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 ...

Only three geometries fit this description: flat, spherical and hyperbolic. Let’s explore these geometries, some topological considerations, and what the cosmological evidence says about which shapes ...

geometry and dynamical systems, has died of cancer at the age of 40. This is our 2014 profile of her life and work. Thirty years after William Thurston articulated a grand mathematical vision, a proof ...

In hyperbolic geometry, we have formulas for working out what happens with shapes on this kind of surface." As hyperbolic shapes grow and take up space, they can twist and turn in different ways ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don’t apply: angles of a triangle add up to less than 180 degrees and Euclid’s parallel ...

The crinkled edges of a lettuce leaf curve and expand in a shape that has perplexed mathematicians for centuries. Those curves -- an example of a high-level geometry concept called the hyperbolic ...

In the study, the similarity and popularity variables are combined to give rise to the hyperbolic geometry of the model, which emerges as the natural geometry representing the hierarchical ...