Venn and (the art of) happiness

I am irresistibly drawn to Venn diagrams. They make me very happy.

I love how accessible they are to emerging mathematicians. We can draw a Venn diagram on the ground and use it to sort objects — even ourselves! — into categories. An animal-sorting example: those that live on land (green hoop), those that live in the water (blue hoop), those that live in both (in the intersection of green and blue), and those that live in neither (outside of both green and blue). Or a shape-sorting example: the green ‘hoop’ contains quadrilaterals, the red ‘hoop’ contains triangles, and the yellow ‘hoop’ contains shapes with right angles.

img_0044
Source: education.vic.gov.au

Counting the number of regions in a Venn diagram with n sets is a neat argument. Suppose we have a Venn diagram with three sets labelled A, B, C. Then any region is: inside or outside of set A, inside or outside of set B, inside or outside of set C. There are two possibilities for each of three sets, so there are 2×2×2 = 23 = 8 possible regions. We can generalise this argument to n sets.

Venn diagrams also fascinate experienced mathematicians. See, for example, the survey by Frank Ruskey and Mark Weston in the Electronic Journal of Combinatorics. I am particularly taken with this symmetric Venn diagram1 for seven sets, and not only because it is named after my home city of Adelaide.

AdelaideRain

Venn diagrams can be clever, comedic or both. Below I share some of my favourites. I’ve tried to attribute authors, where known. If you can fill in the gaps, please let me know. And, do share your favorites with me! (Update: while looking for authors, I found this tumblr account, Fuck Yeah Venn Diagrams, and this twitter account: @venn_diagrams. Ohhhh yeah.)

 

richardosman_2013-Feb-25.png
Source: twitter.com/Andrew_Taylor
university_website.png
Source: xkcd.com/773

werna__2015-Dec-10.jpg

Maths314_2015-Sep-17.jpg

Unintentional-Venn-Diagram.png

CDK2Ry2WAAAm8P8.jpg

CiR5gDCW0AAR_GY.jpg
Source: http://www.worldofmoose.com
CcoOD2QWwAAA_nH.jpg
Source: http://www.worldofmoose.com

 


[1] Image source: www.maths.tcd.ie/EMIS/journals/EJC/Surveys/ds5/gifs

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