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Two hexagons from A4 minus square | by Michał Kosmulski
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Two hexagons from A4 minus square

Have you noticed that the strip which stays behind when you cut a square from an A4 sheet of paper, is just the right size for cutting two small hexagons? No origamist likes wasting paper and this is great scenario fo reuse. Assuming the short side of the whole sheet has the length a, the short side of the rectangle left after cutting off the square is h = a*(sqrt(2)-1), and the wasted area is 2*h*h/2/sqrt(3) + h*(a-2*2*h/sqrt(3)) = a*a*(sqrt(2)-1)*(sqrt(2)-1)/sqrt(3) + a*(sqrt(2)-1)*(a-4*a*(sqrt(2)-1)/sqrt(3)) = a*a*((3-2*sqrt(2))/sqrt(3) + sqrt(2)-1-4*(3-2*sqrt(2))/sqrt(3)) = a*a*(sqrt(2)-1-3*(3-2*sqrt(2))/sqrt(3)) = a*a*(sqrt(2)-1-(3-2*sqrt(2))*sqrt(3)) ~= a*a*0.117 which amounts to only about 8% of the A4 sheet (a × a*sqrt(2)) going to waste.

 

Additionally, I sometimes use the small triangular pieces left over after cutting the hexagons as bookmarks.

 

The whole rectangle you get left over by cutting a square from A4 paper happens to have dimensions and proportions simiara to a US dollar bill, so you can use the whole rectangle for dollar-bill origami models as well.

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Taken on October 23, 2020