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Fun with Venn and Euler Diagrams

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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.

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Courtesy University of Manchester
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History
148 Lost Alan Turing Papers Discovered in Filing Cabinet
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Courtesy University of Manchester

You never know what you’re going to uncover when you finally get around to combing through that decades-old filing cabinet in the back room. Case in point: The University of Manchester recently unearthed 148 long-lost papers belonging to computer science legend Alan Turing, as ScienceAlert reports.

The forgotten papers mostly cover correspondence between Turing and others between 1949 and his death in 1954. The mathematician worked at the university from 1948 on. The documents include offers to lecture—to one in the U.S., he replied, “I would not like the journey, and I detest America”—a draft of a radio program he was working on about artificial intelligence, a letter from Chess magazine, and handwritten notes. Turing’s vital work during World War II was still classified at the time, and only one document in the file refers to his codebreaking efforts for the British government—a letter from the UK’s security agency GCHQ. The papers had been hidden away for at least three decades.

A typed letter to Alan Turing has a watermark that says 'Chess.'
Courtesy University of Manchester

Computer scientist Jim Miles found the file in May, but it has only now been sorted and catalogued by a university archivist. "I was astonished such a thing had remained hidden out of sight for so long," Miles said in a press statement. "No one who now works in the school or at the university knew they even existed." He says it’s still a mystery why they were filed away in the first place.

The rare discovery represents a literal treasure trove. In 2015, a 56-page handwritten manuscript from Turing’s time as a World War II codebreaker sold for more than $1 million.

[h/t ScienceAlert]

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Can You Figure Out How Many Triangles Are in This Picture?

Time for another brain teaser. How many triangles do you see here? A Quora user posted the image above (which we spotted on MSN) for fellow brainiacs to chew on. See if you can figure it out. We’ll wait.

Ready?

So, as you can see, all the smaller triangles can combine to become bigger triangles, which is where the trick lies. If you count up every different triangle formed by the lines, you should get 24. (Don’t forget the big triangle!)

Some pedantic Quora users thought it through and realized there are even more triangles, if you really want to go there. There’s a triangle formed by the “A” in the signature in the right-hand corner, and if we’re counting the concept of triangles, the word “triangle” counts, too.

As math expert Martin Silvertant writes on Quora, “A triangle is a mathematical idea rather than something real; physical triangles are by definition not geometrically perfect, but approximations of triangles. In other words, both the pictorial triangles and the words referring to triangles are referents to the concept of a triangle.” So yes, you could technically count the word “triangle.”  (Silvertant also includes a useful graphic explaining how to find all the pictorial triangles.)

Check out the whole Quora discussion for in-depth explainers from users about their methods of figuring it out.

[h/t MSN]

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