Phil Jackman, author of Collected Wisdom.Louie Palu/The Globe and Mail
Welcome to Collected Wisdom's brute-force origami class. First, take this sheet of paper and fold it in half eight times …
THE QUESTION: Is there a formula that explains why you can't fold a piece of paper in half more than seven times? Lynn Snider of Burlington, Ont., wants to know.
THE ANSWER: "There are two things that need to be taken into account when folding paper (or any thin material) in half repeatedly," writes Brett Stevens, an associate professor in the school of mathematics and statistics at Carleton University in Ottawa. "The first is obviously the thickness; when repeatedly folding in half, you are doubling the thickness each time. Even something very thin will get very thick very fast when doubling."
Indeed it will, says Steve White of Seattle. "When you get to seven folds, you have a thickness of 128 times the original thickness." At this point, he writes, a normal piece of letter paper will be virtually all "fold."
Back to Prof. Stevens: He says the second thing you have to keep track of is the additional paper you will need to form the outer layers of paper in each fold. "They need to be longer to fold around the inner layers (much as the outside path in the curved part of a racetrack is longer than the inside track)."
He points out that high-school student Britney Gallivan of Pomona, Calif., worked out the precise relationship of these factors in 2001 and found that if she took the thickness and additional length into consideration, she could fold a very long piece of toilet paper in half 12 times.
Mr. White agrees that you can fold more than seven times. "The secret is to get a paper size that's very large compared with its thickness. Like this newspaper. Open a normal double-page sheet … and start folding," he says, and you should be able to do it eight times, proving that seven folds is not a universal limit.
CW tried this with part of the Sports section. We did manage eight folds, but the last one almost gave us a hernia.
FURTHER NOTICE
Last week, while talking about trucking, we said that one tractor pulling two trailers uses just 30 per cent more fuel than it would pulling one trailer, a fuel saving of 70 per cent over two tractors pulling one trailer each.
However, Patrick Flanagan of Huntsville, Ont., points out that our math was a bit wonky.
He uses this example: A tractor pulling a single trailer burns 100 units of fuel, two tractors each pulling a single trailer burn 200 units of fuel in total, and a tractor pulling two trailers burns 130 units of fuel. Therefore, the tractor pulling two trailers saves 70 units of fuel, so the percentage saving is 70 divided by 200 and multiplied by 100 - 35 per cent, not 70 per cent.
HELP WANTED
- Why are sports scores in North America always listed with the visiting team first? In European soccer, the home team is always listed first, says Nick Hoekstra of Powell River, B.C. Why the difference?
- Why were so many old farm houses in rural Ontario built so far back from the road? Jean Macintosh of Brockville, Ont., wants to know.
Send answers and questions to wisdom@globeandmail.com . Please include your name, location and a daytime phone number.