In this paper a novel general methodology is introduced for the computer-aided reconstruction of the magnificent wall-paintings of the Greek island Thera (Santorini), painted in the middle of the second millennium BC. These wall-paintings are excavated in fragments and, as a result, their reconstruction is a painstaking and a time-consuming process. Therefore, in order to facilitate and speed up this process a proper system has been developed based on the introduced methodology. According to this methodology each fragment is photographed, its picture is introduced to the computer, its contour is obtained and subsequently all fragments contours are compared in a manner proposed herein. Both the system and the methodology presented here, extract the maximum possible information from the contour shape of fragments of an arbitrary initially unbroken plane object, to point out possible fragments matching. This methodology has been applied to two excavated fragmented wall-paintings consisting of 262 fragments, with full success but most important it has been used to reconstruct, for the first time, unpublished wall-paintings parts from a set of 936 fragments. 2 A. INTRODUCTION-PROBLEM DESCRIPTIONThe discovery of the wall-paintings at Akrotiri of the Greek island Thera (Santorini), is of outstanding importance for human knowledge of the early Aegean world and not only. According to prominent archaeologists these wall-paintings rank alongside the greatest archaeological discoveries.The late professor Marinatos originated the excavations, which are now successfully continued by Professor Christos Doumas. As with the treasures of Pompeii and Herculaneum, the wall-paintings of Thera were preserved due to the seal of the pumice from the great eruption of a volcano [1]. As a rule, the walls decorated with paintings no longer survive. They collapsed together with their painted coat before the volcanic eruption, due to particularly strong earthquakes. Thus, a single painting is usually scattered into many fragments mixed with the fragments of other wall-paintings, too. The restoration of the wall-paintings from the fragments is a very painstaking and time consuming process frequently demanding many months or even years of dedicated, experienced personnel work for a single wallpainting restoration. Therefore, the development of a system that will contribute to the automatic restoration of these wall-paintings is of fundamental importance for this archaeological research, but for many others too, which face the problem of an image reconstruction from excavated fragments.Each excavated wall-painting fragment after being cleaned, is being photographed with a very strict protocol, so that very similar illumination conditions, a fixed distance of the fragment plane from the camera focus and minimal photo distortion are ensured. Subsequently, the obtained image is processed and eventually each photographed fragment is embedded into a white background frame, which we call the absolute frame of reference of the specific fragmen...

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This paper investigates the role of tools in the formation of mathematical practices and the construction of mathematical meanings in the setting of a telecommunication organization through the actions undertaken by a group of technicians in their working activity. The theoretical and analytical framework is guided by the first-generation activity theory model and Leont'ev's work on the three-tiered explanation of activity. Having conducted a 1-year ethnographic research study, we identified, classified, and correlated the tools that mediated the technicians' activity, and we studied the mathematical meanings that emerged. A systemic network was generated, presenting the categories of tools such as mathematical (communicative, processes, and concepts) and non-mathematical (physical and written texts). This classification was grounded on data from three central actions of the technicians' activity, while the constant interrelation and association of these tools during the working process addressed the mathematical practices and supported the construction of mathematical meanings that this group developed from the researchers' perspective. Technicians' emerging mathematical meanings referred to place value, spatial, and algebraic relations and were expressed through personal algorithms and metaphorical and metonymic reasoning. Finally, the educational implications of the findings are discussed.

In this paper, an original general methodology is introduced to establish whether a handmade shape corresponds to a given geometrical prototype. Using this methodology, one can decide if an artist had the intention of drawing a specific mathematical prototype or not. This analysis is applied to the 1650 B.C. wall paintings from the prehistoric settlement on Thera, and inferences of great archaeological and historical importance are made. In particular, strong evidence is obtained suggesting that the spirals depicted on the wall paintings correspond to linear (Archimedes) spirals, certain shapes correspond to canonical 48-gon and 32-gon, while other shapes correspond to parts of ellipses. It seems that the presented wall paintings constitute the earliest archaeological findings on which these geometrical patterns appear with such remarkable accuracy.

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