You have my consent to kill me
You have my consent to kill me
42 comments
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I can sense a middle finger coming from this image, somehow.
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I see what you mean
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I see an amongi
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The rub with this design is that the length of the sides of the little squares is not an even integer division of the length of the sides of the big square, though.
Doing it the naive way, i.e. keeping all the edges parallel, you can only fit 16. However it's trivial to fit 17 in there without it looking like a warehouse accident, like so:
Or, a slightly easier to follow rendering:
This may correlate with #17 on your linked list, but I was not rigorous with the math. (I.e. I just traced this off of the screenshot.)
I'm positive I've seen this as a 3D printed puzzle somewhere at some point...
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The posted arrangement is the tightest known packing of 17 squares. The outer square has a side length of 4.6756 times a small sqare's. So unless you've just found one no mathematician has thought of since 1998 yours is slightly larger.
Edit:
I found this tool to play around and your packing is 4.7 https://markorastas.github.io/PackingProblem/Edit edit:
I'm a dummy you just need pythagoras, yours is 4+√0.5≈4.7071 -
Yep, if I'm not mistaken, your version has s = 4 + sqrt(2) which is approximately 4.70710678119. Very close to the ideal 4.67553009360455 !
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There's a link for alternate packings on that page, where you can see older versions, some with more aesthetically pleasing patterns of minimal tilted squares or symmetry. All of them use a larger value for
sthough and it's hard to tell where your version would fit in. -
Blender calculates this as the optimal packing. It's smaller than the ideal, but I've seen Blender be wrong before.
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WITCHCRAFT!
(... which makes it very cool!)
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42 comments
Lovecraft talked about that shit in his stories a lot. Impossible shapes and angles that would drive normal men to madness.
I like the concept of Eldritch horror that it is so fearful and alien that its impossible to describe in terms that could make you feel it. The most that words could do would give a view of the shadow of it instead of the horror itself. To finally understand the horror requires surrendering your sanity. If nothing else its a great literary tool.
This makes all the difference between a good Call of Cthulhu DM and a bad one.
The 'firefall' novels ('blindsight' and 'echopraxia') are... Not exactly that, but very close, and better written than lovecraft could dream of. 'Echopraxia' does not hold your fucking hand at all though.
"crikey mate that shit's fucked, anyway i need to get to work"
Non-euclidian fuckery
Good name for a mathrock band.
If you look at renderings of what 4D objects would look like intersecting 3D space, this is what I imagine for those. Seeing 3D cross sections morphing continuously but inconceivably into each other without being able to even comprehend the true form of the thing you're seeing glimpses of would be terrifying.
You should look at higher than 4D renderings, like high dimensional hypercubes, as don't forget non-euclidean geometry
I believe the idea of eldritch is in being able to comprehent the true form - but only temporarily, since our minds cannot hold that knowledge, only to be left with a frayed hole in our thoughts
But also as people mentioned, there's some cursed geometries. Hyperbolic and parabolic geometry is interesting (see Hyperholica and Hyperrogue), but things get worse with Nil and Solv
For a more plain existential horror also see Fractal Block World, pretty fun seeing the sense of scale as you shrink yourself ever further revealing detail you couldn't perceive before, and also the sense of scale, as a tiny room becomes an incomprehensibly vast space you cannot hope to cross in your lifetime.
but this is not impossible or out of ordinary though. you can even imagine stacking a couple cardboard boxes into that shape. i think it's out of place because it's too ordinary, because you'd expect some kind of symmetry, regularity, etc. from idealized mathematical shapes, but you didn't. instead you just get some random looking stack of boxes.
Fyi this is just the best known packing of 17 squares, there might be a better one. We just haven't been able to proove it or find a better one since 1998
If killing Cthulhu is all it takes to solve the box-packing problem, Amazon would have already done it. No, this is something far more sinister than that.