Tags » Hyperbolic Geometry

The many faces of the hyperbolic plane

is the unique (up to isometry) complete simply-connected 2-dimensional Riemann manifold of constant sectional curvature -1.

  1. It is diffeomorphic to as a topological space (or, indeed, isometric as a Riemannian manifold, if we give a left-invariant metric): to show this, we note that has isometry group , and the subgroup of isometries which stabilize any given is isomorphic to .
  2. 211 more words
Hyperbolic Geometry

Fuchsian vs. Kleinian

Or, all the fun you could have in one additional dimension.

The former, of course, may be viewed as a special case of the latter; the more general Kleinian case shares many, but not all, of the characteristics of the simpler Fuchsian case. 776 more words

Hyperbolic Geometry

The Iron Genie meets Escher at the Dulwich Picture Gallery

I was thrilled when the Dulwich Picture Gallery requested the loan of my steel harmonograph The Iron Genie for an interactive installation in the gallery in October 2015. 1,195 more words

Art And Science

History Facts next level

I hope you had a great Christmas for those that celebrated, or a great holiday and some relaxing time. I just realized that I haven’t posted about the event: … 961 more words

Mathematics

188

July 7 – 188

Mathematica 10.1 – The Poincaré disk is a model for hyperbolic geometry in which a line is represented as an arc of a circle whose ends are perpendicular to the disk’s boundary. 16 more words

One Image A Day - 364 Days

Hyperbolic Cubes (Spheres X)

The hyperbolic plane is a geometry whose points are those of a disk, and the lines are circular arcs that meet the boundary circle of the disk at a right angle. 298 more words

Mathematics

Schläfli - for lush, voluminous polyhedra

Because of some turbulence in real life (™) over the last few months, it’s been somewhat hard to concentrate on research. Fortunately the obligation of teaching sometimes exerts the right sort of psychological pressure to keep my mind on mathematics in short bursts. 2,283 more words

Hyperbolic Geometry