Skip to content

Euler and Venn diagrams

February 24, 2013

Diagram

I’m just about to launch into probability with my year 12 statistics class. I like to show the way that the intersect and union notation looks in Venn diagrams and remember hearing about Euler diagrams too so I looked them up.

Euler diagrams have a number of closed curves (often circles) to show how different groups of things are related. The curves may intersect or not. Some curves may be wholly contained within another curve.

Venn diagrams are a subset of Euler diagrams in that while they still have a number of closed curves (still often circles*), all the possible intersecting regions must be included in the diagram. For any number of curves, n, the number of regions will be 2 to the power n. The curves cannot be contained within another curve.

It somewhat amused me that the fact that Venn diagrams are a subset of Euler diagrams can be nicely shown with a Euler diagram (but couldn’t be shown with a Venn diagram).

I say ‘often’ meaning for the case of 2 or 3 regions. It can’t be circles for 4 or more.

Advertisements

From → Uncategorized

4 Comments
  1. I love Euler diagrams, I use them when explaining the relationships between natural numbers, integers, rational, irrational, real imaginary and complex numbers.

Trackbacks & Pingbacks

  1. John Venn is 180 | The Aperiodical
  2. 4 cross curricular ideas and coloured boxes TMmaths 4/4 | reflectivemaths's Blog

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: