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How to Wrap a Present With Mathematical Precision

It's not hard to wrap a box if you don't care how much wrapping paper or tape you use, but what if you care about efficiency? What if your aim is to use only what you need?

Mathematician Sara Santos, who specializes in finding entertaining ways to popularize math, worked out the formula for a wrap that uses paper and tape most efficiently. If you have a three dimensional box you can solve for the dimensions of the two dimensional square of paper that makes for the best wrap.

For a square box, it works out to be the diagonal added to one and a half times the height of the box. This video by Aimee Daniells offers a beautiful demonstration:

For a rectangular box, things get more complicated. You can still figure it out by solving for the following:

Not only does the power of math let you optimize for paper and tape usage, it also lets you prettily match up the pattern on the wrapping paper where the edges meet. Check out the magic at the 3 minute mark on this video from BBC's The One Show:

Now get out your rulers, spreadsheets, and calculators, and get to work on your most satisfyingly exact giftwrapping season ever!

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The Evolution of "Two" in the Indo-European Language Family
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The Indo-European language family includes most of the languages of Europe as well as many languages in Asia. There is a long research tradition that has shown, though careful historical comparison, that languages spanning a huge linguistic and geographical range, from French to Greek to Russian to Hindi to Persian, are all related to each other and sprung from a common source, Proto-Indo-European. One of the techniques for studying the relationship of the different languages to each other is to look at the similarities between individual words and work out the sound changes that led from one language to the next.

This diagram, submitted to Reddit by user IronChestplate1, shows the word for two in various Indo-European languages. (The “proto” versions, marked with an asterisk, are hypothesized forms, built by working backward from historical evidence.) The languages cluster around certain common features, but the words are all strikingly similar, especially when you consider the words for two in languages outside the Indo-European family: iki (Turkish), èjì (Yoruba), ni (Japanese), kaksi (Finnish), etc. There are many possible forms two could take, but in this particular group of languages it is extremely limited. What are the chances of that happening by accident? Once you see it laid out like this, it doesn’t take much to put *dwóh and *dwóh together.

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infographics
Beyond Plumbing: 19 Other Jobs on Mario's Resume
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Nintendo made news this week by subtly announcing that Mario is no longer a plumber. In fact, they're really downplaying his whole plumbing career. On the character's Japanese-language bio, the company says, "He also seems to have worked as a plumber a long time ago."

But Mario has always had plenty of jobs on the side. Here's a look at his resume:

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