Matthias Schwar
How to make a better? hexagon
The classical layout to cut a hexagon from a rectangle is shown in part B, left part. It works, but i was never able to obtain a "perfect" hexagon. It may only be obtainable with a stencil (advantage: completely free of creases, disadvantage: fixed stencil size). I have come up with an improved folding method (B right part, C) which gave me better results than the classical method. It shifts the hexagon away from the edge of the paper (the creases here tend to be inaccurate due to bending) and it uses more reference points/lines. The extra creases will get folded anyway in a standard edge aligned grid. A drawback is that the residual paper is obtained in 2 smaller parts compared to the classical method, a pity if expensive paper is used.
It is useful to understand how the required angle of 60° (yellow) is obtained (shown in part A). The bottom raw edge must be folded upwards so that the bottom right corner touches the vertical which divides the bottom edge in half. Because the now void space and the folded flap are equal, the angle in the red triangle is bisected. Substracting this value from 90° gives 60°, which we are after. Here it is just a coincidence that the red and yellow angles are equal, in other examples (the vertical can be shifted to obtain other angles) this is not the case.
This method can also be used for other grid divisions, as shown by Robin Scholz (Link 1, 2). The short edge of the rectangle is first divided into the required parts. I like to use the equidistant line method (3), because it is accurate and does not introduce extra creases. Then, using the 60°-method, the hexagon is created.
There is another universal way to divide paper into nths, based on folding only (4, 5), but it requires extra creases. They can be reduced to pinch marks, but at the risk of greater inaccuracy.
How to make a better? hexagon
The classical layout to cut a hexagon from a rectangle is shown in part B, left part. It works, but i was never able to obtain a "perfect" hexagon. It may only be obtainable with a stencil (advantage: completely free of creases, disadvantage: fixed stencil size). I have come up with an improved folding method (B right part, C) which gave me better results than the classical method. It shifts the hexagon away from the edge of the paper (the creases here tend to be inaccurate due to bending) and it uses more reference points/lines. The extra creases will get folded anyway in a standard edge aligned grid. A drawback is that the residual paper is obtained in 2 smaller parts compared to the classical method, a pity if expensive paper is used.
It is useful to understand how the required angle of 60° (yellow) is obtained (shown in part A). The bottom raw edge must be folded upwards so that the bottom right corner touches the vertical which divides the bottom edge in half. Because the now void space and the folded flap are equal, the angle in the red triangle is bisected. Substracting this value from 90° gives 60°, which we are after. Here it is just a coincidence that the red and yellow angles are equal, in other examples (the vertical can be shifted to obtain other angles) this is not the case.
This method can also be used for other grid divisions, as shown by Robin Scholz (Link 1, 2). The short edge of the rectangle is first divided into the required parts. I like to use the equidistant line method (3), because it is accurate and does not introduce extra creases. Then, using the 60°-method, the hexagon is created.
There is another universal way to divide paper into nths, based on folding only (4, 5), but it requires extra creases. They can be reduced to pinch marks, but at the risk of greater inaccuracy.