Contribution to Research of Mathematical Properties of Pre-Christian Slavic Sacred Landscape Structures

Considerable amount of interpreted data indicates that the ancient Slavs positioned their sacred sites in a way which refers to characteristic Sun angles. The article addresses the question whether distances among such sites are based on a common unit of length. In particular, this article tackles that question applying the mathematical formalism on the following two assumptions: (i) the absolute value of a distance between sacred sites was significant to the pre-Christian Slavic priests, along with the angles between lines connecting pairs of sites; (ii) the distances were prevalently measured utilising the projections of isosceles right triangle on the horizontal plane, with the exceptions of flat grounds for which the distances were measured by walk. That assumption follows from the frequent occurrence of ratio 1:√2 in the analysed sacred sites. Based on the two stated assumptions the attempts are done to find the best possible length modules by using the probability distribution method of arithmetic sequences. The main property of length modules which are the least probable to appear by mere chance is that they account for as many as possible of distances from the analysed set of distances. The stated method is applied on numerous sacred systems described in literature. The result is that several common modules are extracted. The modules are subsequently correlated with the modules extracted in my recent article using the novel method which extracts the optimal common sub-module. Value of the length module thereby obtained is 30,9 m. It has 60 sub-units 0,515 m long (a cubit) and 100 sub-units 0.309 m long (a foot). Multiples of 100 or 365 sub-units, respectively, are regularly encountered in the analysed set of sacred sites in the form of sub-harmonics of the observed distances. One may argue that results of the analysis of the distances contributed to the fact that the ancient Slavs were giving a lot of attention to a solar calendar and accurate determination of the time of a year