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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.
The center lens of the 2-circle figure is called a vesica piscis, from Euclid. Two circles are also called Villarceau circles as a plane intersection of a torus. The areas inside one circle and outside the other circle is called a lune. The 3-circle figure resembles a depiction of Borromean rings and is used in 3-set theory Venn diagrams.
The intersections of any two circles represents the mutual information for the two associated variables (e.g. I ( x ; z ) {\displaystyle I(x;z)} is yellow and gray). The union of any two circles is the joint entropy for the two associated variables (e.g. H ( x , y ) {\displaystyle H(x,y)} is everything but green).
Venn diagrams are a more restrictive form of Euler diagrams. A Venn diagram must contain all 2 n logically possible zones of overlap between its n curves, representing all combinations of inclusion/exclusion of its constituent sets. Regions not part of the set are indicated by coloring them black, in contrast to Euler diagrams, where membership ...
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 ...
Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry was split into two new subfields: synthetic geometry, which uses purely geometrical methods, and analytic geometry, which uses coordinates systemically. [23] Analytic geometry allows the study of curves unrelated to circles and lines.
At such points the second derivative of curvature will be zero. Ccircles which have two-point contact with two points S(t 1), S(t 2) on a curve are bi-tangent circles. The centers of all bi-tangent circles form the symmetry set. The medial axis is a subset of the symmetry set.
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.