# Four Color Theorem

## Why Map Coloring?

I started the year by looking at Map Coloring and the Four Color Theorem, the lesson plans and worksheets can be found in the “Numbers & Patterns“ section of this website.

I decided to use this lesson because it is fun and demonstrates the difference between a proof and a conjecture, that there can be more then one way to solve a problem, and there are many different types of math. (Most of the English world uses the word “maths” to reflect the many different branches of math.)

Although Map Coloring is a topic of Graph Theory, the basic idea is simple and can be used in other classes.

## Interactive Notebook directions and script:

Fill out Four Color Theorem note page

a) cut out and glue to page

b) What is the difference between a proof and a conjecture?

c) Did we prove that there were only 4 colors needed to color any map?
— No, it was only a conjecture

d) How long did it take to prove this conjecture? (124 years)

e) “The proof for the 4-color theorem was controversial since it required a special tool that had never been used before on a major proof. Can you guess what tool was used?“ (a computer)

f) “Although mathematicians thought they found the proof for this conjecture in 1879 and 1880, mistakes were found in each of these proofs. Still the mathematicians learned a lot from the work they did and were able to use the information to prove other ideas (including that you need no more then 5 colors).”
i.e. Respect your and others mistakes and learn from them.

g) “So far you have been exposed to many different types of maths such as: Arithmetic, Algebra, and Geometry. This activity is part of a branch of math called Graph Theory.” 