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.


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.


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.


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.


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.


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.


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.


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.


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.

No One Can Figure Out This Second Grade Math Problem

Angie Werner got a lot more than she bargained for on January 24, when she sat down to help her 8-year-old daughter, Ayla, with her math homework. As Pop Sugar reports, the confusion began when they got to the following word problem:

“There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?”

Many people misread the problem and thought it was a trick question: if there are 36 more small dogs and the question is how many small dogs are competing, then maybe the answer is 36?


Frustrated by the confusing problem, Angie took to a private Facebook group to ask fellow moms to weigh in on the question, which led to even more confusion, including whether medium-sized dogs should somehow be accounted for. (No, they shouldn’t.) Another mom chimed in with an answer that she thought settled the debate:

"Y'all. A mom above figured it out. We were all wrong. If there is a total of 49 dogs and 36 of them are small dogs then there are 13 large dogs. That means 36 small dogs subtracted by 13 large dogs then there are 23 more small dogs than large dogs. 36-13=23. BOOM!!! WOW! Anyone saying there's half and medium dogs tho just no!"

It was a nice try, but incorrect. A few others came up with 42.5 dogs as the answer, with one woman explaining her method as follows: "49-36=13. 13/2=6.5. 36+6.5=42.5. That's how I did it in my head. Is that the right way to do it? Lol I haven't done math like this since I was in school!"

Though commenters understandably took issue with the .5 part of the answer—an 8-year-old is expected to calculate for a half-dog? What kind of dog show is this?—when Ayla’s teacher heard about the growing debate, she chimed in to confirm that 42.5 is indeed the answer, but that the blame in the confusion rested with the school. "The district worded it wrong,” said Angie. “The answer would be 42.5, though, if done at an age appropriate grade."

Want to try another internet-baffling riddle?

Here's the answer.

[h/t: Pop Sugar]

If You Can Solve This Math Puzzle, You Might Be a Genius

by Reader's Digest Editors

Do you think of yourself as a secret mathematician? This math brainteaser has even the biggest number nerds scratching their heads.

People’s Daily, China tweeted out this math puzzle in which each picture represents a number.

These algebra problems might seem easy at first glance, but hold on. People’s Daily was nice enough to give away the answer before you began. If you didn’t get 16, you did something wrong. Take a closer look at the pictures—you probably missed a few key details.

Still stumped? We’ll walk you through it. For the sake of the explanation, we’ll call the shoes S, the cat C, and the whistle W.

The first equation sets up the whole math puzzle. Three pairs of shoes added together equal thirty. S + S + S = 30, so divide 30 by three. Each pair of sneakers represents the number 10. Easy enough.

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Now the second equation is clearer. Sub the shoes out for a 10, and you’ll find out 10 + C + C = 20. Subtract 10 from each side, so C + C = 10. Each cat must represent the number 5.

Look closely at the next equation before you jump into it. In the third equation, there are two whistles in each line, but the final one only has one whistle. So 5 + 2W + 2W = 13. If 4W = 8, then each whistle represents the number 2.

OK, so that clears up a bit of the next equation—until you plug the numbers in. Sub S + C x W for 10 + 5 x 2. Remember your order of operations? Multiply first, then add. So 10 + 10 = 20. What went wrong?

The key is in the cat’s clothes. In the second and third equations, the cat has a whistle around its neck—but not in the last one.

No need to go back and redo all your hard work. Just change the last equation to S + (C – W) x W. Now plug the numbers in: 10 + (5 – 2) x 2. Work your way through it. The equation goes to 10 + (3) x 2, then 10 + 6. Finally, you get 16—problem solved!


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