What should a tablet look like? Or, put another way (since a tablet is basically a portable, touchable display): What should a tablet’s dimensions be? Whatever you’re picturing, it’s probably not what Google has in mind.

Measured diagonally, the 10.2-inch display on Google’s new Pixel C tablet is pretty comparable to the 9.7-inch iPad Air and 10.1-inch Fire HD. But what makes the Pixel C an innovative device isn't its crosswise measurement. It's the unusual ratio between its width and its height. No one’s going to mistake this thing for an iPad—and that’s exactly what Google wants.

I Knew Him, Ratio

To understand what makes the Pixel C both odd and seemingly effective, we need to talk about aspect ratios—the aspect ratios of tablets, specifically, which until now have fallen pretty definitively into two main camps. Apple has opted for a 4:3 ratio on every size and iteration of the iPad to date. It's a bit of a tradeoff. On one hand, the display is so tall that video playback requires the addition of distracting black letterboxes. But its height also makes web browsing easier, and increases the information density of apps. It’s also great for for displaying comic books and magazines.

That’s one way to do it, and, because of the iPad’s popularity, it's probably the most widely recognized. The other option, more common among both pure Android devices and Amazon’s Fire HD tablets, is to use a 16:9 or 16:10 aspect ratio, which gives you a display that’s either tall and skinny or long and short, depending on the device's orientation. These are also the same dimensions you find on an iMac, and most widescreen HDTVs.

With the Pixel C, Google has ignored both of these conventions. Instead, it's gone with an aspect ratio of 1:√2, which translates to about 1:1.41. It's done this not for the cheap thrill that comes from tossing around mathematical symbols, and it's not just being different for different’s sake. It’s just what happens, says Andrew Bowers, Google's director of consumer hardware, when you look at tablets with a fresh set of eyes.

“We’ve taken the approach of rather than using things off the shelf and standard in the industry, trying to come up with things that are better to use from a user standpoint,” explains Bowers. “One of the reasons we moved away from 16:9 or even 16:10 is because those were primarily driven by the TV industry, so it ended up on laptops, etc.”

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That skinnier form does work just fine for watching videos on a tablet. But tablets in general, and the Pixel C in particular, have a much broader range of potential uses in their sights. To accommodate all that the next generation of computing has to offer, one has to think outside the rectangle.

Hip to Be Squarer

As Google pointed out when it introduced the Pixel C, 1:√2 is the same aspect ratio used in international standard paper sizes like A4. (If you're reading this wondering what the hell A4 paper is, you might be from North America, where 8.5 x 11-inches is the go-to letter paper size.) But it's also pretty close to the display proportions on another Google product: the Chromebook Pixel. The Pixel's aspect ratio isn’t quite 1:√2, but at 3:2 it’s fairly close, and it, too, raised eyebrows for being so square when it first launched in 2013. But Bowers insists that these dimensions make sense, when you consider what people are actually using these devices for.

Because the Chromebook Pixel is a laptop, you basically use it in one orientation: landscape. "That’s where vertical real estate [afforded by a 3:2 aspect ratio] is really important," says Bowers, "for scrolling on a web page or an application." But a tablet you can use in two orientations, landscape or portrait. When you take a tablet with an aspect ratio of 16:9 and hold it in portrait mode, says Bowers, " it makes a lot of applications very narrow... so it’s a little bit harder to use." The Pixel C's 1:√2 ratio, he says, is meant to give you a little extra width when using it in portrait mode.

That extra vertical real estate when the tablet is in landscape mode will help define user experiences on the Pixel C. It makes the web more comfortable to roam, and not just for browsing, either; the spaciousness also makes web apps, which tend to scale better on a screen with those dimensions, more appealing. All of this suits Google's interests quite nicely—after all, the more time users spend on the web (as opposed to siloed apps), the more immersed they are in Google’s ecosystem.

There’s another property of the 1:√2 ratio worth mentioning. Remember that sheet of A4 paper? If you fold it in half vertically (i.e. hamburger-style) and cut along its crease, the two resulting rectangles will both have the same 1:√2 aspect ratio as the A4 rectangle from whence they came. Divide your two new rectangles in half again, and you’ll end up with four identical rectangles, each with a 1:√2 aspect ratio. You can keep doing this until your thumbs tire out. That’s not just the world’s most boring parlor trick; it has pretty clear implications for scalable, split-screen multitasking.

Putting It Together

Despite all of its apparent benefits, the 1:√2 aspect ratio is still a compromise on Google's part.

“We wanted something that was easy to use as a tablet, but also gave us enough room for the keyboard,” says Bowers. “It’s balancing the trade-offs between the size of the keyboard and screen real estate… One of the things we could have done is go with a wider screen that would allow us to put more keyboard there, but then we have that trade-off of where, when you’re in portrait, it gets more narrow.”

It remains to be seen whether these compromises will pay off, or whether the Pixel C will resonate with consumers who are still warming up to the hybrid computing model. It’s also unclear how many developers will optimize their apps for the wider form factor, and how quickly.

In fact, it’s far too early to say much at all about Apple or Microsoft or Google’s vision for what the ideal tablet, or tablet/laptop hybrid, should look like. If there's one thing the Pixel C does make clear, it's that the future isn't settled; it’s as much 4:3 as it 3:2 as it is 1:√2, as it is whatever else is in the pipeline.

“If we go take risks in places and really prove out that things work, then that’ll help move technology forward across the entire ecosystem,” says Bowers. Whether they end up working seems almost beside the point; it helps the entire ecosystem simply to try.