### Matematyczne uzasadnienie operacji wyznaczania osi fałdu z diagramu foliacji

#### Abstract

MATHEMATICAL MOTIVE FOR DETERMINING FOLD AXIS FROM FOLIATION DIAGRAM

Summary

There are two equivalent methods of determining food axis on the basis of foliation measurements, given by B. Sander (1948). 1. On a spherical projection we mark poles of planes tangential to foliation, i.e. planes the orientation of which is given by the results of measurement. The poles tend to group at a large circle, making a belt. The axis of the belt (π) determines the fold axis (Fig. 2). 2. On a spherical projection we mark planes tangential to foliation in the form of an arc. The arcs tend to intersect at one point (β). This point determines the fold axis (Fig. 1). These methods have been developed on an empirical way. They may be motivated mathematically, when we go out of an equation of cylinder plane, to which the actual foliation planes of a properly formed cylindrical fold approach. To the equivalent methods of determining food axis on the basis of foliation measurements given by B. Sander correspond two equivalent interpretations of mixed product deduced on the basis of general equation of cylinder plane.

Summary

There are two equivalent methods of determining food axis on the basis of foliation measurements, given by B. Sander (1948). 1. On a spherical projection we mark poles of planes tangential to foliation, i.e. planes the orientation of which is given by the results of measurement. The poles tend to group at a large circle, making a belt. The axis of the belt (π) determines the fold axis (Fig. 2). 2. On a spherical projection we mark planes tangential to foliation in the form of an arc. The arcs tend to intersect at one point (β). This point determines the fold axis (Fig. 1). These methods have been developed on an empirical way. They may be motivated mathematically, when we go out of an equation of cylinder plane, to which the actual foliation planes of a properly formed cylindrical fold approach. To the equivalent methods of determining food axis on the basis of foliation measurements given by B. Sander correspond two equivalent interpretations of mixed product deduced on the basis of general equation of cylinder plane.