This unusual shape looks sort of like a coiled, corrugated garden hose – but it’s actually a mathematical shape that, until recently, were thought to be impossible to visualize in three dimensions. Flat tori were first demonstrated in the 1950s, and io9 gives a suitably adorable description of exactly how to imagine one. They say: “To imagine a flat torus, imagine a video game with a wraparound screen — for instance, if you go up the top side, you emerge from the down side. […] Imagine taking a square flat torus, wrapping it into a tube, and then bending its ends so they met to form a ring.”

Until now, it was assumed that an object like this couldn’t be demonstrated in 3D because of the distortion that takes place with the wrapping and the bending. But researchers in France thought outside of the tube and added corrugations to the shape, overcoming the distortion problem. These surfaces are known as smooth fractals, which are somewhere between regular surfaces and fractals. Apparently the discovery could help mathematicians do their thing…but all we can think of is a sudden craving for smooth fractal donuts.

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Have you heard the one about the tortoise who proved a complicated mathematical theory? It sounds like the beginning of a bad joke, but flipping tortoises over and watching them right themselves actually did help mathematicians Gábor Domokos and Peter Várkonyi prove the existence of a long-theorized (but, until now, unbuilt) three dimensional shape called the Gömböc. In effect, they discovered an entirely new shape.

Simply put, a Gömböc is a self-righting object with exactly one unstable equilibrium point and exactly one stable equilibrium point. It is homogeneous (meaning it is built of just one material, rather than containing weights to make it self-right) and convex (meaning its sides are not allowed to bulge inwards). Mathematicians had assumed that such a shape simply did not exist, but had long been unable to disprove the existence of such an object in three dimensions, so Domokos set out to find the definitive answer. Rather than disproving its existence, he and Várkonyi ended up surprising themselves by finding that the object actually does exist.

The discovery of the Gömböc was not only important in and of itself; it opens up a world of possibilities for future discoveries. The Gömböc is kind of a “stem cell” in that other three-dimensional shapes can be derived from its existence. The Gömböc is the starting point for proving all three-dimensional objects with higher numbers of equilibrium points. And in the world of math, that’s a very exciting proposition. Gömböcs are being produced for purchase, but it’ll run you anywhere from $215 to $870 (more for a special edition) – a little pricey for a grown-up Weeble.

The post Weeble Wobble: New Self-Righting 3-Dimensional Shape first appeared on Gajitz.