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The commonly-used diagram for the Borromean rings consists of three equal circles centered at the points of an equilateral triangle, close enough together that their interiors have a common intersection (such as in a Venn diagram or the three circles used to define the Reuleaux triangle).
Expanding sets have 1, 7, 19, 37, 61, 91, 127, etc. circles, and continuing ever larger hexagonal rings of circles. The number of circles is n 3-(n-1) 3 =3n 2-3n+1=3n(n-1)+1. These overlapping circles can also be seen as a projection of an n-unit cube of spheres in 3-dimensional space, viewed on the diagonal axis. There are more spheres than ...
A Venn diagram, also called a set diagram or logic diagram, shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set.
To convert this diagram to the one we're talking about, just increase the diameter of each circle by a factor of 2/√3 (or about 1.155; that is, make each circle about 15.5% wider) so that they overlap enough to fill the gaps. This diagram shows how three of the circles overlap. If you continued the pattern, the overlaps would form a hexagonal ...
An Euler diagram (/ ˈ ɔɪ l ər /, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramming technique, Venn diagrams. Unlike Venn diagrams, which show all possible relations between ...
Parts of these same circles are used to form the triquetra, a figure of three overlapping semicircles (each two of which form a vesica piscis symbol) that again has a Reuleaux triangle at its center; [76] just as the three circles of the Venn diagram may be interlaced to form the Borromean rings, the three circular arcs of the triquetra may be ...
A Venn diagram is a representation of mathematical sets: a mathematical diagram representing sets as circles, with their relationships to each other expressed through their overlapping positions, so that all possible relationships between the sets are shown. [4]
The three circles model - Raz 2002. The diagram presents a partial overlapping between the three circles. One must keep in mind, the relations among the circles are dynamic and their borders depend on the situation being studied. The model is not an area model and doesn't intend to describe certain numeric relations.