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In this work, the method of drawing of nine celebrated Minoan Late Bronze Age wall-paintings, is studied. Four of these frescoes were unearthed at Akrotiri, Thera, while the other five were excavated in Crete; these frescoes have never been thoroughly studied before, concerning their method of drawing. The authors demonstrate that practically all actually drawn contours in these frescoes, optimally fit six geometric stencilsguides, namely, four hyperbolae and two Archimedes' (linear) spirals. It is important to note that the hyperbola and the linear spiral do not exist in nature, definitely not with the precision encountered here. We would like to stress that all wall-paintings the authors have studied so far, i.e. more than twenty-five (25), had been drawn via the use of the same stencils, a fact that renders the eventuality that this was indeed the method of drawing of these frescoes, almost certain. The considered wall-paintings cover a period of at least two centuries, located both before and after the gigantic eruption of Thera volcano. Moreover, here, possible methods of construction of the determined stencils are proposed, as well as the most probable one, according to our opinion. Methodologically, the authors determine couples of the longest contour parts, CP, appearing in the studied frescoes and of a proper sub-curve GPopt of one of the aforementioned stencils; these couples are chosen so as they fit with exceptionally low approximation errors. The latter terms are rigorously defined here, for the first time. Special care is taken, mathematically and programmatically, to ensure the maximum possible smoothness between successive optimally fit stencils' parts GPopt. Next, the authors employed these modern prerequisites, to introduce the more probable sequence of actions taken by the prehistoric artist(s) for drawing the specific frescoes. Finally, crucial queries and conjectures are set, together with a number of plausible answers. [ABSTRACT FROM AUTHOR]