ISBN-13: 9780908830145

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Extra info for Braiding : new and automatic methods for constructing knots and braids

Sample text

When this interbraiding is completed, we have three left bight-boundaries and three right bight-boundaries; hence A = 3 . In the grid-diagram belonging to the Standard Herringbone Pineapple Knot which is obtained after the completion of the Steps 1,2 and 3, a lower-left to upperright half-cycle of the 'Step 1' Turk's Head Knot runs from the left bight-boundary 1to the right bight-boundary 2, a lower-left to upper-right half-cycle of the 'Step 2' Turk's Head Knot runs from the left bight-boundary 2 to the right bight-boundary 1, and a lower-left to upper-right half-cycle of the 'Step 3' Turk's Head Knot runs from the left bight-boundary 3 to the right bight-boundary 3.

Ii) Let us now assume that we want to braid the given Standard Herringbone Pineapple Knot in the following way: Step I. - Braid the component with half-cycle 2 -+2 . Step 2. - Braid the component with half-cycle 1 1. The component in 'Step 1' is the foundation Turk's Head Knot and the component in 'Step 2' is the interwoven Turk's Head Knot. Fig. 38 gives their respective grid-diagrams. Foundation T u r k ' s head 5p/4b Interwoven T u r k ' s head 7p/4b Fig. 38 - The interbraided Turk's Head Knots.

L-R : 2u-20-u-20-2u-20. 8. R L : u-20-2u-20-2u-20-U. After completion of 'Step 2'' we are ready to start with 'Step 3'' which is the interbraiding of the Turk's Head Knot with s = 5 parts. When this interbraiding is completed, we have three left bight-boundaries and three right bight-boundaries; hence A = 3 . In the grid-diagram belonging to the Standard Herringbone Pineapple Knot which is obtained after the completion of the Steps 1,2 and 3, a lower-left to upperright half-cycle of the 'Step 1' Turk's Head Knot runs from the left bight-boundary 1to the right bight-boundary 2, a lower-left to upper-right half-cycle of the 'Step 2' Turk's Head Knot runs from the left bight-boundary 2 to the right bight-boundary 1, and a lower-left to upper-right half-cycle of the 'Step 3' Turk's Head Knot runs from the left bight-boundary 3 to the right bight-boundary 3.

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Braiding : new and automatic methods for constructing knots and braids by A G Schaake; J C Turner; D A Sedgwick


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