A Gömböc is a shape that has two equilibrium points—one stable and one unstable—instead of a minimum of 4 like other shapes. That makes it self-righting so wherever you put it, it’ll always go back to that single point of equilibrium.
In 1995, a Russian mathematician called Vladimir Arnold proposed the class of shapes that the Gömböc is part of and, in 2006, Hungarian mathematicians Gábor Domokos and Péter Várkonyi proved the conjecture by creating the shape. It derives from a type of tortoiseshell (which only 3 species have, such as the Indian star tortoise):
There is something about a turtle on its back that twists your heart. With neck craning toward the ground and legs waving to no effect, it is the image of helplessness. But, malicious kids aside, turtles almost never end up upended. And it turns out that the apparent risk factor for that predicament—the turtle’s rigid carapace—is less a liability than an asset, surprisingly well-suited to the turtle’s goal of righting itself. The secret is in the mathematics of its shape.via Natural History Mag
Due its design, the Gömböc has inspired a wide range of applications including a Gömböc-style insulin capsule (which has lent itself to a thing for the oral delivery of the COVID vaccine), a piece of simulation software that helped New Zealand’s 2017 America’s Cup team optimise their catamaran’s performance (which is also used by naval architects).
The Action Lab made a 5-minute video for it on their YouTube channel explaining the Gömböc in more detail.
Stream it below.