.

This machine can only be folded nine times.

Just do the math. If the thickness of the paper reaches half of the folding surface, it is difficult to fold, so it can be inferred that if the paper is square, its side length is a and its thickness is h, when it is folded once, its side length is unchanged, and its thickness is 2 times h, when it is folded twice, its side length is half of the original side length, and its thickness becomes 4 times h, among which it is also folded, and a formula can be deduced: when the number of folds is even, it is 2/3. According to the general paper situation, when the thickness is about 0. 1mm and the side length is 1m, according to the above formula, n >:8. 19 18 cannot be folded, that is to say, the thickness is about 0. 1mm and the side length is/. When considering a large piece of paper with constant thickness and side length 1Km, according to the above formula, N >；; 14.8357 cannot be folded, that is, 14 times can only be folded. So the number of folds is related to the value of l/h. If L/H is infinite, then its logarithm is infinite, and the number of natural folds is infinite. Of course, these are all theoretical conclusions. As for whether or not such a large piece of paper can be folded, how to fold it is impossible to demonstrate.

One last question, if a piece of paper with 1 mm is folded 100 times, its thickness can be calculated as 2 100 * 0.005438+0 m = 65438+65438.5008808886

Theoretically, if the thickness of paper is zero, it can be folded in half countless times. However, due to the actual thickness of the paper, this theory does not exist, because the width of the folded paper cannot be less than or equal to the thickness of the paper, that is, a piece of paper with a thickness of 1 mm should be greater than1mm.

So how many times a piece of paper can be folded in half at most is actually a variable, depending on the actual thickness and size of the paper. Folding a piece of paper with a thickness of 1mm in half for 100 times can exceed the distance from the earth to the moon, which is just an unrealistic mathematical theoretical reasoning diagram.

According to the actual calculation, the size of the base paper of the new board is 840mm× 1 188mm (that is, the size of 16 sheets of A4 paper). If the paper thickness is 1mm, the size of paper folding 1 time should be 840mm×593.5mm (including 0.5). The actual size of two folds is 593.5mm×4 19.5mm, and the size of three folds is 295.75mm× 41mm. Theoretically, the paper size should be 3.28 125mm×3.330625mm when it is folded for the 16th time (excluding the loss of folding edge). However, if the folding loss is calculated, it can only be folded for the 12th time.