Venn Diagrams as Cartographic Symbols

Abstract

The subject of this article is the graphic representation of data which are shown, in formal logic, by a Venn diagram. The linguistic censuses of Alsace are used as an example. With trivial exceptions, circles cannot show three non-mutually-exclusive sets of attributes of a population if the areas are to be proportional to the size of the respective segments of the population. Regular polygons are also very limited in the data they can represent. Many-sided polygons have relatively stringent constraints, and even squares are logically and practically difficult. Equilateral triangles are more useful figures. They too are limited, and not all possible sets of values can be represented correctly by overlapping triangles. However, the limitations are much less severe and the calculation of the relative positions of the three triangles is much easier than for other polygons.