- You take a standard thickness piece of paper (0.1mm) and fold it in half. Then you fold the resulting piece it in half, and again, and so on until you have made 50 folds in all. How thick do you think the stack will be after these 50 folds? Are you naturally intuitive with math? How close was your ‘intuitive’ answer compared to your calculated answer? (For simplicity let’s assume the paper is large enough to easily fold 50 times, and it folds smoothly without creases or bulges).
112589990.684262 KM thick.
Myth busters did the fold over, I believe seven times with a football sized piece of paper and barely got it done. I think we are looking at a solar system sized piece of paper to have anything close to 50 folds.
~Matt
4.19.10^21mm
.
The equation is actually pi x thickness 2^(3(n-1)/2)) where n is the number of folds
.
The equation is actually pi x thickness 2^(3(n-1)/2)) where n is the number of folds
Equation for what? The thickness or the size of the paper you need? I just took the size and continued to double it 50 times to get the thickness. Each time you fold it it doubles in thickness. I have no clue how you’d arrive at an equation for the size of paper needed. I just know it’s gonna be big 
~Matt
The thickness after folding. You can’t just double the size. I’ll let you figure out why…
Hint: there is a pi in the equation 
And the size is S = pi.t/6 x (2^n+4)(2^n-1)
.
“you can’t just double the size”
I think we need a ruling from the OP. From his instructions, it seems that is what he is inferring. Maybe not, and the OP figures that the rounded edge adds thickness. If so, only you mathz dudes can play?
I felt the the purpose of the puzzle was to show how far off our intuitive guess was.
The thickness after folding. You can’t just double the size. I’ll let you figure out why…
I think you’re going to have to tell me. Piece of paper, just measured, .0037. Folded in half .00745, Pretty close to double. Again, .01465. Again .02925…I’m seeing a pattern. It is slightly larger directly on the fold, .02945 or so. One would assume because the paper is not completely compressed there. Assuming that the corners are compressed, it is paper and will break down, the thickness should double across the entire area.
Maybe this is one of those theoretical versus real world issues.
~Matt
At the edge you actually add the half circumference of a (very small) circle. There are a couple of papers out on the topic. Never checked the maths really since
I don’t really see the interest, but I do remember stuff like equations.
When the OP stated that we should assume tha paper folds smoothly with no creases or bulges, I think he was implying that we should discount any additional depth added by anything other than the thickness of the paper itself.
(.1mm) * (2**50)
but Matt beat me to it.
When the OP stated that we should assume tha paper folds smoothly with no creases or bulges, I think he was implying that we should discount any additional depth added by anything other than the thickness of the paper itself.
This ^^^^ was my operating assumption as well. It’s no different than cutting the stack into two halves (rather than folding) and placing the halves on top of one another. I didn’t put any additional thought into it and came up with the ~112.6E06 km.
112589990.684262 KM thick.
Myth busters did the fold over, I believe seven times with a football sized piece of paper and barely got it done. I think we are looking at a solar system sized piece of paper to have anything close to 50 folds.
~Matt
Is this a trick? I thought it was impossible to fold a piece of paper more than 7 times?
That’s a myth. The size of the paper grows exponentially with the number of folds required though.
“you can’t just double the size”
I think we need a ruling from the OP. From his instructions, it seems that is what he is inferring. Maybe not, and the OP figures that the rounded edge adds thickness. If so, only you mathz dudes can play?
I felt the the purpose of the puzzle was to show how far off our intuitive guess was.
OP here… including curvature into the problem is a far more advanced query than a simple engineer like me could conceive. I’ll leave that sort of painful permutation to you S&M types (that’s Stats and Maths).
112589990.684262 KM thick.
Myth busters did the fold over, I believe seven times with a football sized piece of paper and barely got it done. I think we are looking at a solar system sized piece of paper to have anything close to 50 folds.
~Matt
Is this a trick? I thought it was impossible to fold a piece of paper more than 7 times?
This is the correct answer. Regardless of the size of the paper.
I fold my infinitessimally thin piece of paper 50 times and it is 0 mm thick.
I think you’re going to have to tell me. Piece of paper, just measured, .0037. Folded in half .00745, Pretty close to double.
What do you do for work that you have tools to get those precise measures? Whatever it is, sweet.
Maybe this is one of those theoretical versus real world issues.
In theory, theory and practice are the same
Your paper’s thickness is converging to 0 faster than 2^n?