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This Puzzling Math Brain Teaser Has a Simple Solution

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Fans of number-based brainteasers might find themselves pleasantly stumped by the following question, posed by TED-Ed’s Alex Gendler: Which sequence of integers comes next?

1, 11, 21, 1211, 111221, ?

Mathematicians may recognize this pattern as a specific type of number sequence—called a “look-and-say sequence"—that yields a distinct pattern. As for those who aren't number enthusiasts, they should try reading the numbers they see aloud (so that 1 becomes "one one," 11 is "two ones," 21 is "one two, one one,” and so on) to figure the answer.

Still can’t crack the code? Learn the surprisingly simple secret to solving the sequence by watching the video below.

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entertainment
Why the Film You're Watching on HBO Might Not Be the Whole Movie
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In the days before widescreen televisions, most of the movies you watched on VHS or on cable looked a little different than their big-screen versions. The sides of the image had to be cropped out so that you could watch a movie made for a rectangular screen on the small screen. Today, those little black bars on the top and bottom of the screen that allow you to watch the same movie scaled to any shape of screen are everywhere. But it turns out, cropping for aspect ratios is alive and well—on HBO, as YouTube film vlogger Patrick Willems explains.

In his latest video, which we spotted on Digg, Willems explains why aspect ratios matter, and how the commonly used aspect ratios can fundamentally change a movie.

Most old-school televisions have 4:3 aspect ratios, meaning movies had to be significantly cropped to fit wide-screen films on the small screen. Now, most computers and televisions use 16:9 aspect ratios, which is approximately the same as the one used for movies, typically 1.85:1, so many movies expand to fit TV screens perfectly. The catch: Some Hollywood movies are shot with even wider angles to show even more of an image at once. And even though viewers are familiar with the sight of those black bars, it seems the streaming sites are determined to limit their use, even for movies that don’t fit on a normal screen. As a result, you may only be seeing the central part of the image, not the whole thing. You could be missing characters, action, and landscape that’s happening on the far sides of the screen.

Since 1993, the Motion Picture Association of America has mandated that any film that’s been altered in a way that changes the original vision of its creators—say, to edit out swear words, adjust the run time, or to make it fit a certain screen—run with a disclaimer that says as much. That’s why before movies run on TV, they usually show a note that says something like “This film has been modified from its original version. It has been formatted to fit this screen.” But this doesn’t seem to apply to streaming.

In 2013, Netflix was accused of cropping films, too, showing wide-angle movies to fit the standard 16:9 screen instead of running the original version with black bars. The streaming giant claimed it was a mistake due to distributors sending them the cropped version, and those films would be replaced with the originals. However, as of 2015, users were still complaining of the problem. According to Willems, it’s a problem that still plagues not just HBO, but Starz and Hulu, too, and there isn’t any clear rationale for it other than that perhaps people don’t like looking at black bars. But frankly, that seems better than seeing a version of a film that the director never intended.

You can get all the details in the video below:

[h/t Digg]

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The Prehistoric Bacteria That Helped Create Our Cells Billions of Years Ago
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We owe the existence of our cells—the very building blocks of life—to a chance relationship between bacteria that occurred more than 2 billion years ago. Flash back to Bio 101, and you might remember that humans, plants, and animals have complex eukaryotic cells, with nucleus-bound DNA, instead of single-celled prokaryotic cells. These contain specialized organelles such as the mitochondria—the cell’s powerhouse—and the chloroplast, which converts sunlight into sugar in plants.

Mitochondria and chloroplasts both look and behave a lot like bacteria, and they also share similar genes. This isn’t a coincidence: Scientists believe these specialized cell subunits are descendants of free-living prehistoric bacteria that somehow merged together to form one. Over time, they became part of our basic biological units—and you can learn how by watching PBS Eons’s latest video below.

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