Research on several special folding methods in the art of tuanhua paper-cutting
Chinese folk paper-cutting has a very long history. The earliest paper-cutting objects discovered so far are five paper-cutting works from the Northern Dynasties that were unearthed near the Flame Mountain in Turpan, Xinjiang. These five paper-cuts are all made in the form of folding, which is what we often call Tuanhua paper-cuts now. But what exactly is Tuanhua paper-cutting? What is the definition of Tuanhua paper-cutting? There is currently no completely accurate statement in the paper-cutting art world. Therefore, in the innovative research on the experimental teaching of tuanhua paper-cutting, we mainly start from the following aspects.
First of all, after years of summarization and deliberation, after referring to a large amount of paper-cutting materials and consulting experts in paper-cutting, a relatively accurate definition of Tuanhua paper-cutting was summarized: Tuanhua paper-cutting is to cut a square After folding the paper several times, use the center point of the square paper as the radiating point, divide it into several equal parts, design a pattern on only one part, make it, and then unfold it to form a complete continuous paper-cut pattern. A form of paper-cut design.
Secondly, the previous paper-cut folding methods were troublesome to design. Folding methods such as one fold, two folds, four folds, and eight folds were relatively easy. You only need to fold in half again based on the previous fold. Thats it. Folding methods such as three-fold, five-fold, sixty-fold, seventy-fold, and ninety-fold are very troublesome. The previous method was to first calculate the equal fractions of the square paper used in these folding methods, and then use these Divide 3600 from equal parts, so you can calculate the angle of each part after folding, then use a protractor to measure the angle on the paper after the first fold, and finally fold it, which is very inconvenient, and after folding too many times , the errors caused by the overlapping of the folded marks are much greater.
In response to this problem, with the help of several mathematics teachers, we used the third fold as a breakthrough point to conduct research. The theoretical basis of our research is: the principle of Pythagorean numbers. "Pythagorean Numbers" originated from the ancient arithmetic "Zhou Mu Suan Jing" written in my country in the 11th century BC. The book records a conversation between Shang Gao and Zhou Gong in about the 11th century AD: "Therefore, when the rules are broken, it is thought that Gou Guang San, Gu Xiu Four, Sutra Five." Among them &l"Hook" is the shorter right-angled side of the triangle, "strand" is the other right-angled side, and "meridian" is the hypotenuse. In other words, if one right-angled side of the right triangle is 3 and the other right-angled side is 4, then The length of the hypotenuse must be 5. 3, 4, and 5 are a set of Pythagorean numbers.
In mathematics, there is also an axiom: "In a right triangle, the right side corresponding to the 30. angle is 1/2 of the hypotenuse."
First fold the square paper once and then twice. After the second fold is completed, do another parallel fold and unfold the parallel folds (mainly to use the crease points left by the parallel folds), and then use the square paper Fold at an angle with the center point as the top. Make one corner of the folded part coincide with the parallel fold crease of the unfolded part. Then the folded corner must be 60". In this way, this square paper can be made without any Measuring tool, the three-fold is completed accurately. Some other folding methods are based on this folding method and further apply the principles of fuzzy mathematics to design free-hand folding, such as fifty-fold, seventy-fold, ninety-fold, no matter how you design or There will be some errors more or less. When we design the folding method, we only need to control the errors within the allowable range of the design.
