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I have a problem that I can't solve. It says:

"If you rotate a square 45º you get a 8-pointed star. Prove that you can divide that star in 8 parts with which you can build a new square"

I have calculated that if the original side of the square was 1, the new side is $\sqrt{4-2\sqrt2}$, and I don't know how I can do a division to obtain this side. Any suggestion? Thanks!

Thanks you very much. I haven't solved the problem yet, but I have done more steps: In Moti's picture, the segment IJ has lenght $\sqrt{4-2\sqrt{2}}$ as we want. This triangle is rectangle in F so the angles FIJ, IJF are supplementary. With 4 triangles like that we can build a square with side IJ, but in the middle we obtain a new empty square with side $\sqrt 2 /2 $ (and diagonal 1). But I don't know how to do the partition.

Thanks!

Daniel Fischer
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Relativo
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    It looks as though you get that edge length as the length of the segment between two opposite concave vertices. So cutting the star in half along such a cut might be a good first step. I still have trouble with some of the smaller pieces, though. – MvG Dec 19 '16 at 10:08
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    The original square may be divided into 4 shapes of which the laager square may be structured in which the four additional triangles will fit. Let me know if you need help... – Moti Dec 27 '16 at 01:20
  • Thanks you very much Moti, but I'm still having problems. With the 4 additional triangles I'm building a new square with side $\sqrt 2 - 1 $ and I'm trying to divide the original square in triangles like FIJ... – Relativo Dec 27 '16 at 18:13

1 Answers1

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The following picture should serve as a very close to solution hint.

enter image description here

Moti
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