In manual origami, we often encounter the problem of how to divide a corner into three equal parts and then fold it!
How to trisect an angle? According to Galois theory, it is simply impossible to do it using only a ruler and compass, so you can just give up on this attempt. However, you may be able to find some approximations. But in this origami or paper-cutting, what is needed is absolutely accurate angle division!
You may need to know about this angle dividing method that will be introduced below.
The answer we need to find is how to draw the two dotted lines in the picture, and those two dotted lines, plus the upper realization and the bottom edge, exactly trisect the angle we set.
Suppose we can draw 3 equal right triangles as shown in the picture.
These triangles are equivalent to three equal parts of the angle we focused on before (the inside is a right triangle, with equal sides and equal angles), so we only need to know how to "place" them there!
Select any height h close to the bottom edge, use the horizontal line of this height as the crease, fold the bottom edge upward, and then restore it, leaving this crease.
What we need to use at this time is the blue line drawn in the picture, and the length of this line should be twice the height h of the previous step, which is twice the h.
We can fold the bottom edge upward twice in a row according to the previous height h in the paper, so that we get another crease.
Having such a "ruler" makes it very convenient for us to find the imaginary line.
Fold point b to point B, and fold point d to point D. Points b and d are on the left side of the shape, point B is on the earliest crease made, and point D is on the closest to the bottom. on the edge crease. After folding it, we can simply use a pencil to lightly draw the red line.
In this way, we have found the side that finally completes the trisection of the angle!
