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#### Math Made Easy: Middle School and High School Math Tutoring (30 Minutes)

### Map Makers and Math-Makers: Exploring Appel and Haken’s Four Color Theorem Proof

Barbara Alldredge

Grab some colored pencils and doodle along as we explore the answer to this 150 year old mathematics and cartography question, “Can any map really be colored with just four colors?”

#### Class experience

For 125 years, mathematicians and cartographers claimed that any map could be colored with just four colors but every attempt at proving this conjecture was discredited. Then in 1976, this “Four Color Theorem” became the first major mathematical theorem to be proved by the use of a computer. Kenneth Appel and Wolfgang Haken showed that when two adjacent (touching) regions on a map must have different colors, only four colors are needed for coloring the entire map. Other mathematicians...

This topology course is part of a series of advanced mathematics topics presented in a hands-on format that is accessible to middle school students. Students will be introduced to the use of counter-examples in mathematical proofs. Students will be given the opportunity to explain the premise of the four color theorem, namely that “given any separation of a plane into contiguous regions, the regions can be colored using at most four colors so that no two adjacent regions have the same color.” Students will explore the concept of reduction. That is, replacing a complex problem with a simplified version to find potential patterns that can be applied to the more complex situation.

2 files available upon enrollmentColored Pencils Regular Pencil Several Sheets of Blank White Paper Sample Four Color Maps (Downloadable file provided. Please print before class.)

Learners will not need to use any apps or websites beyond the standard Outschool tools.

#### Meet the teacher

I teach math. And other stuff. But mostly math. I have a Professional Educator license for the state of Utah and a Level 4 Math Endorsement. That’s a fancy way to explain that I took a LOT of math in college. I’m qualified to teach a variety of...

###### Group Class

#### $10

per classMeets once

45 min

Average rating:4.8Number of reviews:(6)

Completed by 19 learners

Live video meetings

Ages 10-13

1-10 learners per class

###### This class is no longer offered

##### Financial Assistance

##### Outschool International

##### Tutoring

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