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The First Simple Symmetric 11-Venn Diagram found
- akent 14y agoAre there any practical uses for this?
- jaredhansen 14y agoYes, in the way that there are practical uses for a fair amount of mathematics in general: http://mathoverflow.net/questions/10334/what-practical-applications-does-set-theory-have http://mathoverflow.net/questions/10334/what-practical-appli...
- knowtheory 14y agoSure, there are both interesting and practical uses of mathematics. However, venn diagrams are not synonymous with set theory. Venn diagrams are a type of visualization, and once you're dealing with 11 overlapping sets... I don't really see the utility, since these are not human friendly and don't help viewers understand the relationship between sets and their intersections.
- Pinckney 14y agoThis isn't set theory. (Venn diagrams can be interpreted in a set theoretic way, but this isn't particularly useful within set theory itself, and the symmetric and simple properties of the Venn diagram are unnecessary for this interpretation. We've had a construction for a simple Venn diagram of n curves since Venn's original paper -- it's the symmetry that's new.)
- aik 14y agoThere are practical uses for much math but in very many cases it's only practical in extremely specialized fields/cases. Meaning, in most cases very impractical if speaking strictly in terms of practicalities. Yet, it's widely taught, widely misunderstood, and so widely hated. The idea has become humorous to me -- math, a natural pervasive wonder of our universe, hated by many. Very impressive feat. On this topic this book is great: A Mathematician's Lament by Paul Lockhart. It opened my eyes to the concept of viewing much of math not in terms of something strictly practical, but rather in broader terms, ie. natural art and beauty with very practical applications mixed in here and there. Just as one person enjoys painting, another enjoys dabbling in mathematics taking pleasure from the elegance.
- ordinary 14y agoThe essay that preceded the book is also food for thought. It's freely available online: http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf
- Foy 14y agoWhen I think of practical uses for a venn diagram I think of writing labels in each distinct section... this doesn't seem very practical in that regard. What would be really cool (and practical) is if all the different segments / sections were of relatively similar sizes. Anyone know if there's a way to draw that? The examples shown in the article have really large areas and really small areas... EDIT: It seems venn diagrams lose their "functionality" after 5 sets. After that they are far too complicated.
- megrimlock 14y agoWe have a print-out of an N-set Venn diagram on the wall which we use to illustrate the peril of having too many features with subtle interactions. It resonates because many of us have worked on areas of the code preceded by comments indicating which subset of interacting features you need to keep in mind. There's at least 7 such features, so it's not a small space. We've been desperately struggling to make these features more orthogonal and having a succinct diagram of the problem (read: "enemy") has helped us stay motivated.
- lwat 14y agowat
- walrus 14y agomegrimlock has a poster of a Venn diagram on the wall. The intersections in the diagram represent interdependencies between different parts of a piece of software (in object-oriented programming terms: places where encapsulation is broken). The Venn diagram is there to motivate the removal of those interdependencies.
- ktizo 14y agoWell, some of them are quite pretty and would look good on the wall.
- bung 14y agoCame for this, also the 1/11th would be nice on a t-shirt or something too.
- walrus 14y agoProbably not, but that's not really the point. People do this this kind of math because it's fun.
- nuclear_eclipse 14y agoThat doesn't look very "simple".
- deleted 14y ago[deleted]
- Pinckney 14y ago"A simple Venn diagram is one in which no more than two curves intersect at a common point." http://www.combinatorics.org/files/Surveys/ds5/VennWhatEJC.html http://www.combinatorics.org/files/Surveys/ds5/VennWhatEJC.h...
- Jach 14y agohttp://www.infoq.com/presentations/Simple-Made-Easy http://www.infoq.com/presentations/Simple-Made-Easy
- showerst 14y agoIf you were to 'color' these like a four color map problem, are they all trivially colorable with just two colors? It looks that way from the pictures, but I lack the math intuition to prove it.
- shasta 14y agoYes, the intersection of a number of curves defining regions is color-able with two colors: any point covered by an odd number of regions is black and any point covered by an even number of regions is white (i.e. a checkerboard pattern). Works as long as the boundary intersections are transverse. The proof is simply that if you cross a boundary, you must be decreasing or increasing the region count by one, changing the parity.
- jgeralnik 14y agoEach color is touched by at most one color on top and one color on bottom. Looking at the original 7-Venn we get Red->Orange->Yellow->Green->Blue->Purple. Change the odd colors to white and the even colors to black and you're done.