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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 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).
The first step is to mark two arbitrary points of the plane (which will eventually become vertices of the triangle), and use the compass to draw a circle centered at one of the marked points, through the other marked point. Next, one draws a second circle, of the same radius, centered at the other marked point and passing through the first ...
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]
An order-n Venn diagram, for instance, may be viewed as a subdivision drawing of a hypergraph with n hyperedges (the curves defining the diagram) and 2 n − 1 vertices (represented by the regions into which these curves subdivide the plane).
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 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.
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.