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Sagot :
Sure! Folding a flat square of paper one or more times and then punching a hole through it can create various hole patterns depending on the number and type of folds you make. Let's explore this step-by-step for different numbers and types of folds.
1. Folding Once:
- Suppose you take a flat square of paper and fold it in half. For example, fold it once from left to right.
- If you punch a hole through the folded paper, the punch will go through two layers of the paper.
- When you unfold the paper, you will see two holes. They will be symmetric around the fold line.
2. Folding Twice:
- Now, let's fold the paper twice. For instance, first fold it in half from left to right, and then fold it again in half from bottom to top.
- If you punch a hole through the folded paper, the punch will go through four layers of paper.
- When you unfold the paper, you will see four holes. They will be arranged in a square pattern and will show symmetry along both fold lines.
3. Folding Three Times:
- Suppose you fold the paper three times. This could be done by folding in half from left to right, then bottom to top, and then again from left to right.
- If you punch a hole through the folded paper, the punch will go through eight layers of paper.
- When you unfold the paper, you will see eight holes. The distribution of the holes will display symmetry, forming a pattern based on the folds.
4. Folding Four Times:
- If you fold the paper four times, for example by folding in half from left to right, bottom to top, left to right again, and then bottom to top again.
- Then, you punch a hole through the folded paper. The punch will go through sixteen layers of paper.
- Upon unfolding, you will see sixteen holes. Their arrangement will be even more complex showing symmetrical patterns based on all the fold lines.
5. Folding Five Times:
- For five folds, suppose you fold in half in a similar pattern of alternating directions.
- Punching a hole through the folded paper will now go through thirty-two layers of paper.
- When you unfold it, thirty-two holes will be visible, showing an intricate pattern based on the fold symmetries.
To summarize, the placement and number of holes after unfolding depend on the initial number and orientation of folds. Each additional fold increases the number of paper layers the hole punch goes through, leading to more holes in a complex, symmetrical pattern when unfolded.
1. Folding Once:
- Suppose you take a flat square of paper and fold it in half. For example, fold it once from left to right.
- If you punch a hole through the folded paper, the punch will go through two layers of the paper.
- When you unfold the paper, you will see two holes. They will be symmetric around the fold line.
2. Folding Twice:
- Now, let's fold the paper twice. For instance, first fold it in half from left to right, and then fold it again in half from bottom to top.
- If you punch a hole through the folded paper, the punch will go through four layers of paper.
- When you unfold the paper, you will see four holes. They will be arranged in a square pattern and will show symmetry along both fold lines.
3. Folding Three Times:
- Suppose you fold the paper three times. This could be done by folding in half from left to right, then bottom to top, and then again from left to right.
- If you punch a hole through the folded paper, the punch will go through eight layers of paper.
- When you unfold the paper, you will see eight holes. The distribution of the holes will display symmetry, forming a pattern based on the folds.
4. Folding Four Times:
- If you fold the paper four times, for example by folding in half from left to right, bottom to top, left to right again, and then bottom to top again.
- Then, you punch a hole through the folded paper. The punch will go through sixteen layers of paper.
- Upon unfolding, you will see sixteen holes. Their arrangement will be even more complex showing symmetrical patterns based on all the fold lines.
5. Folding Five Times:
- For five folds, suppose you fold in half in a similar pattern of alternating directions.
- Punching a hole through the folded paper will now go through thirty-two layers of paper.
- When you unfold it, thirty-two holes will be visible, showing an intricate pattern based on the fold symmetries.
To summarize, the placement and number of holes after unfolding depend on the initial number and orientation of folds. Each additional fold increases the number of paper layers the hole punch goes through, leading to more holes in a complex, symmetrical pattern when unfolded.
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