Folding a Paper in Half... Repeatedly

I remember the dare from childhood that said nobody can fold a piece of paper 7 times. I tried and failed, of course. Since nobody else seemed able to do it either, I assumed it had to do with strength (or rather, the lack of it).

 

But that’s not the answer, explains Steven Strogatz in The Joy of x. The reason is more prosaic:

“Each folding approximately doubles the thickness of the wad, causing it to grow exponentially (1, 2, 4, 8, 16…). Meanwhile, the wad’s length shrinks in half every time, and thus decreases exponentially fast (1, ½, ¼, 1/8…)”

That much is obvious. But here’s the next step in the train of thought that most of us don’t think of:

“For a standard sheet of notebook paper, after seven folds, the wad becomes thicker than it is long, so it can’t be folded again. It doesn’t matter how strong the person doing the folding is… (It) can’t happen if the wad is thicker than it is long.”

 

Britney Gallivan, in high school, derived the formula for how many times a piece of paper can be folded!


Where L = length of the paper, T = thickness of the paper, n = number of times it can be folded.

 

She then went and bought a really long of toilet paper, unrolled it, and with the help of her parents, “smashed the world record by folding the paper in half twelve times”!

 

Who’d have thought this was a maths problem, not a strength problem?!

Comments

Post a Comment

Popular posts from this blog

Student of the Year

Image
As a toddler, my daughter loved Alia Bhatt’s songs, esp. the ones from Student of the Year . (That movie did have many good songs and well-choreographed dances). Fast forward to present day, when she is 12 yo. She rarely watches Hindi movies now, but one of the few ones she likes of late, Raja aur Rani ki Prem Kahani has, yes, Alia Bhatt.   If I had any hopes that there was anything to be read in the name of her toddler-time favorite ( Student of the Year ), they have been dashed. Our conversations come exam time are perfectly captured by this photo and its caption: In fact, the pic below captures how she and I look at her answer sheets – me intently, she with an expression of “It’s over, so why are you even looking at it?”   Of late, we pull her leg and tell her that she isn’t showing any signs of academic prowess, she’d better find a rich guy to marry. Some time later, she showed us this meme on the Internet: “Me No Study, Me No Care Me Go Marry Millionaire If He Die
Read more

Animal Senses #7: Touch and Remote Touch

Instinctively, we think touch is based on contact. Not entirely true, explains Ed Yong in Immense World – there’s a more important aspect than contact: “These incredible feats are possible through movement. If you rest a fingertip upon a surface, you can get only a limited idea of its features. But as soon you’re allowed to move, everything changes. Hardness becomes apparent with a press. Textures resolve at a stroke.” As you run your fingers over a surface, they hit the tiny peaks and troughs and set off vibrations in the mechanoreceptors at their tips.   At the tip of its snout, the star-nosed mole has many pairs of hairless appendages. It uses them to touch things around itself. Alive or dead? Food or ignore? It does these movements at an insane speed. In the time it takes to blink our eyes, the star-nosed mole can probe, identify and swallow its food. “Light may be the fastest thing in the universe, but light sensors have their limits, and the star-nosed mole’s sense of
Read more

The Retort of the "Luxury Person"

Image
Coming up with biting and witty retorts. It’s something we dream of, but rarely manage to pull off. Worse, the more we stew over the offending remark, the more likely we are to come up with that dream retort, as Calvin ruefully points out: During our last holiday at the Taj Resort, seeing my wife carrying towels to our poolside chairs, one of the kids there mistook her for a member of the staff and asked for a towel. When my wife narrated this to us, I did not imagine that my 8 yo daughter would come up with her own retort. But a day later, my daughter recapped the incident, an incident that didn’t even involve her in the first place , and said, “You know what I’d have told that kid who asked for the towel?”. And without waiting for an answer, she told us anyway: “I don’t work here. I too am a luxury person who is living at this resort. Go get your own towel.” We were highly amused by the phrase she had coined: “luxury person”. It certainly captures the kind of holid
Read more