Yesterday (4th August) we celebrated the 180th birthday of John Venn and Google doodle did it right again. If yesterday was a busy day for you (like it was for me) you can check it here (and I also recommend reading how they came up with the idea of the doodle, it is extremely interesting). Also, if you want to know how much we use the Venn diagrams in everyday life check this article (The Guardian have interesting articles when it comes to this things). So these are all the extra recommendations, lets start the math…

When it comes to mathematics we use the Venn diagrams especially with sets. It is very easy to understand any set operations using this diagrams. Basically we learn the definition of union, intersection, symmetric difference and any other things using the diagrams. So I am sure that everyone that studied sets had to look, work and understand these:

For me, they were always funny and I wanted to play with as many operations as possible and as many sets to see how everything looked like ( using different colors was a must for this activity). Something like this:

As you saw in the above pictures, we normally do not use it with a lot of sets, it becomes extremely difficult to use them with a lot of sets and understand them when it comes to drawing them in 2D. So, it seems natural that we started playing with 3D things. Here are some interesting representations from en.wikipedia.org:

Shown below, four intersecting spheres form the highest order Venn diagram that has the symmetry of a simplex and can be visually represented. The 16 intersections correspond to the vertices of a tesseract (or the cells of a 16-cell respectively).

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