Euclidean geometry is the kind you were taught at school, the world of sines and cosines, and the square on the hypotenuse ...

We construct a Kahler structure (J, Ω, G) on the space L(H³) of oriented geodesics of hyperbolic 3-space H³ and investigate its properties. We prove that (L(H³), J) is biholomorphic to P¹ × P¹ - Δ̅, ...

Let Mn be an n-dimensional complete connected and oriented hypersurface in a hyperbolic space Hn+1 (c) with constant k-th mean curvature Hk > 0(k < n) and with two distinct principal curvatures, one ...

I believe that the principle of Embodied Cognition is probably one of the most significant and important concepts to understand about virtual reality. Cognitive science researchers have been ...

Atomic interactions in everyday solids and liquids are so complex that some of these materials’ properties continue to elude physicists’ understanding. Solving the problems mathematically is beyond ...

Reducing redundant information to find simplifying patterns in data sets and complex networks is a scientific challenge in many knowledge fields. Moreover, detecting the dimensionality of the data is ...

• There are three possibilities for the curvature of the universe: space can be flat, spherical or hyperbolic • The geometry of the universe depends on its curvature and also on its topology, which ...

Virtual reality can take you to some far-out places — mountaintops, distant cities and even fantastical game worlds. A team of artists and mathematicians is now adding to that list: universes where ...