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2. Note on Knots on Endless Cords

Published online by Cambridge University Press:  15 September 2014

A. B. Kempe Esq.
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Extract

  1. 1. Each crossing divides the cord into two loops.

  2. 2. Any other crossing either lies on both these loops, say is linked to the former crossing, or on one loop only, say is not linked to the former crossing.

  3. 3. It can be shown without difficulty that if crossing a is linked to crossing b, then crossing b is linked to crossing a; and therefore, also, if crossing a is not linked to crossing b, crossing b is not linked to crossing a.

  4. 4. Hence pairs of crossings are of two sorts, viz., linked and unlinked.

Type
Proceedings 1886-87
Information
Proceedings of the Royal Society of Edinburgh , Volume 14 , 1888 , pp. 36 - 37
Copyright
Copyright © Royal Society of Edinburgh 1888

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