Historically Speaking,—: Venn diagrams

1963 ◽  
Vol 56 (2) ◽  
pp. 98-101
Author(s):  
Sister M. Stephanie
Keyword(s):  
Symbolic Representation ◽  
Closed Curve ◽  
Venn Diagram ◽  
Venn Diagrams ◽  
Mathematics Text

Hardly a mathematics text appears today without its quota of Venn diagrams, those ubiquitous, interlaced circles—plain, labeled, shaded, cross-hatched, and even colored. When did they originate and where, and who was John Venn? E. J. McShane defines a Venn diagram as a “symbolic representation of a set, obtained by letting the parts of the plane represent the objects under consideration, and letting each set be represented by the points inside of some closed curve.”1*

Sets and Venn diagrams.

2021 ◽  
pp. 85-94
Author(s):  
Donald Quicke ◽  
Buntika A. Butcher ◽  
Rachel Kruft Welton
Keyword(s):  
Venn Diagram ◽  
Venn Diagrams

Abstract This chapter focuses on sets and Venn diagrams. Venn diagrams, also known as set diagrams, are commonly used to represent the overlap between sets. However, there is no in-built Venn diagram function in R so packages are used.

Generalized Euler-Venn Diagrams for Fuzzy Sets

2020 ◽  
Vol 7 (4) ◽  
pp. 34-43
Author(s):  
Yu. Mironova
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Venn Diagram ◽  
Linguistic Variables ◽  
Venn Diagrams ◽  
Time Of Year ◽  
Special Case ◽  
Three Dimensional Space

The fuzzy set concept is often used in solution of problems in which the initial data is difficult or impossible to represent in the form of specific numbers or sets. Geo-information objects are distinguished by their uncertainty, their characteristics are often vague and have some error. Therefore, in the study of such objects is introduced the concept of "fuzziness" — fuzzy sets, fuzzy logic, linguistic variables, etc. The fuzzy set concept is given in the form of membership function. An ordinary set is a special case of a fuzzy one. If we consider a fuzzy object on the map, for example, a lake that changes its shape depending on the time of year, we can build up for it a characteristic function from two variables (the object’s points coordinates) and put a certain number in accordance with each point of the object. That is, we can describe a fuzzy set using its two-dimensional graphical image. Thus, we obtain an approximate view of a surface z = μ(x, y) in three-dimensional space. Let us now draw planes parallel to the plane. We’ll obtain intersections of our surface with these planes at 0 ≤ z ≤ 1. Let's call them as isolines. By projecting these isolines on the OXY plane, we’ll obtain an image of our fuzzy set with an indication of intermediate values μ(x, y) linked to the set’s points coordinates. So we’ll construct generalized Euler — Venn diagrams which are a generalization of well-known Euler — Venn diagrams for ordinary sets. Let's consider representations of operations on fuzzy sets A a n d B. Th e y u s u a l l y t a k e : μA B = min (μA,μB ), μA B = max (μA,μB ), μA = 1 − μA. Algebraic operations on fuzzy sets are defined as follows: μ A B x μ A x μ B x ( ) = ( ) + ( ) − −μ A (x)μ B (x), μ A B x μ A x μ B x ( ) = ( ) ( ), μ A (x) = 1 − μ A (x). Let's construct for a particular problem a generalized Euler — Venn diagram corresponding to it, and solve subtasks graphically, using operations on fuzzy sets, operations of intersection and integrating of the diagram’s bars.

scholarly journals Venn Diagrams with Few Vertices

10.37236/1382 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
Bette Bultena ◽  
Frank Ruskey
Keyword(s):  
Lower Bound ◽  
Planar Graph ◽  
Connected Region ◽  
Venn Diagram ◽  
Closed Curves ◽  
Venn Diagrams ◽  
Intersection Points ◽  
Few Vertices

An $n$-Venn diagram is a collection of $n$ finitely-intersecting simple closed curves in the plane, such that each of the $2^n$ sets $X_1 \cap X_2 \cap \cdots \cap X_n$, where each $X_i$ is the open interior or exterior of the $i$-th curve, is a non-empty connected region. The weight of a region is the number of curves that contain it. A region of weight $k$ is a $k$-region. A monotone Venn diagram with $n$ curves has the property that every $k$-region, where $0 < k < n$, is adjacent to at least one $(k-1)$-region and at least one $(k+1)$-region. Monotone diagrams are precisely those that can be drawn with all curves convex. An $n$-Venn diagram can be interpreted as a planar graph in which the intersection points of the curves are the vertices. For general Venn diagrams, the number of vertices is at least $ \lceil {2^n-2 \over n-1} \rceil$. Examples are given that demonstrate that this bound can be attained for $1 < n \le 7$. We show that each monotone Venn diagram has at least ${n \choose {\lfloor n/2 \rfloor}}$ vertices, and that this lower bound can be attained for all $n > 1$.

scholarly journals ggVennDiagram: An Intuitive, Easy-to-Use, and Highly Customizable R Package to Generate Venn Diagram

2021 ◽  
Vol 12 ◽  
Author(s):  
Chun-Hui Gao ◽  
Guangchuang Yu ◽  
Peng Cai
Keyword(s):  
Open Source ◽  
Open Source Software ◽  
Source Code ◽  
R Package ◽  
Venn Diagram ◽  
Free Access ◽  
High Quality ◽  
Venn Diagrams ◽  
Label Edge ◽  
The Cost

Venn diagrams are widely used diagrams to show the set relationships in biomedical studies. In this study, we developed ggVennDiagram, an R package that could automatically generate high-quality Venn diagrams with two to seven sets. The ggVennDiagram is built based on ggplot2, and it integrates the advantages of existing packages, such as venn, RVenn, VennDiagram, and sf. Satisfactory results can be obtained with minimal configurations. Furthermore, we designed comprehensive objects to store the entire data of the Venn diagram, which allowed free access to both intersection values and Venn plot sub-elements, such as set label/edge and region label/filling. Therefore, high customization of every Venn plot sub-element can be fulfilled without increasing the cost of learning when the user is familiar with ggplot2 methods. To date, ggVennDiagram has been cited in more than 10 publications, and its source code repository has been starred by more than 140 GitHub users, suggesting a great potential in applications. The package is an open-source software released under the GPL-3 license, and it is freely available through CRAN (https://cran.r-project.org/package=ggVennDiagram).

Situation-Theoretic Account of Valid Reasoning with Venn Diagrams

1996 ◽  
Author(s):  
Sun-Joo Shin
Keyword(s):  
Semantic Analysis ◽  
Formal System ◽  
Venn Diagram ◽  
Formal Proofs ◽  
Representation System ◽  
Venn Diagrams ◽  
Linguistic Representation ◽  
Deductive Systems ◽  
Representation Systems ◽  
Mathematical Tradition

Venn diagrams are widely used to solve problems in set theory and to test the validity of syllogisms in logic. Since elementary school we have been taught how to draw Venn diagrams for a problem, how to manipulate them, how to interpret the resulting diagrams, and so on. However, it is a fact that Venn diagrams are not considered valid proofs, but heuristic tools for finding valid formal proofs. This is just a reflection of a general prejudice against visualization which resides in the mathematical tradition. With this bias for linguistic representation systems, little attempt has been made to analyze any nonlinguistic representation system despite the fact that many forms of visualization are used to help our reasoning. The purpose of this chapter is to give a semantic analysis for a visual representation system—the Venn diagram representation system. We were mainly motivated to undertake this project by the discussion of multiple forms of representation presented in Chapter I More specifically, we will clarify the following passage in that chapter, by presenting Venn diagrams as a formal system of representations equipped with its own syntax and semantics:. . . As the preceding demonstration illustrated, Venn diagrams provide us with a formalism that consists of a standardized system of representations, together with rules of manipulating them. . . . We think it should be possible to give an informationtheoretic analysis of this system, . . . . In the following, the formal system of Venn diagrams is named VENN. The analysis of VENN will lead to interesting issues which have their ana logues in other deductive systems. An interesting point is that VENN, whose primitive objects are diagrammatic, not linguistic, casts these issues in a different light from linguistic representation systems. Accordingly, this VENN system helps us to realize what we take for granted in other more familiar deductive systems. Through comparison with symbolic logic, we hope the presentation of VENN contributes some support to the idea that valid reasoning should be thought of in terms of manipulation of information, not just in terms of manipulation of linguistic symbols.

Sets and Venn diagrams.

2021 ◽  
pp. 85-94
Author(s):  
Donald Quicke ◽  
Buntika A. Butcher ◽  
Rachel Kruft Welton
Keyword(s):  
Venn Diagram ◽  
Venn Diagrams

Abstract This chapter focuses on sets and Venn diagrams. Venn diagrams, also known as set diagrams, are commonly used to represent the overlap between sets. However, there is no in-built Venn diagram function in R so packages are used.

BioVenn – an R and Python package for the comparison and visualization of biological lists using area-proportional Venn diagrams

Data Science ◽  
2021 ◽  
pp. 1-11
Author(s):  
Tim Hulsen
Keyword(s):  
R Package ◽  
Venn Diagram ◽  
Data Sets ◽  
Web Interface ◽  
Web Browser ◽  
Venn Diagrams ◽  
File Formats ◽  
Source Data ◽  
Copy And Paste ◽  
Python Package

One of the most popular methods to visualize the overlap and differences between data sets is the Venn diagram. Venn diagrams are especially useful when they are ‘area-proportional’ i.e. the sizes of the circles and the overlaps correspond to the sizes of the data sets. In 2007, the BioVenn web interface was launched, which is being used by many researchers. However, this web implementation requires users to copy and paste (or upload) lists of IDs into the web browser, which is not always convenient and makes it difficult for researchers to create Venn diagrams ‘in batch’, or to automatically update the diagram when the source data changes. This is only possible by using software such as R or Python. This paper describes the BioVenn R and Python packages, which are very easy-to-use packages that can generate accurate area-proportional Venn diagrams of two or three circles directly from lists of (biological) IDs. The only required input is two or three lists of IDs. Optional parameters include the main title, the subtitle, the printing of absolute numbers or percentages within the diagram, colors and fonts. The function can show the diagram on the screen, or it can export the diagram in one of the supported file formats. The function also returns all thirteen lists. The BioVenn R package and Python package were created for biological IDs, but they can be used for other IDs as well. Finally, BioVenn can map Affymetrix and EntrezGene to Ensembl IDs. The BioVenn R package is available in the CRAN repository, and can be installed by running ‘install.packages(“BioVenn”)’. The BioVenn Python package is available in the PyPI repository, and can be installed by running ‘pip install BioVenn’. The BioVenn web interface remains available at https://www.biovenn.nl.

scholarly journals KONSEP HIMPUNAN DAN DIAGRAM VENN PADA SMP NEGERI 07 BENGKULU BERBASIS MULTIMEDIA

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Mahdarena Mahdarena ◽  
Siswanto Siswanto ◽  
Sapri Sapri
Keyword(s):  
High School ◽  
High School Students ◽  
Junior High School ◽  
Junior High ◽  
Lesson Plan ◽  
Venn Diagram ◽  
High School Mathematics ◽  
School Students ◽  
Venn Diagrams ◽  
Level Of Understanding

One of the competencies that must be mastered students currently studying mathematics in junior high school (SMP) and is listed in the RPP (lesson plan) made by the teacher of junior high school mathematics is able to complete the concept of sets and Venn diagrams. In the current study the concept of sets and Venn diagrams, mastery of competencies was very important because it will be the main prerequisite when students learn the concept of sets and Venn diagrams on the next steps. Difficulties faced by teachers of mathematics and junior high school students in the form of low level of understanding of the students about the concepts related to the concept of sets and Venn diagrams and low skills in mennyelesaikan concept of sets and Venn diagrams. With such a reality, the use of instructional media using Macromedia Flash is one of supporting the achievement of an effective learning objectives and easy to understand The concept of Association and Venn Diagram multimedia applications on SMP 07 Bengkulu generated based Multimedia can provide convenience to the teachers of secondary school (SMP) 07 State of Bengkulu in providing the subject matter of the concept of Association and Venn Diagrams in SMP Negeri 07 Bengkulu based Multimedia.Keywords: Macromedia Flash, Concepts Association and the Venn Diagram, SMP 07 Bengkulu based Multimedia

scholarly journals Half-Simple Symmetric Venn Diagrams

10.37236/1839 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Charles E. Killian ◽  
Frank Ruskey ◽  
Carla D. Savage ◽  
Mark Weston
Keyword(s):  
Prime Number ◽  
Research Paper ◽  
Venn Diagram ◽  
Venn Diagrams ◽  
Rotationally Symmetric ◽  
Intersection Points

A Venn diagram is simple if at most two curves intersect at any given point. A recent paper of Griggs, Killian, and Savage [Elec. J. Combinatorics, Research Paper 2, 2004] shows how to construct rotationally symmetric Venn diagrams for any prime number of curves. However, the resulting diagrams contain only ${n \choose {\lfloor n/2 \rfloor}}$ intersection points, whereas a simple Venn diagram contains $2^n-2$ intersection points. We show how to modify their construction to give symmetric Venn diagrams with asymptotically at least $2^{n-1}$ intersection points, whence the name "half-simple."

scholarly journals Spherical Venn Diagrams with Involutory Isometries

10.37236/678 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Frank Ruskey ◽  
Mark Weston
Keyword(s):  
Boolean Lattice ◽  
Venn Diagram ◽  
Antipodal Point ◽  
Chain Decomposition ◽  
Venn Diagrams ◽  
Reflective Symmetry

In this paper we give a construction, for any $n$, of an $n$-Venn diagram on the sphere that has antipodal symmetry; that is, the diagram is fixed by the map that takes a point on the sphere to the corresponding antipodal point. Thus, along with certain diagrams due to Anthony Edwards which can be drawn with rotational and reflective symmetry, for any isometry of the sphere that is an involution, there exists an $n$-Venn diagram on the sphere invariant under that involution. Our construction uses a recursively defined chain decomposition of the Boolean lattice.

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