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Four-color theorem linked to crystal’s magnetic properties

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Posted June 10, 2014
four color theorem
Domain patterns can be understood in terms of color theorems. (a) Image of the domains in a crystal material and (b) the domains colored in accordance with the four-color theorem. (c) Image of the domains in a second crystal material and (d) the domains colored in accordance with a two-step version of the color theorem: domains are either dark or light, as well as one of three colors. These domain patterns, along with their associated coloring schemes, are closely related to the materials’ magnetic properties. Credit: Horibe, et al. ©2014 American Chemical Society

Sometimes mathematical theories have implications that extend far beyond their original purpose. This situation holds true for the four-color theorem, which was originally used by cartographers hundreds of years ago to draw maps. According to the theorem, four colors are sufficient to color different countries on a 2D map so that no two adjacent countries have the same color (excluding intersecting corners). However, today the four-color theorem is less interesting to cartographers than it is to mathematicians due to the complexity of its proof, which was achieved in 1976.

 

Now, a team of mathematicians, physicists, and chemists from the US, South Korea, and Japan has discovered that the four-color theorem can be used to understand the  and magnetic properties of a complex material. Their paper is published in a recent issue of the Journal of the American Chemical Society.

Read more at: Phys.org

 

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