Alex Therrien Week 11 - Hyperbolic Space

 This came out a lot later than I wanted. I forgot about this for a bit. Whoops. Anyways I should be able to catch up on everything.

N - A type of non euclidean space where every point has a negative curvature (thing pringle/saddle shaped instead of spherical) The straight lines form hyperbolas in this type of space.

This wasn't really much of a vocab word to be honest, but more of an interesting topic I learned about and did a bit of research on to learn more about. Anyways, Hyperbolic space is where every direction of travel is in a hyperbola. Due to this, equilateral triangles have angles of less than 60 degrees, and circles are rather strange. In euclidean geometry, a circle’s circumference is C=2pi*r. This is a linear relationship. However, in hyperbolic space this relationship is hyperbolic (C = 2πsinh(r)). This means that a 2D circle in hyperbolic space would have to be displayed in 3D euclidean space as wrinkled in order to actually fit the extra circumference. This is what hyperbolic crochet is, which apparently is a thing.

 

I found that a good way to figure out what is happening is to look at a gif of moving through a 2D hyperbolic space comprised of a repeating pattern, in this case triangles.

It should look like things expand as they get closer to the center, and shrink as they get farther away. This is what happens when hyperbolic space is portrayed in euclidean space.

So yeah, this is probably as much as I can confidently explain about hyperbolic space without getting things horribly wrong. I just thought this is kind of cool.