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This paper studies a set of wall-paintings of the Late Bronze Age (c. 1650bc) initially decorating the internal walls of the third floor of the edifice called ‘Xeste 3’, excavated at Akrotiri, Thera, whose restoration is now in progress. It deals with the methods used for the drawing of the geometrical figures appearing in these wall-paintings. It is demonstrated that most of the depicted configurations correspond with accuracy to geometrical prototypes such as linear spirals and canonical polygons. It is pointed out that the steady lines of the figures, their remarkable repeatability, the precision of the geometrical shapes and their even distribution in the wall-paintings indicate a very distinctive use of the ‘Xeste 3’ third floor, which is now investigated. [ABSTRACT FROM AUTHOR]

The present paper offers strong evidence that there was a particularly advanced, for the era, sense and application of geometry in the prehistoric civilization of the island of Thera (Santorini), Greece, ca. 1650 BC. First, by applying an original method, it is demonstrated that specific shapes, depicted on so far unpublished wall paintings initially decorating the third floor of Xeste 3, correspond to advanced geometric configurations with remarkable accuracy. Thus, it is shown that there are configurations corresponding to linear spiral prototypes, others matching elliptical prototypes and sets of points lying on isogonal lines that are radii of regular polygons with 48, 32, and 24 angles. Subsequently, it is shown that the use of geometric archetypes for drawing played a prominent role in the Late Bronze Age Thera civilization. In fact, it is demonstrated that celebrated wall paintings have border lines that impressively match a limited number of linear (Archimedes’) spirals, hyperbolas, and ellipses in a piecewise manner. This practically excludes the probability that these wall paintings were drawn by freehand, while, on the contrary, it strongly suggests that they were mainly drawn by means of geometric stencils. [ABSTRACT FROM AUTHOR]

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.