## The History of the Venn Diagram

Venn Diagrams are often seen flying around the internet as shareable memes and political commentaries, but these diagrams originated as a respected educational tool. Venn Diagrams were first popularized by logician, John Venn in 1880, but research suggests that similar diagrams have been around since the mid 13^{th} century! Philosophers and mathematicians were the first to use Venn Diagrams as comparison tools and visual representations of their findings.

Early Venn Diagrams were quite serious. Take a look at the philosophical example below.

In the mid 2000s Venn Diagrams became an internet sensation. They lost their serious academic nature and exploded as a favored comic tool of bloggers. Venn Diagrams have now been coined the perfect tool for making absolutely ridiculous comparisons. Check out the examples below for an idea of what we’re talking about.

It’s safe to say though, that despite their fleeting internet popularity Venn Diagrams are still an educational staple. A favorite for teaching set theory and compare/contrast lessons.

## Basic Venn Diagrams

The most popular type of Venn Diagram is the famous diagram which is comprised of two overlapping circles. Each side represents a set and the middle section, which overlaps, represents similarities between the _two sets.

Let’s take a look at some examples:

This diagram compares even numbers and prime numbers.

This diagram shows that the sets of even numbers and prime numbers have **very** little overlap. Only one number in fact, the number 2.

While this one, changes just one set to compare odd numbers and prime numbers.

You can see that by changing just one of the sets we’re looking at (Even Numbers to Odd Numbers) we end up with quite a different diagram! These two sets have far more overlap than the original two sets we examined. In fact, there is only one single number that is prime but not odd. The number 2.

## Three Way Venn Diagrams

Three way Venn Diagrams take things to the next level. You can now compare three sets and examine where each of them overlaps with the others.

Let’s take a look at some examples:

This diagram compares double digit numbers, odd numbers and prime numbers.

In this example one set is empty! This tells us that there are **no** double digit prime numbers that are not odd. In other words, all double digit prime numbers are odd. We can also see that there is overlap in between all of the other sets and that there is even overlap in the very middle. This means that all three sets have some numbers in common.

How about this example? It compares odd numbers, double digit numbers and numbers divisible by 5.

As you can see from the diagram each of these sets has overlap *and* there are some numbers which are a part of all three examined sets.

First, we can look at each set individually. Numbers that are divisible by five but are not odd or double digit would include all numbers ending in zero with 3, 4, 5, 6, 7 digits or more. Odd numbers that are not divisible by five includes 1 and 7 as well as many odd numbers in the triple, quadruple digits and on that end in 1, 3, 7 or 9. All even double digit numbers that do not end in zero would fit in the top set. They are not odd, they are not divisible by five and they are double digit.

Then, we can look at the overlaps. There are many numbers that are both odd, divisible by five and not double digits. These include, 5 as well as every 3, 4, 5, digit and on number that ends in five. There are also many numbers that are both double digit and divisible by five but are not odd. This overlapping section includes all double digit numbers that end in zero. Finally, we look at numbers that are odd and double digit, but not divisible by five. This section includes double digit numbers that end in 1, 3, 7 and 9.

…The most exclusive part of a three way Venn Diagram is in the center. The most central section represents the area where all three sets overlap. In this case, numbers that are odd, double digit and also divisible by five. In this section we find all double digit numbers that end in five.

## Venn Diagrams in Other Subjects

Although Venn Diagrams are often thought of as math tools (and rightly so) many other

academic subjects also find great use in Venn Diagrams as comparison tools.

Let’s take a look at these examples:

This Venn Diagram was used in a science classroom to compare plant cells and animal cells. You’ll see they all have some things in common (note the overlap) and also some things that are unique.

This Venn Diagram illustrates a social studies concept and examines the differences and

similarities between the two world wars. Again, you’ll note that each war as some things that are specific to itself and the two wars also have some similarities (noted in the middle, overlapping section).

As you can see, Venn Diagrams are versatile and very useful. They can be used to compare the simple and the mundane or the complex and valuable. They can be filled with numbers words or pictures. And can be used both by young children and doctorate level educators. Many thanks to John Venn for popularizing the diagram we all know today.

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