We have built a world of largely straight lines – the houses we live in, the skyscrapers we work in and the streets we drive on our daily commutes. Yet outside our boxes, nature teams with frilly, crenellated forms, from the fluted surfaces of lettuces and fungi to the frilled skirts of sea slugs and the gorgeous undulations of corals.
These organisms are biological manifestations of what we call hyperbolic geometry, an alternative to the Euclidean geometry we learn about in school that involves lines, shapes and angles on a flat surface or plane. In hyperbolic geometry the plane is not necessarily so flat.
Yet while nature has been playing with hyperbolic forms for hundreds of millions of years, mathematicians spent hundreds of years trying to prove that such structures were impossible.
But these efforts led to a realisation that hyperbolic geometry is logically legitimate. And that, in turn, led to the revolution that produced the kind of maths now underlying general relativity, and thus the structure of the universe.