Theoretical master—Haga’s second and third theorems

Theoretical master—Haga’s second and third theorems

I introduced Fagas first theorem to you earlier. I believe that after your careful study and repeated consideration, you should have almost understood it. Although the theory of origami may seem boring, if you master it well, it can be of great benefit to your future paper art career! In the past, when our ancestors no longer had theory as a guide, they relied more on their own experience and exploration. Now that we have theory, we should learn from it and use it to arm our beautiful hearts and dexterous hands. Now Let’s continue with Hoga’s second theorem and Hoga’s third theorem.

Hagas second theorem

a. Preparation materials: 15cm×15cm two-color paper and one piece of A4 paper.

b. Operation: Mark the four corners of the square as A, B, C, and D. Take the midpoint E of AD as the point where the crease line will be folded, and extend it to intersect at the point.

c. Think: where to point on the line segment

d. Conclusion: The point is the trisection point.

Fagas second theorem:In the square ABCD, take the line connecting the midpoints E and D of AD as the crease line, fold A to get point F, and extend EF to intersect CD at G It is the third equal point.

e. Several extended conclusions:

(1) The area of ??S1~S2 can be calculated;

(2) It can be obtained that H'F=1/5 AD, HF=2/5 CD;

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Hogas third theorem

a. Preparation materials: 15cm×15cm two-color paper and one piece of A4 paper.

b. Operation: Mark the four corners of the square paper as A.B.C.D. Take the midpoint E of AD, let the point E fall on the projection line HF of CD, and the corresponding point H of point C fall on AB.Fold the square paper as shown in Figure 2.8 to get the crease line LG,

c. Think: Where is point H on line segment AB

d. Conclusion:Point A is the third bisecting point of line segment AB. For square origami ABCD, take the midpoint E of AD and fold the square so that the corresponding point H of point C falls on On AB, point E falls on the projection line of CD, then the corresponding point H of point C is the trisection point of AB. This is Fagas third theorem.

Tips:

An introduction to Faga’s third theorem

This theorem was named by Kazuo Faga himself at the Third International Origami Annual Conference in 1992. However, Fagas first and second theorems named after him were named by others.

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Up to now, I have finished learning Fagas three major theorems. If you are still a little confused about these three theorems, the easiest way is to memorize them. You will gradually be able to understand them in your future studies. I understand~Paper art is the art of origami and thinking. Origami is done with hands, and thinking and innovation are done with the brain. Don’t choose which one~^^