Jeszcze o interpretacji typogramu F. Uhorczaka jako narzędzia prezentacji i typologii zjawisk wielocechowych

W artykule przedstawiono propozycję matematycznej i numerycznej interpretacji kartotypogramów Franciszka Uhorczaka, uzupełniając ją nowymi możliwościami analitycznymi. Zaprezentowany algorytm metody oraz graficzne przedstawienie w postaci wykresu zbiorczego jest oryginalnym, autorskim opracowaniem.

F.Uhorczak's Typograms are used to present multicharacter phenomena. The typogram alone is used less and often. Structural graduated symbols and their modifications are used instead, ahereas the typology is most often presented using typical statistical tools, thanks to the readily available software packages. An important feature of a Typogram (which is almost intuitively understood even by a nonspecialists) is the fact that Typograms have the graphic form of an irregular polygon, each axis of which presents the share of each phenomenon in the whole feature. The proposed interpretation of the Uhorczak's Typograms and other cartotypograms does not alter their geometric construction. It should rather be understood as an attempt to formulate certain mathematical relations as well as an attempt to falsity certain opinions on this graph. A sum of consecutive vectors can be considered as a logical equivalent of a phenomenon presented with a Typogram. Therefore, the formula (1) can be considered as a mathematical formula for the structural Uhorczak's Typogram. Graphic representation of a set of (Carto-) Typograms can be presented as cumulative graphs in the form of regular polygons (equilateral triangle, square, regular pentagon). Each point on a graph represents a unique shape of a Typograms. The interpretation rule is as follows: the closer to the vertex the point is, the more regular the shape of the Typogram. The proposed name for the cumulative graph is the Vector Typogram (Werner 1997). This graph seems to be a valuable tool for representation of structural phenomena, and it would also allow to perform a numerical analysis, which is a good complement to the method of Uhorczak's Typograms.