Roman Dodecahedron
Image from Wikipedia
A discussion on the Roman Dodecahedron, by A.C. Sparavigna
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 was 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). This article 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. 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.
In fact, on 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. Vitruvius deeply describes in his De Archtectura, how to prepare the analemma (see for instance, Measuring times to determine positions, http://arxiv.org/abs/1202.2746).
The roman dodecahedron is not the best instrument for measuring time.
I have discussed its possible use for measuring distance. I used a dodecahedron, found at Jublains, the ancient Nouiodunum, dating from the 2nd or 3rd century AD, to create a model. Looking through the model, it is possible to test it for measurements of distance based on similar triangles. Therefore the Dodecahedron can be an ancient rangefinder for ballistics. It is simple to use. During the Middle Age, other instruments had been developed: probably, the use of the dodecahedron was lost after the collapse of the Roman Empire.
See my papers:
A Roman Dodecahedron for measuring distance, by Amelia Carolina Sparavigna, arXiv, 29 Apr 2012.
Here I am discussing a possible use of a Roman Dodecahedron, a bronze artifact of gallo-roman origin,
for measuring distance. A dodecahedron, found at Jublains, the ancient Nouiodunum, dating from the
2nd or 3rd century AD, is used to create a model. Looking through the model, it is possible to test it for
measurements of distance based on similar triangles. Comments: Ancient surveying methods
Subjects: Popular Physics (physics.pop-ph)
Cite as: arXiv:1204.6497v1 [physics.pop-ph]
http://arxiv.org/abs/1204.6497
Ancient and modern rangefinders, by Amelia Carolina Sparavigna, arXiv, 9 May 2012.
Rangefinders are instruments used for ballistics and for surveying in general.
Here a short discussion of some of them, ranging from the ancient Rome to the modern methods. Comments: Surveying
Subjects: Popular Physics (physics.pop-ph)
Cite as: arXiv:1205.2078v1 [physics.pop-ph]
Sui Dodecaedri Romani sono state proposte molte teorie: porta-candele (ma all'epoca si usavano le lucerne), dadi per la divinazione (ma questi oggetti hanno le facce con masse diverse e quindi cadono sempre sulla faccia più pesante), strumenti astronomici (per stabilire gli equinozi, ma gli antichi usavano le meridiane) e altro ancora. Purtroppo non è facile districarsi tra le varie teorie, anche perché spesso non si trovano gli articoli originali da studiare. Quello che appare chiaro è che questi dodecaedri di bronzo sono cavi, con facce che hanno buchi perfettamente circolari di diametri diversi. Cercando in rete ho trovato l'articolo di alcuni archeologi che descrivono con precisione un dodecaedro di bronzo, trovato a Jublains, l'antica Nouiodunum, del secondo o terzo secolo DC. Usando i dati sui diametri dei fori ho creato un modello di cartone. Guardando attraverso il modello ho capito che poteva essere uno strumento ottico per misurare la distanze e funzionare come un telemetro. Come molti telemetri, la misura si basa sui triangoli simili. I dettagli del dodecaedro come strumento telemetrico sono pubblicati in un articolo pubblicato su arXiv http://arxiv.org/abs/1204.6497 (In italiano http://porto.polito.it/2497004/ ). Il dodecaedro ha quattro differenti range di misura. I dodecaedri cavi, aventi struttura con buchi di diverso diametro, erano strumenti militari per determinare le distanze in balistica. Ed in effetti, questi oggetti sono stati trovati lontano dall'Italia, nei paesi che sono stati al confine dell'Impero. Ho scritto anche un confronto con strumenti medievali e moderni su arXiv,http://arxiv.org/abs/1205.2078
Il dodecaedro era uno strumento facile da usare. Per cambiare il range di distanza, bastava ruotare il dodecaedro. Se si guardano le foto dei dodecaedri, si vede che avevano delle piccole sferette ai vertici. Esse rendevano più facile la presa dello strumento nelle operazioni veloci.
Durante il Medioevo sono stati creati altri telemetri poiché l'uso del dodecaedro, che era uno strumento dell'esercito romano, si era perso col crollo dell'Impero. Questi oggetti medievali, conosciuti come "fore-staff", erano molto più ingombranti e con parti mobili da cambiare se cambiavano le distanze da valutare. Il dodecaedro romano è in fondo un comodo "telemetro a coincidenza". Gli archeologi che hanno trovato il dodecaedro a Jublains dicono che esso è un dado per la divinazione. I Romani, come gli Etruschi, avevano dei dadi dodecaedrici per il gioco o la divinazione, ma essi erano molto diversi. Si veda per esempio http://arxiv.org/abs/1205.0706 oppure la pagina di questo sito sul dodecaedro etrusco.
On Romam Dodecahedra many theories have been proposed: candlestick holders (but at that time people used oil lamps), dice for divination (these objects have faces of different masses and therefore they always fall on the heaviest face), astronomical instruments (to determine the equinoxes, but the ancients used sundials), and so on. Unfortunately it is not easy to dela with so many theories. What is clear is that these bronze dodecahedra are hollow, with faces that have perfectly circular holes of different diameters.
Searching the Web I found the article written by some archaeologists that accurately describe a dodecahedron made of bronze, found at Jublains, the ancient Nouiodunum, dated to the second or third century AD. Using the data on the diameters of the holes I made a cardboard model. Looking through the model I found it could be an optical instrument for measuring distances, being therefore a rangefinder. Like several rangefinders, the measure is based on similar triangles. The details of the dodecahedron as an instrument for telemetry are published in arXiv http://arxiv.org/abs/1204.6497 (In Italian http://porto.polito.it/2497004/). The dodecahedron has four different measuring ranges. The dodecahedra, having a structure with holes of different diameters, were military devices to determine distance for ballistics. And in fact, these objects have been found outside of Italy, at the border of Roman Empire. I also wrote a comparison with medieval and modern instruments, arXiv,http://arxiv.org/abs/1205.2078
The dodecahedron was easy to use. To change the range of distance, it was enough to turn the dodecahedron. If you look at pics of dodecahedra, you can see the small knobs. They made easier to grip the tool during quick operations.
During the Middle Ages, rangefinders have been created different from the dodecahedron, which was an instrument of the Roman army. Probably its use was lost with the collapse of the Empire. These medieval objects, known as "fore-staff," were bulkier and had the necessity to change and move some parts of it, for different ranges. The Roman dodecahedron is basically a "coincidence rangefinder." Archaeologists that have found the dodecahedron at Jublains say that it is a dice for divination. The Romans, like the Etruscans, had dodecahedra for the game of dice or divination, but they were quite different. See, for example http://arxiv.org/abs/1205.0706 or the page of this site on the Etruscan Dodecahedron.