Spinning With Rubik's Cube Speedcubers
From Nation, For Nation - Pulse of the Nation
Are Bionic Jellyfish the Key to Exploring the Depths of the Ocean?
How to Fold a Piece of Paper in Half More Than Seven Times
Although doing so is mightily difficult and can take some clever thinking, many people still believe it is impossible to fold a piece of paper in half more than seven times. In truth, it can be and has been done, though you’re not likely to be able to achieve this feat without help.
Why Seven Times?
For many years, school children were told they couldn’t fold any piece of paper (no matter how long or thick) more than seven times. The belief was it would be mathematically impossible to do so. In most instances upon hearing this assertion, kids were baffled, tried it, found it to be true on their one and only attempt, and then never thought about it again.
The reason for this is two-fold: most people who tried it all used the same general type of paper, and they weren’t willing to try more than once or think outside the box.
A regular piece of paper is about 300 mm long and .05 mm thick. When you fold it in half, you divide the length in half and double the thickness (150 mm and .1 mm, respectively). As your folding continues, you make the paper shorter but thicker, making it harder and harder to achieve a fold.
Still, not everyone was stumped during their school years by this seemingly impossible task.
Britney Gallivan, Paper Folder and Mathematician
Like most kids, Britney Gallivan of Pomona, California was told this myth, but she correctly believed more than seven folds could be achieved with the right combination of factors. In 2002, when she was a junior in high school, Britney and her friends used a unique type of toilet paper to create a piece of paper that was 4,000 ft or 1,200 m in length. From it, they were able get 12 folds!
But that wasn’t the end of Britney’s tale. She even created her own equation where t represents the paper’s thickness or width and the answer, L, will provide you with how long the paper will need to be in order to be able to fold it.
paper fold theorem
One of the ways in which Britney thought outside the box was this: who ever said the paper had to be folded in alternating directions? As such, Britney’s equation is specifically designed for folding paper in the same direction each time. Since then, her story was mentioned on several TV shows, and in 2006, she was the keynote speaker at the convention for the National Council of Teachers of Mathematics. A year later, she graduated from the University of California, Berkley with an environmental science degree.
Try It Yourself!
After Britney’s triumph, others have taken cues from her and also managed to fold a single piece of paper more than 7 times. The current record is 13 folds, held by several students from St. Mark’s School in Massachusetts. They used 54,000 ft of toilet paper to achieve this feat!
Let this be a lesson, then, to all of us: things that seem impossible may instead be achievable with the help of several friends, some tenacity, and a healthy skepticism about long-held beliefs in unproven concepts.
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From Globe, For Globe - Pulse of the Planet
Twinkle, twinkle, little star? Not exactly.
Do Stars Twinkle?
“Twinkle, twinkle, little star.” They must get tired of us saying that to them because the truth is stars actually don’t twinkle. Even though you can look outside at night and see the flashing of different levels of light emanating from the same star, what you’re really seeing is interference from the atmosphere making the stars look like they’re twinkling when they’re not.
What Is Astronomical Scintillation?
Astronomical scintillation is the technical term for what we are seeing when the stars seem to twinkle. It’s actually caused by the atmosphere, which is made up of several different layers. The different layers have different temperatures, densities, and other variables that cause the light coming from a faraway star to bend and refract, causing changes in the way it looks.
The star is extremely far away with all of its light coming from a very small, very fixed point. This is why, when we look at the night sky and a star that is shining its light through our atmosphere from very far away, we see the light change and shift.
Why Don’t Planets Twinkle?
If we see stars through the same atmosphere as the planets we see, why don’t planets appear to twinkle? The truth is that planets are affected in exactly the same way as stars, and they do undergo the twinkle or astronomical scintillation effect. But when we’re looking at them, we don’t notice it like we do when we look at the stars.
This is because planets are much closer to us than stars are, so they look bigger, rather than like one pinpoint of light. The scintillation or twinkling rarely happens over the entire surface of the planet in the same way at the same time, so it seems fixed and unmoving. The stars, however, are so far away that we barely see any light from them at all: just a little dot in the sky. This makes them more vulnerable to the refraction effects caused by the atmosphere.
Our Atmosphere’s Effects on Stars
Our atmosphere does a great job of protecting us and making our planet habitable. However, it sometimes annoys astronomers that it’s so difficult to see stars as a stationary point because of the atmosphere. This is why telescopes now exist with technology specifically designed to de-twinklefy the stars so scientists can better see them.
The Keck observatory uses data from multiple telescopes to de-twinkle stars.
What’s more, it’s why the famously crisp photos taken by the Hubble telescope are such a phenomenon. It may look strange to see stars that don’t twinkle, but in space, there is no atmosphere, allowing us to see the stars in their natural state, free from that pretty but circumstantial effect.
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