Easy Way to Fold Paper in Half and Half Again
Folding a slice of paper in one-half
By David, 29 October 2013
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This activity sounds super like shooting fish in a barrel from the title, but there'due south more than to it than you might wait!
You will need
Fold your sheet of paper pinnacle-to-bottom, then left-to-right.
- Sheet of A4 paper
- Coil of inexpensive toilet paper – the thinner the better
What to do
- Earlier you commencement, try answering this question: How many times do you think y'all could fold a piece of newspaper in one-half?
- Take the sheet of A4 paper and fold it in one-half.
- So fold it in one-half over again, and again, until yous tin can't fold it in half anymore.
- Recall how many times y'all folded it in one-half. Was it more or less than you expected?
- Detect a long infinite to whorl out the toilet paper – if it is very at-home, you might be able to practise this outside.
Find a long place to unroll your toilet newspaper.
- Roll out equally much paper as you lot can.
- Accept one finish of the paper and bring it back to the other end.
- Straighten the folded piece of newspaper.
- Now, take the folded terminate of the paper and bring it to the open ends of the length of newspaper. Straighten out the paper again.
- Proceed folding the paper in half in this style, until you can't fold it in half any more.
- How many times did you fold information technology in half? Was information technology more or less than y'all expected?
What's happening?
There are two things that are happening when you fold paper in half, and they both mean that the more folds you've fabricated, the harder it is to fold again.
Advisedly bring the terminate back to the start
Every fourth dimension yous fold a piece of newspaper in one-half, its surface area is halved. If y'all start out with an A4 sheet, and so after four or five folds, it starts getting quite minor. If you could fold it in one-half nine times, information technology would merely exist nearly one square centimetre in area!
The other problem you run into is that the newspaper keeps getting thicker. A piece of paper is very thin – the standard sheet of A4 newspaper is about 1/10 of a millimetre thick. But every time you fold the newspaper in one-half, you double the thickness. So afterwards ii folds, it's four times as thick as a single sail, and after iii folds, information technology's eight times thicker. After nine folds (if you brand information technology that far) information technology volition be 2 10 two x 2 x 2 x 2 x 2 10 two x ii x two = 512 times thicker. If a single sheet of newspaper is one/ten of a millimetre thick, then afterward you folded it nine times, it would be over 5 centimetres thick!
Applications
Did y'all end up with every bit many folds equally you predicted?
Information technology is oft said that it's not possible to fold a piece of newspaper in half more than seven times. In 2002, a loftier school student named Britney Gallivan proved it was possible to exercise a lot more than vii folds. Britney was challenged by her teacher to fold a canvas of paper in one-half 12 times. To help her understand the problem, she came up with two formulas working out how much newspaper you need to start with. One worked by folding in different directions, like yous would with a sheet of paper, and 1 where you keep folding in the same direction, like you would with a roll of toilet paper.
Her formula said that she needed a sheet that was a lot wider than it was thick, so she tried using a very thin canvass. Newspaper doesn't get much thinner than 1/10 of a millimetre, but gilt comes in sheets that are only a few atoms thick. Starting with a square about ten centimetres on each side, she managed to fold the gilt 12 times.
When she presented her solution to her teacher, the teacher said that she had to fold a piece of paper, not a sheet of gold. In order to make 12 folds in a slice of newspaper, she had to find a special roll of toilet paper that cost $85 and was one.2 kilometres long. Subsequently seven hours folding, she somewhen managed to get her paper folded in half 12 times.
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Source: https://blog.doublehelix.csiro.au/fold-paper-in-half/