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Okay, why isn't the number four? Is this diagram of his not flat in the plane? I messed around with the 4 color theorem as a kid and I heard it was proved at some point. How is this one different?Ackbach said:
topsquark said:Okay, why isn't the number four? Is this diagram of his not flat in the plane? I messed around with the 4 color theorem as a kid and I heard it was proved at some point. How is this one different?
-Dan
The chromatic number of the plane is the minimum number of colors needed to color every point in the plane such that no two points of the same color are adjacent.
The chromatic number of the plane is at least 5 because it has been proven that a plane cannot be colored with 4 or fewer colors without violating the rule of no adjacent points having the same color.
The significance of the chromatic number of the plane being at least 5 is that it has important implications in graph theory and discrete mathematics, and has connections to various fields such as computer science, physics, and biology.
The chromatic number of the plane is determined through various methods such as the use of mathematical proofs and algorithms. It is a complex problem that has been studied by many mathematicians and continues to be an active area of research.
Yes, the chromatic number of the plane is always at least 5. This is a fundamental property of the plane and has been proven by various mathematicians through rigorous mathematical proofs.