a perspective on mathematics, the pattern, and the abstract

Posts tagged: hyperbolic geometry

This is what it would look like to spin around in 3 dimensional hyperbolic space tiled by regular right angled dodecahedron.

Created with Curved Spaces.

This is what it would look like to do a front flip in 3 dimensional hyperbolic space tiled by regular right angled dodecahedron.

Created with Curved Spaces.

Flying though a tiling of regular right angled dodecahedron in three dimensional hyperbolic space. There is more of an explanation here.

Created with Curved Spaces.

Hyperbolic geometry is an example of a non-Euclidean geometry.

Source:
matrixeditions.com

Notes: 157
9/25/11 — 12:56pm
Filed under:
#geometry
#hyperbolic geometry
#math
#papers

This is a tiling of regular right angled dodecahedron in three dimensional hyperbolic space shown through 4 iterations. 12 generators of the tiling are reflections in each of the 12 dodecahedron’s faces.

Source:
bulatov.org

Notes: 41
8/20/11 — 5:01pm
Filed under:
#math
#hyperbolic geometry
#dodecahedron
#photoset
#tilings
#tessellation
An ideal rotation around the point at infinity in the disc and upper half plane model of the hyperbolic plane

Source:
bulatov.org

Notes: 41
8/12/11 — 5:10pm
Filed under:
#GIF
#animation
#math
#geometry
#hyperbolic geometry

Rotation around the symmetry axis of 4th order in the disk and upper half plane models

A Moebius transformation can be used to transform the disk model to the upper half plane model of the hyperbolic plane.

Source:
bulatov.org

Notes: 20
8/12/11 — 3:32pm
Filed under:
#GIF
#animation
#math
#Moebius transform
#conformal
#hyperbolic geometry
Hyperbolic translation along the horizontal axis in the disc model, and along both horizontal and vertical directions in the band model

Source:
bulatov.org

Notes: 25
8/12/11 — 2:43pm
Filed under:
#GIF
#animation
#math
#geometry
#hyperbolic geometry
An ideal rotation around the point at infinity in the disc and band model of the hyperbolic plane

Source:
bulatov.org

Notes: 5
8/12/11 — 1:50pm
Filed under:
#GIF
#animation
#math
#geometry
#hyperbolic geometry

Rotation around the symmetry axis of 4th order in the disk and band models

Source:
bulatov.org

Notes: 18
8/12/11 — 12:58pm
Filed under:
#GIF
#animation
#math
#geometry
#rotation
#hyperbolic geometry

This is a hyperbolic tiling with right angled regular pentagons shown in the disk model and the band model. The animation shows how one model is transformed to the other using the complex map

The points +1 and -1 get sent to +∞ and -∞, respectively, and the points +i and -i remain fixed.

Source:
bulatov.org

High-res
Notes: 9
8/12/11 — 12:34pm
Filed under:
#GIF
#animation
#math
#geometry
#conformal map
#hyperbolic geometry
This is a hyperbolic tessellation with Schläfli symbol {4, 12} shown in the Poincaré disk model and in the band model. The animation displays a rotation of the hyperbolic plane.

Source:
images.math.cnrs.fr

Notes: 32
8/11/11 — 6:48pm
Filed under:
#GIF
#animation
#math
#geometry
#tessellation
#hyperbolic geometry
#tilings
#papers

Hyperbolic ring tilings make use of conformal maps.

Source:
images.math.cnrs.fr

High-res
Notes: 25
8/11/11 — 6:46pm
Filed under:
#math
#geometry
#hyperbolic geometry
#tilings
#tessellation
Source:
dodecahedral.com

High-res
Notes: 82
6/30/11 — 2:49am
Filed under:
#math
#geometry
#topology
#hyperbolic geometry
#dodecahedron
#tilings