Fibonacci

Professional photographer and polar guide, Piet van den Bemd, was flying a drone across the dark blue waters of the Antarctic when his camera caught sight of an emerging pattern, rising from the deep.The unfurling coil of light blue bubbles created a shape on the ocean surface that looked remarkably like a Fibonacci spiral – the famous mathematical pattern that often appears in the natural world, from plant to animal life.Only when the spiral was complete did van den Bemd realize what had made it.From the center of the…

If your eyes have ever been drawn to the arrangement of leaves on a plant stem, the texture of a pineapple, or the scales of a pinecone, then you have unknowingly witnessed brilliant examples of mathematical patterns in nature.What ties all of these botanical features together is their shared characteristic of being arranged in spirals that adhere to a numerical sequence called the Fibonacci sequence.These spirals, referred to as Fibonacci spirals for simplicity, are extremely widespread in plants and have fascinated…

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…

A team of physicists say they managed to create a new phase of matter by shooting laser pulses reading out the Fibonacci sequence to a quantum computer in Colorado. The matter phase relies on a quirk of the Fibonacci sequence to remain in a quantum state for longer.Just as ordinary matter can be in a solid, liquid, gas, or superheated plasmic phase (or state), quantum materials also have phases. The phase refers to how the matter is structured on an atomic level—the arrangement of its atoms or its electrons, for example.…