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Benvenuti in queste pagine dedicate a scienza ed arte. Amelia Carolina Sparavigna

Thursday, April 26, 2012

Roman Dodecahedra

Recently I have read a very interesting paper entitled "The magic dodecahedron of Gauls, that saved Roman legions: Mirror of Universe  and gauge of seasons." by Cinzia di Cianni, published on La Stampa,   in Italian  (Il dodecaedro magico dei Galli che salvò le legioni romane: Specchio dell’Universo e misura delle stagioni:, July 28, 2010). Here I  shortly discuss this article.
It starts with the following questions. Was is it, "a sacred symbol for Druids or the tip of a scepter? A gauge or a candlestick? Nobody knows what it is really, in spite of the fact that in museums and private collections, we find over than a hundred of them. It is a small hollow object of metal, dating from the fourth century and having a Gallo-Roman origin." The object exists in a variety of designs and sizes, always consists of 12 regular pentagons and this is known as "Roman dodecahedron". All the found "Roman dodecahedra"  have a diameter between 4 and 11 cm. and have at the center of the 12 faces holes of different sizes. Each of the 20 vertices is surmounted by one or three knobs, may be to fit them on some surfaces.
"The Roman dodecahedron is a simple object, actually a "time capsule", containing an incredible density of history and myth. By itself it does not reveal anything relevant because it has no inscriptions on patterned surfaces. No document  speaks about it."  The article continues telling that, in fact,  there are 27 theories about its use, ranging from a game for divination to surveying or military purposes. Scholars gave up probably until some new finds: however, some amateur archaeologists, among them Sjra Wagemans, continue to study this mystery, that is "what was it used for?"
Cinzia di Cianni tells that the first description of the geometrical volume of this object is in the "Timaeus" by Plato. It is a solid as the tetrahedron, octahedron, cube and icosahedron, that is, one of the five Platonic solids. Before Plato, it was also described in the fifth century BC by the Pythagorean Hippasus of Metaponto. "Harmony of proportions and mathematical properties, has continued to captivate artists and scientists, from Euclid to Poincare, from Leonardo to Luca Pacioli, to Escher. So, during several centuries, the dodecahedron had accumulated magic and symbolic features, from Greeks to Celts, from Renaissance to modern times." Di Cianni continues reporting the interest on dodecahedra by  Francesco Maurolico, a Greek mathematician and astronomer of Sicily, who lived in the XVI century, and the contemporary astronomer Jean-Pierre Luminet, who works with data provided by the scientific probe "WMAP" (Wilkinson Microwave Anisotropy Probe), used to observe the cosmic background radiation in the microwave range.
For what concerns the Roman dodecahedra the article tells that all of them, collected in several European museums, always came from Gaul and the lands of the Celts: Great Britain, Belgium, Holland, Germany, Switzerland, Austria and Eastern Europe. A defined scholar theory about their use is still lacking. Recently Sjra Wagemans, of the Dutch multinational DSM Research and amateur  archeology, proposed a theory which assigns an astronomical feature to these objects. Sjra used a bronze copy of a dodecahedron to see that it is possbile to determine the equinoxes of spring and autumn. "The dodecahedron is therefore linked to the agricultural cycle, both sophisticated and simple at the same time, to determine  without a calendar, the most suitable period of time during the autumn for sowing wheat."  And crops were of vital importance for the Roman legions. At the site www.romandodecahedron.com, Wagemans introduced the research and waiting for comments.

Courtesy: DieBuche, Wikipedia

I like very much the discussion by Cinzia di Cianni about this mistery of archaeology.
For what concerns the measurement of time, we know that Romans used gnomons (the Vitruvian equinoxial gnomons) to determine the latitude and that they had very good meridians. In fact, Vitruvius deeply describes in his De Archtectura, how to prepare the analemma. See my Measuring times to determine positionshttp://arxiv.org/abs/1202.2746
It is possible that the dodecahedron was used to determine more precisely the time during the equinoctial period. According to Cinzia, there are  many proposal for their use.
In my opinion it is necessary to study how they can move, since they are biased structures, in order to understand whether they could have been used as dice for divination or bowls for simply playing with them. In a static use of them, the hypothesis for measuring time is quite interesting.
However there is the possibility to use it to measure distances as in the following approach:


Monday, April 23, 2012

Phonons and Auxetics

About me.
One of my researches is on dispersions of phonons.
Quite interesting are the new auxetic materials, providind phononic band-gaps

2011 SPARAVIGNA A.C., Vibrations of a One-Dimensional Host-Guest System, MATERIALS SCIENCES AND APPLICATIONS, Scientific Research, pp. 5, 2011, Vol. 2, pagine da 314 a 318, ISSN: 2153-117X, DOI:10.4236/msa.2011.25041

2007 SPARAVIGNA A., Phonons in conventional and auxetic honeycomb lattices, PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS, APS, pp. 6, 2007, Vol. 76, ISSN: 1098-0121, DOI: 10.1103/PhysRevB.76.134302

2007 SPARAVIGNA A., Phonons dispersions in auxetic lattices, JOURNAL OF PHYSICS. CONFERENCE SERIES, 2007, Vol. 92, pagine da 012100-1 a 012100-4, ISSN: 1742-6596, DOI: 10.1088/1742-6596/92/1/012100

2007 SPARAVIGNA A.C., Phonons in lattices with rod-like particlesarXiv:0706.4076, 2007

2007 SPARAVIGNA A.C., Phonons in honeycomb and auxetic two-dimensional lattices arXiv:cond-mat/0703257, 2007

Sunday, April 22, 2012

Ale's stone boat

Ale's Stones (or Ales stenar) is a megalithic monument in Kaseberga,  southern Sweden. It is a boat of stones,  67 meters long formed. There are 59  boulders of sandstone,  up to 1.8 tonnes each. According to the local  lores,  King Ale lies buried there.
http://en.wikipedia.org/wiki/Ale's_Stones