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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.