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Magical beings have managed to tessellate an entire plan, indefinite, in the way the following figure shows a detail:

picture with black and white hexagons

They have done it by assembling pieces all the same, each of which was formed by a few white or black hexagons.

What fraction of the entire surface of the plane is black?

  • 0
    calculus tag?!? Just count! – 2017-02-02
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    Defining a "fraction of the entire surface" can be a tricky thing. It's simpler to look at just one of the identical pieces that was used to tessellate the plane, and say what fraction of that piece is black. – 2017-02-02
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    One eighth, assuming that the question even makes sense (Per David K.) – 2017-02-02

1 Answers 1

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You may tessellate the plane with this shape made of 8 hexagons (only look at the whole hexagons in the image):

As there is one black hexagon in each shape, the percentage of black hexagons in the limit is $\frac{1}{8}$

But as other have said, it is not trivial to rigorously define "the percentage of black hexagons" in an infinite plane.

enter image description here