Venn Diagrams : A Chart Geek's Favorites

I've heard of Multiple Personality Disorder. If there were such a thing, I'd have Multiple Geek Syndrome (MGS). In fact, I do have MGS, but I prefer to think of it as a feature rather than a bug.

I am many kinds of geek. Info Geek. Bike Geek. Airplane Geek. Map Geek. And: Chart Geek. I really love a good chart. Let's talk charts. One of the types of charts that I like, and that translate well to the general population (a euphemism for non-chart-geeks), are Venn Diagrams.

Charts are symbolic representations of the world. They can describe complex things without many words. Charts are awesome. Sometimes, part of the trick is understanding the implications of the chart design - what it implies, what it denies, etc.


One of my favorite charts types is Venn Diagrams. Venn diagrams are exhaustive in that they show all possible intersections of various sets. Because it is difficult to depict these intersections in two dimensions, Venn's own diagrams only described the relationships of up to four sets, which he used ellipses to depict. This report uses Venn's four-ellipse-set to describe the intersection of the insect and human genome.


Subsequent work has extended Venn diagrams into four, five, and six sets. This includes the work mathematician Charles Dodgson, otherwise known as the writer Lewis Carroll, who depicted a Venn diagram of six sets.



A.W.F. Edwards created symmetrical constructions of Venn diagrams with higher numbers of sets. He projected the Venn diagram onto a sphere, depicted the intersections on the surface of the sphere, and then projected the resulting sets back to the plane to give cogwheel diagrams with increasing numbers of teeth.

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Call to Action

I have not come across any photos of Venn diagram tattoos. If you've got one, please send it over. Thanks, Vannevar.

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A Mathematician's Memorial

A.W.F. Edwards also designed this stained glass window commemorating John Venn, which is placed in the Hall of Gonville and Caius College at Cambridge University, England.


A Euler Diagram is a further development of Venn Diagrams, but Euler Diagrams are not required to be exhaustive; they do not need to show all possible intersections of sets, and they can show non-intersections as well.


Venn diagrams have moved beyond arcane set theory (as enjoyable and satisfying as that can be) into the sphere (sorry) of art. So let me say that understanding Venn diagrams is something to hope for, possibly even something to pray for:

Best Non-Mathematical Venn Diagram I've Ever Seen

Without further ado, I'd like to introduce the Venn diagram that I saw today, which prompted me to write this post. It's the best Venn Diagram I've ever seen. I really appreciate how he uses the nuance of the various intersections to draw out the suggested strategies.

Knowledge is Justified True Belief

This Venn diagram depicts Plato's epistomological assertion that "knowledge is justified true belief".

Make Your Own Venn Diagrams

If you'd like to make your own Venn Diagrams, try Venny, an online Venn-Maker.

Venn Small Amusements

(click for originals, links open in new window)