Interactive Hyperbolic Tiling in the Poincaré Disc
In hyperbolic geometry, the angle sum of a triangle is less than \(\pi\) and the angle sum of a regular polygon with \(p\) sides is less than \((p-2)\cdot\pi\). Let \(\alpha\) be the inner angle of a hyperbolic polygon in a pq-tiling, then: \[ \frac{(p-2)\cdot \pi}{p}\cdot q > \alpha\cdot q = 2\pi \]
NonEuclid - Hyperbolic Geometry Article and Javascript Software
NonEuclid allows the curious explorer to gain experience in Hyperbolic Geometry and to empirically investigate questions such as: "Does the Euclidean geometry method for constructing an equilateral triangle work in Hyperbolic geometry?" or "In Hyperbolic Geometry, are the base angles of an isosceles triangle congruent?"
Hyperbolic space simulation in VR - Physics Forums
2017年7月28日 · Hyperbolic space simulation in VR is a virtual reality experience where users can explore and interact with a simulated hyperbolic space, which is a type of non-Euclidean geometry. It allows for a unique and immersive experience that …
NonEuclid - Hyperbolic Geometry Article + Software Applet
NonEuclid is a Java Software Simulation offering Straightedge and Compass Constructions in both the Poincaré Disk and the Upper Half-Plane Models of Hyperbolic Geometry (a geometry of Einstein's General Relativity Theory and Curved Hyperspace) for use in High School and Undergraduate Education.
Simulating hyperbolic space on a circuit board - Nature
2022年7月28日 · We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a ‘hyperbolic drum’, and in a time-resolved experiment we verify signal...
GitHub - kitoran/Hyperbolic: Hyperbolic space simulator
So here is a proof-of-concept hyperbolic space game engine prototype. You are in hyperbolic space. Move with WASD, jump with spacebar and turn with mouse. There are also keys z and c to move up and down. When you start the application there is just one red triangle snd you stand on it. You can load other environments.
Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experi-ments, and a set of methods to verify the effective hyperbolic metric in this and other...
[2109.01148] Simulating hyperbolic space on a circuit board
2021年9月2日 · Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to ...
[1910.12318] Quantum Simulation of Hyperbolic Space with …
2019年10月27日 · Abstract: We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top ...
Simulating hyperbolic space on a circuit board - PMC
We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a ‘hyperbolic drum’, and in a time-resolved experiment we verify signal propagation along the curved geodesics.