Fun with Venn and Euler Diagrams


A Venn diagram is a mathematical illustration that shows all of the possible mathematical or logical relationships between sets. A Euler diagram resembles a Venn diagram, but does not neccessarily show all possible intersections of the sets. A Euler diagram is often more useful for showing real world data, because not all sets partially overlap with all other sets.

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I used the 3 Circle Venn Diagram Applet to make a diagram of food preferences in my family. I have one child who won't eat much in the way of meat or vegetables, and another who dislikes carbs. The is a classic Venn diagram, which explains why I don't cook as often as I used to.

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This graphic is labeled as a Venn diagram, but it is actually a Euler diagram, because at no point does true happiness intersect with wearing pants. At least for the person who made the diagram.

More diagram fun, after the jump.

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If the circles don't intersect, it's not a Venn diagram. Which can be a very sad thing if you're a circle. This design was found at Threadless T-Shirts. However, Euler diagrams may overlap or not. But Euler is not what the blue circle had in mind.

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I came across this very useful image last week that started my quest to learn the difference between a Venn diagram and a Euler diagram. It explains the geographic terminology used in that area of the eastern Atlantic that confuses Americans. The author labeled the item as The Great British Venn Diagram, then explaned that it was actually a Euler diagram. No doubt people are more familiar with Venn. But no matter how geographically accurate the place names are, Irish commenters predictably objected to being included in anything labeled with the word "British". Another such diagram that includes more islands can be found here.

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These sweet and sour doodles are true Venn diagrams. They were produced by Jessica Hagy of Indexed, a blog full of wonderful diagrams and graphs jotted on index cards.

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Rob Harvilla used Venn and other diagrams to deconstruct the song "This Is Why I'm Hot" by Mims at The Villlage Voice. The diagrams clearly show that the lyrics make no sense at all. Nevertheless, the song was number one at the time this was written.

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Speaking of music, here's a t-shirt for music snobs featuring a two-set Venn diagram. From the product page:

Nothing is any good if other people like it. We've just proven it mathematically. I have a theory that the only thing cartoonists bothered learning in math class was Venn Diagrams.

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Randall Munroe at xkcd has the geekiest love notes ever. This classic Venn diagram is so sweet and simple, until he started to fill in the zones.

Venn diagrams and Euler diagrams are just two more of the many handy learning devices that are used for strange or comedic purposes. See also Periodic Tableware, More Periodic Tableware, and Fun with Flow Charts.