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Roice
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Roice
@roice713
Exploring mathematics through visualization.
Austin, TX Katılım Temmuz 2016
316 Takip Edilen2.7K Takipçiler
Mathematics.
Rubik's Cube for Higher-Dimensional Aliens.
Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: roice3.org/magictile
By @roice713, used with permission.
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Roice retweetledi
Our new website for this very fun project is live!
Rémi Coulon@LaMiReMiMath
Enjoy the latest version of our website 3-dimensional.space to explore Thurston’s geometries! With new videos, real-time VR simulations, HD pictures, etc. We will regularly expand the content with more material. Joint work with @Sabetta_, @henryseg and @stevejtrettel.
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@jagarikin Very nice! Just like the Rubik's cube, if you want to try to solve Megaminx this way, you can try
@roice713's MagicTile roice3.org/magictile/ Choose Start Here -> Classics -> Megaminx. I find it easier than a physical one cuz I don't need to rotate the puzzle to find pieces
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Roice retweetledi
@jagarikin If you want to try solving the Rubik's Cube this way, you should try @roice713 's MagicTile roice3.org/magictile/ You can choose the Rubik's cube among hundreds of puzzles. The stereographic projection makes it look like the animation in this post.
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@Thalesdisciple @TilingBot I haven't yet looked into what that requires. I think I'll watch how things evolve for a while since I'm not yet confident in the future of Mastodon.
For better or worse, I have also been seriously considering retiring the bots from Twitter.
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@Tom_Ruen @NonEuclideanDr1 Yes, only a single (ideal!) point of each edge remains “in” the honeycomb.
I imagine that within the space, the square faces may not even appear so square… the only clue being that they connect with 4 of these ideal points.
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@NonEuclideanDr1 Probably?! All vertices are ultra-ideal, beyond sphere of Beltrami–Klein projection. Do we only see surfaces of square faces.
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{4,3,∞} means infinitely many cubes around each edge, hard to really "see" that at all!
Honeycomb Bot@honeycomb_bot
Regular {4,3,∞}
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Can we cut the square into finitely many pieces and rearrange the pieces into a circle, if we allow ourselves to dilate the pieces as well as simply translate them? Surprisingly, yes!
Source: link.springer.com/article/10.102…
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@neozhaoliang Idk, but the easiest way for me to think of it is as a diminished 600-cell. From wiki: “removing 20 vertices that lie on two mutually orthogonal rings and taking the convex hull of the remaining vertices.” This leaves a bunch of tetrahedra and 2 orthogonal chains of anti-prisms.
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@TilingBot @roice713
I think you should, on April 1st, just post a blank circle, labeling it as an apeirogonal tiling centered on a face.
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Starting tomorrow 👇 Get in touch if you want the Zoom link to listen in on some cool #MathArt talks!
Dr. Martin Skrodzki@msmathcomp
On September 15th and 16th, there will be a 3d #MathArt symposium at the annual @dmv_mathematik meeting. Program here: ms-math-computer.science/projects/dmv_m…. It's hybrid, get in touch if you want access to the Zoom-link. Looking forward to seeing many of you, in-place🤗or virtually🧑💻!
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@bengineer8u Excellent questions and a good starting point to find out. Time to go digging :)
blogs.ams.org/visualinsight/…
e.math.cornell.edu/people/belk/pr…
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@roice713 Is it because they are both infinitely holed? Do the number of holes increase a the sane rate as we go down in scale?
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Fun fact: this pattern is homeomorphic to a Sierpinski carpet!
blogs.ams.org/visualinsight/…
Honeycomb Bot@honeycomb_bot
Regular {7,3,3}
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@bengineer8u It means that the image above is “the same” as the following one.
Some links for further study…
Sierpinski carpet: en.m.wikipedia.org/wiki/Sierpi%C5…
Homeomorphism (a topological sense of being “the same”): en.m.wikipedia.org/wiki/Homeomorp…
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@roice713 Can you explain in simple terms what that means?
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@Yann_LeGall @reasonformath @quagjw Reminds me visually of work by @bulatov_org rendering a cylindrical model of hyperbolic space. bulatov.org/math/1101/
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I was inspired to make a mesh-based "slit-scan" effect after seeing an animation by @reasonformath.
I explored different approaches with @quagjw.
#art #houdini #creativecoding #generativeart #loop
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Took me a month, but the blog post is finally finished! 🫡
Here I'll explain how to write up a generalized space time geodesic ray tracer in GLSL, as well as going in-depth into Lagrangian/Hamiltonian mechanics with derivations of the geodesic equations!👀
michaelmoroz.github.io/TracingGeodesi…
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@saksham0961 The link wouldn't work for me without prepending www. Here's one that did work, in case anyone wants to go check out the talk.
msri.org/workshops/950/…
I was kidding about any real study of NSE, but I do enjoy trying to glean insight from Terry Tao :)
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I've been diving into the Navier-Stokes equations the past few years, taking an intuitive and immersive approach. Finally starting to get them a little :)
en.wikipedia.org/wiki/Navier%E2…
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