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In this paper, the author analyzes the possibility of obtaining the orientation of geologic planes by using GPS tools. Theoretical background for such procedures is represented by an analytical model of finding the attitude by using three noncollinear points. During the experimental stage orientation measurements on synthetic planes were carried out by using GPS tools and geological compass. The output data obtained by GPS and compass was analyzed and compared by using stereographic projection. The measurement unc...

In this paper, the authors discussed one of the Hume-Rothery conditions for occurring substitutional solid solutions in the context of binary relations. The analyzed condition says that substitutional solid solutions may form if the ionic radius of the solute and solvent ions differ by no more than 15%. Because the problem concerns a mathematical connection between two objects, the authors suggested describing this problem using the set-theoretic notion of binary relation. In this context, the possibility of formi...