A superegg is obtained by rotating a super ellipse around one of its axes. It is a solid egg shape with perfect symmetry and zero curvature at the tips, giving it the ability to stand upright on its own. It’s the result of some cool math used to solve a city planning problem. Numberphile looks at how this object came to be.
The concept of a superegg started with Swedish town planners. Sergels torg, a public square in Stockholm, is in the shape of a rectangle, and the locals wanted to create a roundabout in the center of it. A circle wastes too much space in the rectangle, and a regular ellipse, is too small near the top, leading to traffic jams. Peit Hein, a Danish scientist and mathematician, eventually came up with a solution which he called a super ellipse. This was created by changing the equation for an ellipse until it was a perfect combination between an ellipse and a rectangle (exactly halfway in between an ellipse and a rectangle).