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How many colors does it take to color a map so no two regions have the same color?

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Presentation on theme: "How many colors does it take to color a map so no two regions have the same color?"— Presentation transcript:

1 How many colors does it take to color a map so no two regions have the same color?

2 Four Color Theorem ( Guthrie’s Problem) 1… 2… 3… 4…!

3 A Little History… Francis Guthrie, in 1852 was the first to put the four color theorem into words. While coloring a map of counties of England He noticed that only four colors were needed.

4 Defining the Four Color Theorem Any map can in a plane can be colored with only four colors so that now regions having a common boundary have the same color. Those regions that have only a point in common are not considered to have shared boundaries.

5 The four color theorem is a mathematical brainteaser that can be appreciated by non-mathematicians as well as mathematicians.

6 Computer Controversy In 1976, the conjecture was apparently proven by Wolfgang Haken and Kenneth Appel with the aid of a computer. The proof of the four color theorem is a doorway to some interesting questions about the role of human minds and computing machines in mathematics.

7 Consider the coloring of geographical maps, is the problem basically a topological problem? Yes, in that it depends only on the connectives between the countries, not on their specific shapes, sizes, or positions.

8 Flash! -Mathematical Breakthrough! In December 2004, Dr. George Gonthier removed last doubts about the proof of the Four Color Theorem.

9 Contributors Wendy Cozart Dr. Geo. Gonthier Nancy Lutz Thelma Mayes August F. Mobius Kristen Ochs M. Lynne Ryan ToniAnne Tillotson

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