The Fibonacci Numbers Hiding in Strange Spaces

McDuff and Schlenk had been trying to figure out when they could fit a symplectic ellipsoid—an elongated blob—inside a ball. This type of problem, known as an embedding problem, is pretty easy in Euclidean geometry, where shapes don’t bend at all. It’s also straightforward in other subfields of geometry, where shapes can bend as much as you like as long as their volume doesn’t change.

Symplectic geometry is more complicated. Here, the answer depends on the ellipsoid’s “eccentricity,” a number that represents how elongated it is. A long, thin shape with a high eccentricity can be easily folded into a more compact shape, like a snake coiling up. When the

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