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Hyperbolic Tessellation 1

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This was my first project with hyperbolic geometry. Imagine, if you will, a world where lines aren't lines; a world where a line has an infinite number of parallels to it through a single point; a world where straight lines are circles! Yes, it's awesome, I know. This piece is a constructed tessellation of a triangle on Poincaré's hyperbolic model. What does that mean? Well, there's an infinite amount of space inside that circle, and each of those triangles is *the exact same size!* I hope I just blew your mind. If I didn't then... meh... whatever. I've learned SO much from this, and I would like to eventually spruce it up a bit, but for now I'm happy. Enjoy.

I did hand draw this in Illustrator, but I opted to categorize it as fractal art due to its mathematical complexity.

Please comment! (Especially if you're a math nerd like me! :) )
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900x900px 244.13 KB
© 2005 - 2024 drdeseis
Comments15
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Great job! I am trying to do one of these for an upcoming high school project. We are having a geometric art exhibit. I have read through "Compass and Straightedge in the Poincare Disk" but I just don't understand what you do after you have the main center figure. Any help would be greatly appreciated.