# hyperbolic tiling

hyperbolic

memory

Hyperbolic flowers.

I managed to fix the calculations around the edges. Now there are now missing parts like in my previous drawing.

2

Hyperbolic

ain’t no sunshine when she’s gone…

Hyperbolic tiling.

I could fix a lot of things faster than expected. As you can see this version is much better in quality and in details around the edge. Now comes the harder part, I will make it move!

ok so I want to point out a neat geometrical fact and I don’t feel like drawing these things so I’ll just use some Wikimedia images

• now we can replace the hexagons with pentagons (leaving the squares and triangles alone), but obviously there’s too much room in the Euclidean plane for that pattern to work, so we go to a place where there’s less room for stuff: spherical 2-space (aka the sphere), which we can see is completely tiled by this pattern, like this:

• we can also try to replace the hexagons with heptagons, and clearly the Euclidean plane doesn’t have enough room for that, so it turns out that this variant tiles hyperbolic 2-space (where there’s more room), here presented in the form of the Poincaré disk, like this:

i did eventually figure out how to build a hyperbolic tiling like this with a compass and a straightedge (but i was too lazy to do it on paper so i did it in geogebra)

I am currently still working on hyperbolic tools. This is the first tiling I choose to drew. Here 7 equilateral triangles meet at each point. The quality is not too good yet and I want to make it into an animation. Also I have to fix some of the calculation.

Hyperbolic