Non-Euclidean Geometry Online: A Guide to Resources (2008)

pi.math.cornell.edu

47 points·the-mitr··7 comments

Here's an interactive demonstration of 3D hyperbolic honeycombs:

https://www.shadertoy.com/view/XddyR2

And here's the 2D version:

https://www.shadertoy.com/view/3tsSzM

My son just started Euclidean (planar) geometry, also known as synthetic geometry, and it's quite a departure from what I learned in high school -- analytic geometric (cartesian geometry). He's suffering through it so far but he may ditch the course and go for non-Euclidean geometry instead. Thanks for posting this. It's helpful as I'm trying to determine what's best for his desired career path.

What your son is learning (synthetic geometry) and what you learned (cartesian geometry) are essentially two ways of looking at the same stuff. One emphasises coordinates and one does not.

What the post is about (non-Euclidian geometry) is a rather different thing entirely. Its about doing geometry when the space you live on/in is curved (like doing geometry on the surface of the earth).

Thanks for the clarification. I'm taking in as many resources as I can. I'd imagine that if he goes into engineering or CS, and especially into anything having to do with 3D environments, that cartesian geometry would be more useful.

https://www.britannica.com/science/Riemannian-geometry

https://yt.artemislena.eu/watch?v=wZgM3u8UkNs [VIDEO]

related resource: https://www.3-dimensional.space/

Someone should make an awesome list.

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