Nakamura can open 9 origami, to answer the question of how many origami can be opened in Nakamura, we need to understand what origami is and how it works.
Offsetting paper, that is, a flat piece of paper by folding and bending, to make a variety of shapes and forms of handicrafts. In origami, we can fold along the diagonal lines, midpoint lines, etc. of the paper, which creates more symmetry and repetition. In the formal rules of origami, the most basic fold is to fold the paper in half one at a time, i.e. folding in half.
It is a second fold, where the paper is folded again over the folded paper, and the paper is folded into four equal parts. And so on, three folds are eight equal parts, four folds are sixteen equal parts, and so on. Therefore, we can conclude that by making n folds, the paper will end up being folded into 2 equal parts.
And in the problem, we ask Nakamura to open several folds of the paper, which is actually folding the given paper and then cutting out a part of the paper. Assuming that the area of the cut off part is x times the area of the original paper, the original paper is left with an area of (1-x). And what we require is that the paper is finally folded into several equal parts of the original paper, that is, the required number of equal parts is 2n.
Based on the above principle, we can get the following equation: (1-x) = (2=n) multiplied by x, that is, the remaining area of the original paper is equal to k times the area of several equal parts. Solving the equation gives us: x = 1/(2n+1). Since we want the remaining area to be the cut portion, the remaining area must be less than 1, i.e., x < 1.
Therefore, in order to make sure that the value of n is an integer, we need to make sure that x > 1/(2n+1) > 1/2n. The paper will have enough area to be cut and folded into several equal portions only if x > 1/2n. Since the question does not give the exact size of the paper or the number of fractions required, we can base our calculations on this principle. Assuming that we want the paper to be folded into 3 equal parts at the end, which means that 2n = 3, then the value of n should be n = log3/log2. Bringing this into the calculation gives us n ≈ 1.58496.
Development and application of origami
Offsetting is an ancient and interesting handicraft, and it is a very important part of the art form. an ancient and interesting craft art that originated in China and has spread widely across the globe. Over time, origami has evolved from a purely recreational activity into a diverse and creative art form. In addition to entertainment and creativity, origami has practical applications in various fields.
In the field of education, origami is widely used in kindergarten and elementary school art programs. By making animals, plants and objects in various forms, children can develop hands-on skills, spatial imagination and creative thinking. In addition, origami can also teach math knowledge such as geometric concepts, proportions and symmetry.
Offset paper is also used in scientific research. Scientists utilize the foldability and specific configurations of paper to use it in the design and fabrication of miniature devices, such as foldable solar cells, foldable medical devices, and micro-robots. These applications allow scientists to mold complex structures into compact forms and provide convenience and flexibility for research in a variety of fields. In addition, origami has demonstrated a wide range of applications in engineering and design.