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Notes -
I'm still not entirely sure what Non-Euclidean geometries are supposed to look like tbh, other than a sign that creepy shit is about to go down.
I always took his references to non-euclidean geometry to be referencing 4th dimensional structures. But I think I was pre-primed for this interpretation after being exposed to Flatland in school, and a short story from Science Fiction Age.
Funnily enough, over the long years many of the stories I read in Science Fiction Age left a strong impression on me. Strong, but without detail. I read these pages when I was 13-15, and I'm nearly 40 now. I didn't even remember the name of the magazine. I eventually cobbled together what few concrete details I could, and a few of the story titles I was pretty sure I remembered correctly and some google-fuu later, found it.
At first I only discovered that my favorite author in it's pages, Adam-Troy Castro, eventually published his silly short stories about the incompetent criminal masterminds Vossoff and Nimmitz into a book. Which I promptly purchased on ebay. But then I eventually found PDFs of every issue on archive.org, because of course they have it.
So it's with certainty I can now tell you, that short story in the Cthulhu mythos, my first exposure to it actually, was Out of Space, Out of Time in Vol 6, Issue 6 in 1998. I think I'll actually read it now for old times sake.
Edit: I read it again, and it wasn't half bad. Not as good as I remember it, not as catastrophically awful as some things I liked as a kid. A solid yeoman's effort to build on the Cthulhu mythos.
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Play some hyperrogue, and maybe read the blog posts about it.
You will have to make a decent start on understanding hyperbolic geometry if you want to rescue the princess (~10% of the way through the game). I haven't got much farther than that, myself.
I second this, also Hyperbolica. While Hyperbolica is a fairly simple and short adventure game and wouldn't be interesting without its gimmick, its gimmick is that it takes place in a 3d hyperbolic world (and one area in spherical geometry). Not some top down tessellation like Hyperrogue, but with an actual first person perspective walking around in hyperbolic space. While Hyperrogue is a much more interesting (and challenging) game as far as the gameplay is concerned and probably requires more technical understanding of the properties of hyperbolic geometry to solve its puzzles, I think Hyperbolica does a better job of actually getting someone to experience hyperbolic (and spherical) geometry, rather than just having an abstract understanding of its properties.
If it's the one I'm thinking of, I might have seen the dev videos for that a few years ago. Will check it out!
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Look at a globe. Seriously. The surface of a sphere is one of the classic examples of non-Euclidean geometry, a geometry where Euclid's 5th postulate doesn't hold. The exact description of the 5th postulate is a bit arcane (look it up on Wikipedia if you care), but it turns out to be equivalent to saying that all triangles must have corner angles that sum to 180 degrees. On the globe, if you choose a triangle with these corners: the north pole, 0 degrees E on the equator, 90 degrees W on the equator, that triangle will have all its corner angles 90 degrees, for a total of 270 degrees.
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In fairness, there was a little thought out into the choice. Additive magenta is a genuine non-spectral color that does not actually exist in nature and cannot normally be perceived in objects, but can easily be created in projection.
You can find magenta flowers, and it's not on the spectrum but you can get it as a mix of spectral colors. Still better than most alternatives, I'd agree.
I wonder if they could have pulled off using a chimerical color instead, only showing the "impossible" color in brief scenes always subsequent to a scene colored+lit to act as a corresponding fatigue template.
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A premonition of printer inks must have come to Lovecraft in a dream...
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