Eli5: Why can you only fold a paper in half seven times, no matter the size ?
In: 4
You can fold it more than 7 times. That’s not a hard limit. The higher surface area to thickness ratio you have the more times you’ll be able to fold.
But the more you fold it, the more it turns into wrapping the paper around itself.
Lets say you have a square piece of paper that is 100 mm x 100 mm. Its also 1mm thick. Commonly used math would tell you the first fold would result in a 100mm x 50 mm piece that is now 2 mm thick. But that’s not correct. The fold itself is still connected together. It will contain a little over 2 mm -ish of material (top edge to bottom edge along a curve). So you have closer to 100 mm x 49 mm. (49 + 49 = 98, so 2 mm missing)
*Edit to add that the first fold doesn’t normally use that much material since you can crease the paper, which breaks the fibers so it doesn’t actually curve the entire outer diameter. Later folds don’t crease though, so its useful for explaining whats happening.
Second fold. Common math says that you will end up with 50 mm x 50 mm that is 4 mm thick. But the fold is now even worse than the first fold. Its layered. The inside layer is similar to the first and uses a similar amount of material. The outside layer has to wrap around the inside though. So its going to use up roughly twice the material as the first fold. You end up with roughly 48 mm x 49 mm that is 4 mm thick. And the edges of this fold don’t line up. Because its only the OUTSIDE layer of that fold that is 48 mm. The inside is 49. This creates a lot of stress in the paper where its still connected and trying compress and stretch to make the folds.
The more folds you do, the worse the situation gets. You have a greater difference in the amount needed to make the fold for the inside layer vs the outside layer. Very quickly the outer layer no longer has enough material to cover much of the inner layers and you eventually reach the point where the material needed just to connect the top layer to the bottom layer is more than the material available for that layer. You have 12.5 mm of material for the layer left, but the stack is now 32 mm tall.
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