Determination of the method of construction of 1650 B.C. wall paintings

In this paper, a methodology of general applicability is presented for answering the question if an artist used a number of archetypes to draw a painting or if he drew it freehand. In fact, the contour line parts of the drawn objects that potentially correspond to archetypes are initially spotted. Subsequently, the exact form of these archetypes and their appearance throughout the painting is determined. The method has been applied to celebrated Thera Late Bronze Age wall paintings with full success. It has been demonstrated that the artist or group of artists has used seven geometrical archetypes and seven corresponding well-constructed stencils (four hyperbolae, two ellipses, and one Archimedes' spiral) to draw the wall painting "Gathering of Crocus" in 1650 B.C. This method of drawing seems to be unique in the history of arts and of great importance for archaeology, and the history of mathematics and sciences, as well

[1]  Herbert Süße,et al.  Invariant Fitting of Planar Objects by Primitives , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Andrew W. Fitzgibbon,et al.  An Experimental Comparison of Range Image Segmentation Algorithms , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Phillip S. Jones,et al.  The historical roots of elementary mathematics , 1976 .

[4]  Teuvo Kohonen,et al.  Self-Organization and Associative Memory , 1988 .

[5]  C. Doumas The Wall Paintings of Thera , 1993 .

[6]  Daniel Keren,et al.  Fitting Curves and Surfaces With Constrained Implicit Polynomials , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Muhammad Sarfraz Fitting curve to planar digital data , 2002, Proceedings Sixth International Conference on Information Visualisation.

[8]  D. E. Smith,et al.  History of Mathematics , 1924, Nature.

[9]  Á. Szábó The Beginnings of Greek Mathematics , 1978 .

[10]  Michael Werman,et al.  Fitting a Second Degree Curve in the Presence of Error , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Daeryong Lee,et al.  Modified K-means algorithm for vector quantizer design , 1997, IEEE Signal Processing Letters.

[12]  Sir Thomas Heath,et al.  A History Of Greek Mathematics Volume II , 1921 .

[13]  Hans-Jürgen Warnecke,et al.  Orthogonal Distance Fitting of Implicit Curves and Surfaces , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Thomas L. Heath,et al.  A History of Greek Mathematics , 1923, The Classical Review.