Rooster Origami Folding

Assume that a clean sheet of paper is uniformly elastic. Before answering the given problem, consider symmetric folds. For each time a paper is folded, the amount of layers is doubled. For instance, if you start with a clean sheet of paper as shown in the illustration, and you fold it in half, this forms extra layer, which increases its elasticity and volume stress. Relative to the folding line, folding decreases the size of the shapes. Therefore, increasing multiple layers require a lot of force.

There is also a mathematical discovery of folding by Britney Gallivan on 2002 during her education. The equation of the required length of the strip $L$ is $L = \dfrac{\pi}{6}t\left(2^n + 4\right)\left(2^n - 1\right)$ where $t$ represents material thickness and $n$ represents the folds needed. The relationships are that:

• The greater the value of $n$ , the larger the value of $L$ .
• The greater the value of $t$ , the greater the value of $L$ .

Since $L$ depends on both $n$ and $t$ , the folding difficulty relates to these variables. Keeping $n$ and $t$ constant, then we see that $L$ is the minimum bound of the paper length. So if the length of the strip is less than $L$ , then it is difficult for a human to fold the paper, which relates to the given problem.

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