Paper folding

From Wikipedia, the free encyclopedia

Paper folding is the art of folding paper; it is known in many societies that use paper. In much of the West, the term origami is used synonymously with paper folding, though the term properly only refers to the art of paper folding in Japan.

Forms of paper folding:

• Zhezhi, Chinese paper folding
• Origami, from Japan
• Western paper folding, such as the traditional paper boats and paper planes.

Contents 1 The claim of the seven fold limit 2 Mathematical Explanation to Belief 3 See also 4 Notes

[edit] The claim of the seven fold limit

A popular belief holds that it is impossible to fold a sheet of paper in half more than 7 times, possibly due to the difficulty of performing even 6 folds. This belief was debunked by then high school student Britney Gallivan who successfully folded a piece of paper 12 times in "Single Direction Folding".^[1] However, some argued that the folder should fold in half, turn 90 degrees, then fold in half again, rather than folding the same way.

The television series MythBusters "busted the myth" of the 7 fold limit by folding taped-together sheets in half and turning 90 degrees each time, for a total of 11 folds. The first eight folds were completed by hand, while the rest were completed using both steam rollers and fork lifts. ^[2][3] This was accomplished using 17 large rolls of paper taped together to form a very large yet relatively thin "sheet."

One of the reasons why high-fold-count paper folding is so difficult is that the height, and thus width of the paper required and height of the successive folds, grow exponentially. Folding a piece of paper in half 100 times, if it were possible, would produce a stack of paper approximately 8×10²² miles in height.^[4]

[edit] Mathematical Explanation to Belief

To fold a paper, the length of the side that is folded must be at least twice as long as the thickness of the paper that is folded. Let the length and thickness of the paper after 'n' folds be l_n and t_n. If we are to fold the paper 15 times, then

But,

Hence,

Since it is practically impossible to get a sheet of paper whose length is 2³¹ times (or 10⁹ times) its thickness, it is believed that there is a finite limit to the number of times a paper can be folded.

[edit] See also

• Mathematics of paper folding
• Book folding

[edit] Notes

1. ^ "Folding Paper in Half 12 Times". http://pomonahistorical.org/12times.htm. 
2. ^ MythBusters: Underwater Car Episode Trivia - TV.com
3. ^ NASA - This Week at NASA, Week Ending Nov. 17, 2006
4. ^ Derivatives of Transcendental Functions (PDF)