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 ...

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 ...

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 ...

My favorite shape is the loop, a circle with all geometric information stripped ... complement of the figure-eight knot has a complete hyperbolic metric—in fact, a unique such metric.

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 ...

Maryam Mirzakhani, who became the first woman Fields medalist for drawing deep connections between topology, geometry and dynamical systems ... the end of an era in the study of three-dimensional ...

Although such shapes are difficult to visualize ... the tori with multiple holes–can be given what’s called hyperbolic geometry, which makes the surfaces negatively curved at all points.

The third, by Colby College professor Scott Taylor, discussed how hyperbolic geometry can be used to model large data ... whether that be the distance, size, or shape of objects on the map. Thus, ...

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 ...