## Sunday, August 29, 2010

### The "Math" Behind Viking Jewelery

Very interesting, although the translation is somewhat terse.  From the MIT Technology Review blog.

Friday, August 27, 2010
The Mathematical Secret of Viking Jewelry
A long-standing puzzle over the craftsmanship behind Viking bracelets and necklaces has finally been solved--mathematically.

 Gold Armlet of Twisted Wires, Viking Period,  from the Douglas Treasure Trove of 1894.
The beautiful bracelets and necklaces made by Viking artisans leave archaeologists with something of a conundrum. These objects are made from rods of gold and silver which have twisted together into double helices. The puzzle is the regularity of these helices, which are remarkably similar in jewelry found in places as diverse as Ireland, Scotland, the Orkney Islands and Scandinavia.

How could craftsmen have achieved this regularity in such disparate places?

The answer comes today thanks to the work of Kasper Olsen and Jakob Bohr at the Technical University of Denmark. They point out that two wires become maximally twisted when no more rotations can be added with deforming the double helix. They go on to demonstrate the properties of maximally twisted wires. (We looked at a similar but more detailed argument about the properties of old rope a few weeks back.)

Olsen and Bohr then measured the properties of helices in Viking jewelry are twisted. It should come as no surprise to find that Viking jewelry is maximally twisted, which neatly explains why it all looks so similar. "Maximally rotated geometry is universal and therefore independent of the skills of the craftsman," say Olsen and Bohr.

Problem solved.

Ref: arxiv.org/abs/1008.4306: Hidden Beauty in Twisted Viking Neck Rings
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Two wires become maximally twisted when no more rotations can be added with[out] deforming the double helix.

Okay - so how many turns does it take to achieve two maximally twisted gold wires?  Did the craftsmen count the number of turns (or twists)?  What happened if you went one too many - and deformed the piece. Could you untwist it and start over, or would the metal have to be melted down and formed into "wires" again before starting over?  Did different thicknesses of wire require more turns - or fewer - to achieve the perfect helices?  Did longer wires require more turns?  Does this method work with three wires, four, five?

Dr. Kolsen said...

http://arxiv.org/abs/1008.4306

the number of rotations depend on length and thickness, but the endpoint - the maximally rotated geometry - is independent hereof. This behavior is also seen for more wires, I recommend taking a look at

"the ancient art of laying rope"
http://arxiv.org/abs/1004.0814

best, Kasper Olsen, PhD

Jan said...

Thank you!