Monohm, a startup based in Berkeley, California, was founded around this very idea. For the last year, the three-person team has been working a circular, palm-sized device dubbed Runcible.

They cheekily refer to it as the "anti-smartphone," a description that goes for both its form factor and its value system.

The round device is meant to be the antidote to our feed-obsessed, notification-saturated digital existence. It's a challenge to the rectangular status quo and everything it represents. That's a quixotic dream, but an interesting one.

Different Rectangles, Different Effects

Display technologies have a long and rectangular history. Before smartphones there were movie screens, TVs, and computers, not to mention paintings and pages of print. And then of course there are windows—in some ways the original glass rectangles.

In each case, the rectangle's prominence can be attributed in large part to practicality. Whether you're talking about film or glass or stone, rectangles are easy to make. They don't leave much wasted material.

As frames for shaping the world, however, different types of rectangles can produce vastly different effects.

In her book The Virtual Window, which traces the rectangular frame from Renaissance painting up through Microsoft Windows, media theorist Anne Friedberg offers an example from the history of architecture, centering on a public feud between French builder August Perret and the preeminent modernist architect Le Corbusier.

Perret was a strong advocate of the traditional French casement window, which was oriented vertically. Its main function, he said, was to let light into a room. Le Corbusier, making use of new manufacturing techniques, designed his buildings around long, horizontal windows, which were as much about framing the outside world as illuminating the space within. The disagreement influenced architecture for decades to come. The simple act of turning a rectangle on its side gave us entirely new ways to think about space.