posted September 24, 2006 07:38 AM           

http://www.elainecraft.com/instructions/var1.sq.html

but yes i suppose the mystery of macrame belongs over in universal codes......

posted September 28, 2006 02:48 AM           

Knot theory is a branch of topology inspired by observations, as the name suggests, of common knots. But progress in the field does not depend exclusively on experiments with twine. Knot theory concerns itself with abstract properties of theoretical knots — the spatial arrangements that in principle could be assumed by a loop of string.

When mathematical topologists consider knots and other entanglements such as links and braids, they describe how the knot is positioned in the space around it, called the ambient space. If the knot is moved smoothly to a different position in the ambient space, then the knot is considered to be unchanged, and if one knot can be moved smoothly to coincide with another knot, the two knots are called "equivalent".

In mathematical language, knots are embeddings of the circle in three-dimensional space. A mathematical knot thus resembles an ordinary knot with its ends spliced. The topological theory of knots investigates such questions as whether two knots can be smoothly moved to match one another, without opening the splice. The question of untying an ordinary knot has to do with unwedging tangles of rope pulled tight, but this concept plays at best a minor role in the mathematical theory. A knot can be untied in the topological sense if and only if it can be smoothly moved through the ambient space until it assumes the shape of a circle. If this can be done, the knot is called the unknot.

Modern knot theory has extended the concept of a knot to higher dimensions. One recent application of knot theory has been to the question of whether two strands of DNA are equivalent without cutting.

History

Knot theory originated in an idea of Lord Kelvin's (1867), that atoms were knots of swirling vortices in the æther. He believed that an understanding and classification of all possible knots would explain why atoms absorb and emit light at only the discrete wavelengths that they do. We now know that this idea was mistaken, and that the discrete wavelengths depend on quantum energy levels.[1]

Scottish physicist Peter Tait spent many years listing unique knots in the belief that he was creating a table of elements. When the luminiferous æther was not detected in the Michelson-Morley experiment, vortex theory became completely obsolete, and knot theory ceased to be of great scientific interest. Following the development of topology in the late nineteenth century, knots once again became a popular field of study. Today, knot theory finds applications in string theory and loop quantum gravity in the study of DNA replication and recombination, and in areas of statistical mechanics.
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An introduction to knot theory

Creating a knot is easy. Begin with a one-dimensional line segment, wrap it around itself arbitrarily, and then fuse its two free ends together to form a closed loop. One of the biggest unresolved problems in knot theory is to give a method to decide in every case whether two such embeddings are different or the same.
Two unknots
The unknot, and a knot
equivalent to it

Before we can do this, we must decide what it means for embeddings to be "the same". We consider two embeddings of a loop to be the same if we can get from one to the other by a series of slides and distortions of the string which do not tear it, and do not pass one segment of string through another. If no such sequence of moves exists, the embeddings are different knots.
http://en.wikipedia.org/wiki/Knot_theory

posted September 28, 2006 11:02 AM           

I say, macrame aint what is used to be is it...?!

What IS the world a coming to....