Math Embroidery: Venn Diagrams and Set Theory

Four Ellipse Venn Diagram
6 strand cotton and linen floss on 20 count linen

Five Ellipse Venn Diagram
6 strand cotton and linen floss on 20 count linen

I am working on a set of embroidery pieces that detail math concepts using geometry.  The first set I completed are Venn diagrams as related to set theory.

I am no math scholar, but I am combining research, embroidery and lectures via podcast to try to teach myself some of the large concepts in mathematics.  

I understood how Venn diagrams worked before beginning the piece; high school teachers use Venn diagrams often as graphic organizers.  But set theory was new to me.  I learned that entire sets of data can be treated like individual values and manipulated.  For example, a simple proof uses set theory to show that the set of real numbers are infinite.  Take each even number (2, 4, 6...) and match it with each counting number (1, 2, 3...).  You could make a 1:1 match with group and find that you have the same amount of counting numbers and even numbers.  Now you might ask, what about the odd numbers?  If you think about the -set- of even numbers as counting numbers minus odd numbers, which logic tells us must be less than all counting numbers.  But because we can match the set of even numbers to the set of counting numbers, this shows that numbers, both counting and even (and odd) are infinite.  Mathematicians do this with sets of all types of numbers to show they are infinite.  Then using the fact that infinity exists, they go on to explain more complex things.

All of my patterns are based on wiki commons images.

Next up, Archimedes finds pi and the five platonic solids.