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Originally Posted by Iain
How far back does the paper propose such a geometry based design process would have started?
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Coincident with the appearance of the +ULFBERHT+ inscribed blades; about 800 AD.
I think the geometry observations are still a hypothesis in development, but it appears that a fairly large number of swords are fitting the patterns. Remember that the swordsmiths were unlikely to have been working directly with the math, but from templates. As more collections are analyzed with this tool, I suspect confidence will grow (or wane if too many examples otherwise correct for the period do not conform).
(The +ULFBERH+T crucible steel hypothesis was under attack at the conference and we may see it falling from favor; similarly, some sword and hilt forms from central Europe may, in fact, be earlier than previously believed. A lot to digest and I greatly enjoyed the conference and exhibit!)
Thank you, J.G., Carl Koppeschaar's album is far more comprehensive than the set of photographs I had taken and lost. As I placed this in the discussion forums, I shall shall shy away from discussing detailed logistics about acquiring the book except that the rumor at the conference was that direct mail order purchase is apparently somewhat cumbersome as the museum is a unit of the city government and is limited by regulations beyond its control. But, if you have an interest in this area the book is definitely a worthwhile acquisition.