there’s no way to fit even a two-dimensional hyperbolic plane inside ordinary Euclidean space unless we’re willing to distort its geometry. Here, for example, is a distorted view of the hyperbolic ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules ... crocheting has been used before, for example. But she says twisted balloons provide unique ...

Those curves -- an example of a high-level geometry concept called the hyperbolic plane -- were not even defined by geometry theorists until the 19th century. And in the almost 200 years following ...

The example described above is the case of spherical (positive) curvature, but it can also be realized for negative curvature. “This device provides us with a unique table-top experiment in which to ...

Hyperbolic geometry is a mathematical concept so convoluted that just ... a perfect analytic universe toward a more open and intuitive one. When I ask Taimina for examples of hyperbolic forms in her ...

Recent investigations have focussed on rigorous connections between quantum invariants and hyperbolic geometry. For example, work on relative Reshetikhin–Turaev invariants has illuminated the ...

Spherical geometry offers one example — if you draw a triangle on a sphere (like, say, connecting the North Pole to Honolulu to Miami), the angles sum to a number larger than 180. Hyperbolic geometry ...

The first, by YouTuber CodeParade, was on implementing a hyperbolic world in a video ... to be true and turns them on their head. “For example, changing one tiny assumption about the basis of ...

Hyperbolic geometry may be partially responsible for breakthroughs in physics such as general relativity and quantum field theory. But we're not used to seeing curved environments like the ones in ...