Venn Vs Euler: The Diagrams

I know what you're thinking: what's the difference between a Venn diagram and an Euler diagram? Good question. The following diagram should clear things up:

Venn Vs Euler: The Diagrams

Just to clarify, Venn diagrams have regions for all possible combinations of groups whether there are things in those regions or not. You then use shading to indicate if things are actually found in those regions. An Euler diagram (pronounced oy-ler I found out today) on the other hand only shows a region if things exist in that region. The overlaps and non overlaps are therefore chosen according to what exists. For example, here's a Venn diagram:

Venn Vs Euler: The Diagrams

So with three logical groups that describe playing cards (not all logical groups mind, I've missed out the other suit groups and every other grouping you could care to invent), in a Venn you overlap all three so every possible combination has its own region. I've then coloured in grey all the regions that have nothing in them.

The same information in an Euler diagram would look like this:

Venn Vs Euler: The Diagrams

So here, it's the layout that changes according to the logic of the groups. Eg because all spades are black cards, that is to say they are a subset, that group is drawn entirely inside the other. No Red cards are black cards so those two groups are completely separate.


The diagram at the top of this post could be an Euler or a Venn, it's ambiguous. You could argue that it's both which is why a tiny simplified version of itself appears in the overlap! It's a diagram about itself. Here's a sexier recursive version:

Venn Vs Euler: The Diagrams

Phew!

Any diagrams you'd like to see? Let me know in the comments.

Here are some Bryan Adams related diagrams.

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  • http://www.twitter.com/pageantmalarkey Elise

    Can you do one explaining what quadratic equation graphs ACTUALLY show? For example, what practical applications they have?

  • http://www.twitter.com/pageantmalarkey Elise

    Can you do one explaining what quadratic equation graphs ACTUALLY show? For example, what practical applications they have?

  • Michael Eve

    This potentially infinite recurance is really interesting:
    V/E diagrams within V/E diagrams;
    your “had” sketch;
    a picture I saw (I think in the window of an art gallery in Harrogate) of an easel on a beach, holding a picture of an easel on a beach …..;
    a room in a stately house (possibly Hatfield) with large mirrors on opposite walls containing reflections of reflections.

  • Michael Eve

    This potentially infinite recurance is really interesting:
    V/E diagrams within V/E diagrams;
    your “had” sketch;
    a picture I saw (I think in the window of an art gallery in Harrogate) of an easel on a beach, holding a picture of an easel on a beach …..;
    a room in a stately house (possibly Hatfield) with large mirrors on opposite walls containing reflections of reflections.

  • http://www.stevemould.com admin

    Yeah, Gem and I are a bit obsessed with recursion. There’s a fair bit of it in our shows :)

  • http://www.stevemould.com admin

    Yeah, Gem and I are a bit obsessed with recursion. There’s a fair bit of it in our shows :)

  • http://www.stevemould.com admin

    Quadratic equations are great Elise. They describe loads of real word things. If you throw a ball the path it takes is a quadratic equation! I’ll think of some more I’m sure.

  • http://www.stevemould.com admin

    Quadratic equations are great Elise. They describe loads of real word things. If you throw a ball the path it takes is a quadratic equation! I’ll think of some more I’m sure.

  • Laura Donelly

    Cool. I never knew that Euler diagrams were called Euler diagrams. Every day’s a schoolday and all that.

    One of my favourite blogs is http://thisisindexed.com/ which contains both Venn and Euler diagrams.

  • Laura Donelly

    Cool. I never knew that Euler diagrams were called Euler diagrams. Every day’s a schoolday and all that.

    One of my favourite blogs is http://thisisindexed.com/ which contains both Venn and Euler diagrams.

  • David Greenslade

    I am a diagram enthusiast and would like to share something with you – would need to attach – reply if you are interested

    • http://www.stevemould.com admin

      Hi David. You’ve got me intrigued. I’m not sure how to approve attachments for commenters in wordpress but you can email me at stevemould@gmail.com. Thanks

  • David Greenslade

    I am a diagram enthusiast and would like to share something with you – would need to attach – reply if you are interested

    • http://www.stevemould.com admin

      Hi David. You’ve got me intrigued. I’m not sure how to approve attachments for commenters in wordpress but you can email me at stevemould@gmail.com. Thanks

  • Ymkje Kamphuis

    huh that clears that up! but that means that the whole time my teachers taught me about venn diagrams in school they where actually euler diagrams! psssssh

  • joe velikovsky

    Awesome :) Great explanation

    Hey – if this is an animated Venn-Euler, it is a Venneuler?

    http://storyality.wordpress.com/creative-practice-theory/

    JT

    PS. Vannoyler. Like, a Vannoyler-flavoured diagram.