The limit of folding paper in half is a physical phenomenon, the essence of which is that a sheet of plain A4 paper can be folded in half no more than 7 times. It occurs due to the rapid growth of exponential function .
The number of paper layers equals two to the power of n , where n is the number of paper folds. For example: if the paper is folded in half five times, then the number of layers will be two to the power of five, that is, thirty-two.
Content
Phenomenon Equations
Equation for plain paper [1] :
where W is the width of the square sheet, t is the thickness of the sheet, and n is the number of double bends performed.
When using a long strip of paper, the exact value of the length L [1] is required:
where L is the minimum possible length of the material, t is the thickness of the sheet, and n is the number of double bends performed. L and t must be expressed in the same units.
Research
In 2001, American Britney Gallivan , then a schoolgirl, developed a mathematical model for folding paper [1] . She managed to fold the sheet 12 times, however, from a sufficiently thin and flexible gold foil .
On January 24, 2007, in the 72nd episode (season 5, episode 3) of the television show Legend Destroyers , a team of researchers attempted to refute the law [2] . They formulated it more precisely:
Even a very large dry sheet of paper cannot be folded twice more than seven times, making each of the folds perpendicular to the previous one.
On a regular sheet of A4, the law was confirmed, then the researchers checked the law on a huge sheet of paper. They managed to fold a sheet half the size of a football field (51.8 × 67.1 m) 8 times without special tools (11 times using an ice rink and a loader ). According to the fans of the TV show, tracing paper for packaging offset printing form format 520 × 380 mm with rather careless folding effortlessly folds eight times, with effort - nine.
An ordinary paper napkin is folded 8 times [3] , if you break the condition and fold it once not perpendicular to the previous one (the fifth after the fourth roller).
Appearance Conditions
The limitation of folding paper in half occurs when:
- paper size is within the format A (from A0 to A8);
- when folding do not use any technical means.
See also
- The problem of grains on a chessboard
- Math origami
- Flexagon
Notes
- ↑ 1 2 3 “A record from scratch: paper is dealt 12 times” , membrana.ru, November 17, 2005.
- ↑ Mythbusters: Episode Guide (inaccessible link) . Date of treatment August 13, 2008. Archived August 14, 2008.
- ↑ Sheet of paper, folded eight times.
Links
- Weisstein, Eric W. Folding on Wolfram MathWorld .
- Issue 72 of the program “ Legend Destroyers ”, in which the experience “Fold the paper seven times” is held