In topology is proved, that it is always possible to paint over a plane which is broken on area, by four colours so that any adjoining areas were painted in different colours.

Example of the splitted square, that can be painted only with all of four colors is given in figure.

Pattern of the origami model also breaks a square into some areas. Let's consider patterns of the flat origami models. Interestingly, how much colours are enough for colouring of such pattern?

Let's consider for the beginning an examples of such patterns. In pictures are given painted patterns of the classical models seal and frog.

As we see, for this patterns it is enough two colours. And, after we have folded this models all blue areas will be on one side, and all red - in another. This fact has noticed and proved by Japanese connoisseur of origami and mathematics Kawasaki.

It is interesting, that the three-dimensional models do not submit to the given law. As an example it is enough to consider pattern of the classical waterbomb.

Try to consider by yourself some patterns of the flat and three-dimensional models and you will be convinced in the facts, that was presented in this paper.


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