Can you draw a Venn diagram for 4 sets? | Why Venn diagrams are not easy

You can turn subtitles on :), I am sorry about the low audio quality, for I don’t have a mic at the moment :(.

Timestamps
00:00 – Problems with 4 sets
01:55 – Solution
05:12 – Why circles are bad
10:35 – You can’t stick to one curve
13:35 – How Venn did it

Music used: Esther’s Waltz – Esther Abrami (from YouTube audio library)

The pictures I used are from Wikipedia, survey of Venn diagrams, Peter Hamburger’s paper on doodles and doilies, and Grünbaum’s paper on constructing Venn diagrams with convex polygons. The figure for Venn’s construction is actually from Grünbaum’s paper. If you are interested in exploring this topic further, the website: A Survey of Venn Diagrams (https://www.combinatorics.org/files/S...) would be a great start! Also, the Wikipedia article contains a good overview of the constructions.

When I was talking about intersections, I only allowed each pair of curves to have finitely many intersection points. Oops :")

#combinatorics #venn