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Topic: Euler Diagrams

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Venn diagram

Dynkin diagram

commutative diagram

Hertzsprung Russell diagram

Feynman diagram

Cathedral diagram

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state diagram

Hasse diagram

bifurcation diagram

Lineweaver Burke diagram

Johnston diagram

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	Euler Diagrams and Quantified Expressions
		Euler diagrams, inaccurately referred to as Venn diagrams in your text, were an informal way to convey the ideas that are involved in what was subsequently known as quantification.
		Your text provides two alternative Euler diagrams for the statement "All A are B," and claims that this indicates that the statement is ambiguous.
		The two alternative Euler diagrams provided in your text for this universally quantified are shown in the figure to the right.
	www.rci.rutgers.edu /~cfs/305_html/Deduction/EulerDiags.html (942 words)

	Venn diagram - Wikipedia, the free encyclopedia
		Euler diagrams are similar, but do not need to show all the relations; in common usage, this distinction is often ignored.
		Euler diagrams are similar to Venn Diagrams, but do not need all the possible relations.
		Johnston diagrams are used to illustrate statements in propositional logic such as Neither A nor B is true and are a visual way of illustrating truth tables.
	en.wikipedia.org /wiki/Venn_diagram (954 words)

	Euler diagram - Wikipedia, the free encyclopedia
		An Euler diagram is similar to a Venn diagram, but does not have to contain all zones (where a zone is defined as the area of intersection of two or more sets).
		An Euler diagram can be structured so that these nonsensical intersections do not exist, thus defining a universe of discourse for this subject.
		A modern extension to Euler diagrams, is the spider diagram, whereby existential points are added to the diagram, which can be linked.
	en.wikipedia.org /wiki/Euler_diagram (231 words)

	Diagrams (Stanford Encyclopedia of Philosophy)
		Diagrams are usually adopted as a heuristic tool in exploring a proof, but not as part of a proof.
		The weak point in this [Euler diagrams], and in all similar schemes, consists in the fact that they only illustrate in strictness the actual relation of classes to each other, rather than the imperfect knowledge of these relations which we may possess, or may wish to convey by means of the proposition.
		Logical reasoning with diagrams is often carried out in virtue of their depiction of all possible models of a situation, up to topological equivalence of the diagrams (this, of course, depends on the particular diagrammatic system in use).
	plato.stanford.edu /entries/diagrams (7995 words)

	Venn diagram
		Venn diagrams, Euler diagrams (pronounced "oiler") and Johnston diagrams are similar-looking illustrations of set, mathematical or logical relationships.
		Functionally, Venn, Johnston, and Euler diagrams are identical, though some sources argue for their distinctness in original purpose.
		It is likely that the Venn and Euler versions have not been "merged" because Euler's version came 100 years earlier, and Euler has credit for enough accomplishment already, whereas John Venn has nothing left to his name but the diagram.
	www.ebroadcast.com.au /lookup/encyclopedia/ve/Venn.html (157 words)

	A Survey of Venn Diagrams: Generalizations and Extensions
		We have already seen on the "What is Venn Diagram?" page that Venn diagrams are instances of independent families, and in [Gr99], Grünbaum generalized the concept of symmetry in Venn diagrams to independent families.
		Symmetric near-Venn diagrams for non-prime n are maximally symmetric Euler diagrams in the sense that they cannot have any more regions added without either losing their symmetry or repeating regions.
		A near-Venn diagram of 6 curves, drawn to be near-simple.
	sue.csc.uvic.ca /~cos/venn/VennOtherEJC.html (1455 words)

	Diagrams
		This type of result directly refuted a widely-held assumption that diagrams are inherently misleading, and abolished theoretical objections to diagrams being used in proofs [Shin 1994, Hammer 1995].
		Euler claims that the proposition ‘Some C is not B’ can be read off from all these diagrams.
		In the case of Shin's diagram, Venn's shading convention for emptiness, as opposed to Peirce's ‘o’, much more naturally leads the reader to the inference “Some C is not B” than in the case of Peirce's diagram.
	www.science.uva.nl /~seop/archives/fall2002/entries/diagrams (7695 words)

	Euler Diagrams Overview
		The original application of Euler diagrams, as a way of diagrammatically demonstrating logic, is widely used in schools, where they are a great aid to teaching set theory.
		These enhanced Euler diagrams can be seen as hypergraphs, and as such, it should be possible to apply visualization techniques for enhanced Euler diagrams more generally to applications that use hypergraphs.
		If diagrams like those on the left were used, then two items that were intended to be grouped together could appear in different sections of the diagram, even though the semantics of the diagram would be correct.
	www.cs.kent.ac.uk /events/conf/2004/euler/eulerdiagrams.html (1192 words)

	Find diagrams using our Local directory (Site not responding. Last check: 2007-10-31)
		For diagrams our search results bring you accurate and dedicated results from across the UK and from thousands of websites offering information based on your search for diagrams.
		Diagrams targets topics that provide insight into the nature and use of diagrams, including: novel representations that support multiple tasks in substantial domains.
		Diagrams 2000 is an international conference on the \ theory and application of diagrams, which will take place in \ Edinburgh in September 2000.
	www.lifestylelocal.co.uk /search.htm?qLookingFor=diagrams&page=2 (292 words)

	A Survey of Venn Diagrams: Generalizations and Extensions
		We have already seen on the "What is Venn Diagram?" page that Venn diagrams are instances of independent families, and in [Gr99], Grünbaum generalized the concept of symmetry in Venn diagrams to independent families.
		A near-Venn diagram of 6 curves, drawn to be near-simple.
		Since Venn's time, his diagrams have since been extended to Venn-Pierce diagrams, which add extra information in the form of symbols inside the regions to enable them to be used as valid logical proof mechanisms.
	www.combinatorics.org /Surveys/ds5/VennOtherEJC.html (1455 words)

	A Survey of Venn Diagrams: What is a Venn Diagram?
		Simple diagrams are in some sense the "nicest" as they are easiest to draw and understand.
		Readers interested in the applications of Venn diagrams to logical arguments are referred to the excellent introductory article by Glassner [Gl], the book by Shin [Sh], and many standard logic textbooks.
		Diagrams exist for all larger values of n as well; there have been several general constructions published (see [Be], [RRS], [Mo], [AC], and [FGK], for a sampling in chronological order); we explain two of them below.
	sue.csc.uvic.ca /venn/VennWhatEJC.html (902 words)

	Survey of Venn Diagrams -- Euler Diagrams
		In other words, an Euler diagram is like a Venn diagram except that intersections of curve interiors are allowed to be empty.
		Euler wrote four letters in February of 1761 which contain Euler diagrams as defined above (from the Brewster translation) [Eu].
		Euler always drew his diagrams as collections of circles, but remarks in Letter CIII, These circles, or rather these spaces, for it is of no importance of what figure they are of,...
	www.theory.csc.uvic.ca /~cos/venn/VennEulerEJC.html (373 words)

	Diagrams 2006 - Short Paper Program
		We created a sun-ray-like diagram where all the independent variables are on the right side of the circle, and all the dependent variables are on the left -- a heliograph.
		In contrast to the visuospatial properties of traditional static diagrams, the temporal properties of the newly emerging phenomenon of animated diagrams tend to closely reflect attributes of the referent subject matter.
		This paper explores possibilities for extending this tradition of manipulation to the temporal properties of animated diagrams as a way of improving their educational effectiveness, particularly when complex dynamic subject matter is represented.
	www.diagrams-conference.org /short-papers (1440 words)

	Diagrams02: Abstract for Paper 30 (Site not responding. Last check: 2007-10-31)
		Euler diagrams use topological properties to represent set-theoretical concepts and thus are "intuitive" to some people.
		When reasoning with Euler diagrams, it is essential to have a notion of correspondence among the regions in different diagrams.
		This task is interesting in Euler diagrams because some regions of one diagram may be missing from another.
	kogs-www.informatik.uni-hamburg.de /~d2k2/Abstracts/30.html (169 words)

	Venn Diagrams
		Carroll's trilateral diagrams and Euler circles, Venn diagrams are helpful in solving puzzles, and also for validation and derivation of syllogisms.
		Deservedly, Venn diagrams are taught to young children and their teachers while being recommended to their parents, too.
		When used without a proper definition, Venn diagrams are often confused with those of Euler that are more often referred to as Euler circles rather than Euler diagrams.
	www.cut-the-knot.org /LewisCarroll/VennDiagrams.shtml (459 words)

	Lewis Carroll's Logic Game
		If justice is to be served, we should call this an "Euler diagram." Of course, such a name change would add little to Euler's stupendous fame but would obliterate John Venn's reputation altogether.
		The diagrams referred to in the cut-the-knot reproduction are NOT Venn diagrams at all since they do not contain 2^n regions.
		Indeed, the diagram I included is not the full-blown 2^n Venn diagram, and perhaps I was overly harsh in my analysis of Mr.
	www.cut-the-knot.org /LewisCarroll/dunham.shtml (675 words)

	Elena Tulchinsky's M.Sc. research home page (Site not responding. Last check: 2007-10-31)
		Venn diagrams and Euler circles have long been used to express relationship among sets using visual metaphors such as disjointness and containment of topological contours.
		The topology of Venn diagrams of four contours or more is so cluttered that it becomes impractical to use it for visualization of set relationships.
		All Venn-Euler diagrams for the thesis were prepared using visual editor, named CD-Editor, developped as a part of Yan Sorkin thesis.
	www.cs.technion.ac.il /~ssdl/thesis/finished/2002/elena (376 words)

	Projections in Venn-Euler Diagrams - Gil, Howse, Kent, Taylor (ResearchIndex) (Site not responding. Last check: 2007-10-31)
		Abstract: Venn diagrams and Euler circles have long been used to express constraints on sets and their relationships with other sets.
		In order to reduce this clutter, and to focus attention within the diagram appropriately, the notion of a projected contour, or projection, is introduced.
		1 Venn Diagrams (context) - Grfinbaum - 1992
	citeseer.ist.psu.edu /511142.html (440 words)

	Diagrams, - Introduction to UML 2 Class Diagrams (Site not responding. Last check: 2007-10-31)
		Choose from the options on the left to see the diagrams that are available in each category.
		The aim of this workshop is to bring together researchers and users working with Euler diagrams.
		Venn diagrams are illustrations used in the branch of mathematics known as Johnston diagrams and Euler diagrams may be identical in appearance to Venn
	infofeedtech.com /ifft/diagrams.htm (388 words)

	Diagrams02: Abstract for Paper 12
		An automated generation mechanism for Euler diagrams forms the foundations of a generation algorithm for notations such as Harel's higraphs and constraint diagrams (which are based on Euler diagrams).
		An algorithm to generate diagrams is an essential component of a diagram tool for users to generate, edit and reason with diagrams.
		The work makes use of properties of the dual graph of an abstract diagram to identify which abstract diagrams are "undrawable" within given wellformedness rules on concrete diagrams.
	kogs-www.informatik.uni-hamburg.de /~d2k2/Abstracts/12.html (136 words)

	A Survey of Venn Diagrams
		The purpose of these pages is to collect together various facts and figures about Venn diagrams, particularly as they relate to combinatorial and geometric properties of the diagrams.
		There are some Venn diagrams on the pages to follow that have not appeared before in the literature, in particular, most of the symmetric Venn diagrams for n=7.
		All the Venn diagram figures to be found on the following pages, unless otherwise noted, are © the authors and are not to be used without written permission from the authors.
	www.combinatorics.org /Surveys/ds5/VennEJC.html (191 words)

	Information Models - Spatial Notations
		Carroll's bilateral diagrams/trilateral diagrams - visualize the possible combinations of, respectively, two or three Boolean variables.
		Bilateral diagram is Lewis Carroll's device to represent the situation in which objects are considered that may or may not have two properties.
		First used by Euler: «If justice is to be served, we should call [a Venn diagram] an "Euler diagram."» - History entries for Euler and Venn
	web.cs.mun.ca /~ulf/pld/spatial.html (176 words)

	CSUS Philosophy Department
		Change "its method of Venn diagrams can be used on" to "its method of Euler or Venn diagrams can be used successfully on many of" 7.
		Change "method of Venn diagrams:" to "method of Venn or Euler diagrams:" 8.
		Change "Using Venn Diagrams" to "Using Venn or Euler Diagrams" 9.
	www.csus.edu /indiv/d/dowdenb/4/changes.htm (1490 words)

	DrawEuler - An applet for creating area-proportional Euler diagrams
		You are permitted to run the applet for the purposes of testing, but may not use the diagrams for any purpose without written consent from the author.
		The Boolean lattice is decomposed into symmetric chains which are arranged radially to produce an Euler diagram.
		We are also happy to help with diagram requests, but do ask that, if your budget allows, you make a token contribution to our research.
	www.cs.uvic.ca /~schow/DrawEuler/instructions.html (807 words)

	Computer Science: Publication: Layout Metrics for Euler Diagrams
		Aesthetic layout metrics have been found to be useful in graph drawing algorithms, which use metrics motivated by aesthetic principles that aid user understanding of diagrams.
		We have taken a similar approach to Euler diagram drawing, and have defined a set of suitable metrics to be used within a hill climbing multicriteria optimiser to produce “good” drawings.
		There are added difficulties when drawing Euler diagrams as they are made up of contours whose structural properties of intersection and containment must be preserved under any layout improvements.
	www.cs.kent.ac.uk /pubs/2003/1652/index.html (195 words)

	Reasoning with diagrams - Welcome to RwD (Site not responding. Last check: 2007-10-31)
		Proceedings of Diagrams 2006, International Conference on the Theory and Application of Diagrams, Stanford, 267-282, June 2006.
		Proceedings of Diagrams 2006, International Conference on the Theory and Application of Diagrams, Stanford, 109-111, June 2006.
		Proceedings of Diagrams 2006, International Conference on the Theory and Application of Diagrams, Stanford, 148-150, June 2006.
	cmis.mis.brighton.ac.uk /Research/vmg/publications.htm (2057 words)

	RR-4973 : Ensuring the Drawability of Extended Euler Diagrams for up to 8 Sets
		These diagrams are adapted for representing sets inclusions and intersections: each set X_i and each non empty intersection of a subcollection of X_1,...,X_n is represented by a unique connected region of the plane.
		Starting with a description of the diagram, we define the dual graph G and reason with the properties of this graph to build a planar representation of the X_1,...,X_n.
		These diagrams will be used to visualize the results of a complex request on any indexed video database.
	www.inria.fr /rrrt/rr-4973.html (399 words)

	DMANET: [DMANET] CFP: Workshop on Euler Diagrams (Site not responding. Last check: 2007-10-31)
		A web search on Venn or Euler diagrams gives around 200000 results.
		diagrams research and to debate future research directions.
		We look forward to welcoming you to Paris for Euler diagrams 2005.
	mat.gsia.cmu.edu /DMANET/archive/2958.html (497 words)

	Math130F03 > Euler diagrams: Where Logic meets Set Theory (Site not responding. Last check: 2007-10-31)
		Use Euler diagrams to analyze each of the following arguments.
		No cloudy day is a good day to swim.
		Therefore all July days are good days to swim.
	www.yukoncollege.yk.ca /%7Ettopper/Math130/EulerQs.html (37 words)

	Diagrams (Site not responding. Last check: 2007-10-31)
		Scatter diagrams are used to study possible relationships between two variables.Although these diagrams cannot prove that one variable causes the other,.
		Phase diagrams provide a graphical means of presenting the results of experimental...
		As a matter of fact, Venn diagrams are used widely, even by professional.It seems to me that the differences between Venn and Euler diagrams are well.
	www.finebabies.com /diagrams.html (233 words)

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