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Plöp PlöpSomehow whenever I need to research something about tori (just the relative straightforward 3D kind, although right now self intersecting), they want to give me a headache. I just want to know whether a point is on the lemon or apple part of the spindle torus (yes these are the official names), I need neither quantum physics nor higher dimensions nor spiritual uses of tori <a href="https://chaos.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://chaos.social/tags/torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#torus</a>

Drahreg01<a href="https://mastodon.social/@mcc" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@mcc</a> Playing <a href="https://mastodon.social/tags/Ultima" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Ultima</a> 1, you came back left, when you left the screen on the right side. And you came back at the top, when you left it on the bottom.So the earth is a <a href="https://mastodon.social/tags/torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#torus</a>.<a href="https://commons.wikimedia.org/wiki/File:Torus.svg" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://commons.wikimedia.org/wiki/File:Torus.svg</a>

Léo Ducas 🇺🇦 ∀,≡,⊂Ok, here is my very first serious math post. I'm going to do this at least once a week.<a href="https://mathstodon.xyz/tags/Math4Crypto" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math4Crypto</a> <a href="https://mathstodon.xyz/tags/Lattice" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Lattice</a> <a href="https://mathstodon.xyz/tags/Torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Torus</a> <a href="https://mathstodon.xyz/tags/LocalitySensitiveHashing" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LocalitySensitiveHashing</a> <a href="https://mathstodon.xyz/tags/TrainOfMathematicalThought" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TrainOfMathematicalThought</a>. *Locality Sensitive Hashing over the Torus, or how I fooled myself twice.*Locality Sensitive Hashing (LSH) over a metric space is the task of tiling the space such that two close points are likely to fall in the same tile. The tile need not be periodic, but they typically are for algorithmic convenience. One example application is the "Shazam app": quickly find a song from a noisy recording of it, maybe having preprocessed the database of songs. But if you know me, you can certainly imagine that I will use them to break cryptography.It is somewhat similar to two other tasks: coding and quantizing. For coding we want the tiles to have a large inner radius: that is the amount of error tolerated (see my banner !). For quantization (aka: lossy compression from continuous to discrete data), we want minimize the average distance to the center of the tile.For LSH, what we want is that if we add a small error to a random point in a tile, the probability that the error drags us outside the tile is low: that is the probability that you will miss out on detecting a pair of close points. For a small error of radius \(\epsilon\), a tile of volume \(V\) and surface \(S\), you can quickly convince yourself that the failure probability is roughly proportional to \(S \cdot \epsilon / V\). Minimizing \(S/V\) is a well known question: the isoperimetric inequality. The best shape for the tiles would be Eucilidean balls... if only they could tile Eucilidean spaces.1/3

@Om*torus vortex...<a href="https://mastodon.cloud/tags/torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#torus</a> <a href="https://mastodon.cloud/tags/vortex" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#vortex</a> <a href="https://mastodon.cloud/tags/animatedgif" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#animatedgif</a>

Spektrum (inoffiziell)Der Jupitermond Io erzeugt einen Ring aus Plasma entlang seiner Umlaufbahn. Warum er das tut und was das mit der Kernfusion zu tun hat, erfahrt ihr in der neuen Folge der Sternengeschichten: <a href="https://astrodicticum-simplex.at/?p=36914" rel="nofollow noopener noreferrer" target="_blank">astrodicticum-simplex.at/?p=36…</a> 🎙️<a href="https://anonsys.net/search?tag=Astronomie" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Astronomie</a> <a href="https://anonsys.net/search?tag=Universum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Universum</a> <a href="https://anonsys.net/search?tag=Sternengeschichten" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Sternengeschichten</a> <a href="https://anonsys.net/search?tag=Astrodicticum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Astrodicticum</a> <a href="https://anonsys.net/search?tag=Sterne" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Sterne</a> <a href="https://anonsys.net/search?tag=Io" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Io</a> <a href="https://anonsys.net/search?tag=Jupiter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Jupiter</a> <a href="https://anonsys.net/search?tag=Jupitermond" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Jupitermond</a> <a href="https://anonsys.net/search?tag=Plasma" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Plasma</a> <a href="https://anonsys.net/search?tag=Torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Torus</a> <a href="https://anonsys.net/search?tag=Gas-Torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Gas-Torus</a> <a href="https://anonsys.net/search?tag=Plasma-Torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Plasma-Torus</a> <a href="https://anonsys.net/search?tag=Planetologie" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Planetologie</a> <a href="https://anonsys.net/search?tag=Vulkanismus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Vulkanismus</a> <a href="https://anonsys.net/search?tag=Magnetfeld" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Magnetfeld</a> <a href="https://anonsys.net/search?tag=Enceladus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Enceladus</a> <a href="https://anonsys.net/search?tag=Europa" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Europa</a> <a href="https://anonsys.net/search?tag=Kernfusion" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Kernfusion</a> <a href="https://anonsys.net/search?tag=Kultur" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Kultur</a> <a href="https://www.spektrum.de/podcast/sternengeschichten-folge-598-der-gas-torus-von-io/2216397" rel="nofollow noopener noreferrer" target="_blank">Sternengeschichten : Der Gas-Torus von Io</a>

Spektrum (inoffiziell)Der Weltraum wirkt wie eine unermessliche Weite, die sich in alle Richtungen erstreckt. Tatsächlich könnte die Gestalt des Kosmos viel komplexer sein, etwa wie ein seltsamer Donut.<a href="https://anonsys.net/search?tag=Kosmos" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Kosmos</a> <a href="https://anonsys.net/search?tag=Universum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Universum</a> <a href="https://anonsys.net/search?tag=FormdesUniversums" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FormdesUniversums</a> <a href="https://anonsys.net/search?tag=Kosmologie" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Kosmologie</a> <a href="https://anonsys.net/search?tag=Topologie" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Topologie</a> <a href="https://anonsys.net/search?tag=Mathematik" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematik</a> <a href="https://anonsys.net/search?tag=KosmischeHintergrundstrahlung" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#KosmischeHintergrundstrahlung</a> <a href="https://anonsys.net/search?tag=Torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Torus</a> <a href="https://anonsys.net/search?tag=KosmischeTopologie" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#KosmischeTopologie</a> <a href="https://anonsys.net/search?tag=Astronomie" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Astronomie</a> <a href="https://anonsys.net/search?tag=Physik" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Physik</a> <a href="https://www.spektrum.de/news/welche-form-hat-unser-universum/2215345" rel="nofollow noopener noreferrer" target="_blank">Wie viele Löcher hat das Universum?</a>

SiinQuick sketch from recent vision work to be refined and tattooed, when time permits, on someone very dear to me. I feel comfortable sharing because the end result will be personalized and shifted and refined significantly in general, but I was very excited about this concept and the symbolic depth that exists within it. As far as most of my vision work goes, this is one of the most cohesive and universal sets of symbols that has ever come to me, which is really exciting. <a href="https://pagan.plus/tags/Ourobouros" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Ourobouros</a> <a href="https://pagan.plus/tags/Creation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Creation</a> <a href="https://pagan.plus/tags/OccultArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#OccultArt</a> <a href="https://pagan.plus/tags/Generation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Generation</a> <a href="https://pagan.plus/tags/Magick" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Magick</a> <a href="https://pagan.plus/tags/Torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Torus</a> <a href="https://pagan.plus/tags/Sketchbook" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Sketchbook</a> <a href="https://pagan.plus/tags/Siin" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Siin</a>

Spektrum (inoffiziell)Maryam Mirzakhani gewann als erste Frau die prestigeträchtige Fields-Medaille – und zeigte damit allen Frauen, dass auch sie es in der Wissenschaft weit bringen können. <a href="https://www.spektrum.de/kolumne/maryam-mirzakhani-und-die-suche-nach-kurven-auf-donuts/2117469" rel="nofollow noopener noreferrer" target="_blank">Die fabelhafte Welt der Mathematik: Maryam Mirzakhani und die Suche nach Kurven auf Donuts</a> <a href="https://anonsys.net/search?tag=FabelhafteMathematik" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FabelhafteMathematik</a> <a href="https://anonsys.net/search?tag=Mathematik" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematik</a> <a href="https://anonsys.net/search?tag=Geometrie" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometrie</a> <a href="https://anonsys.net/search?tag=Mirzakhani" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mirzakhani</a> <a href="https://anonsys.net/search?tag=Torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Torus</a> <a href="https://anonsys.net/search?tag=Modulraum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Modulraum</a>

@Om*toroidal calibration...<a href="https://mastodon.cloud/tags/torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#torus</a> <a href="https://mastodon.cloud/tags/calibration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calibration</a> <a href="https://mastodon.cloud/tags/colours" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#colours</a> <a href="https://mastodon.cloud/tags/animatedgif" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#animatedgif</a>

rae<a href="https://sunbeam.city/@InvaderXan" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@InvaderXan</a> <a href="https://sunbeam.city/@interneteh" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@interneteh</a> here is the <a href="https://sunbeam.city/tags/torus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#torus</a> house plan that I found years ago, sadly designer Owen Geiger passed away just this past winter. He'd been living in Thailand for years, developing <a href="https://sunbeam.city/tags/earthbag" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#earthbag</a> designs and building a food forest.<a href="http://www.earthbagbuilding.com/plans/torus.htm" rel="nofollow noopener noreferrer" target="_blank">http://www.earthbagbuilding.com/plans/torus.htm</a>

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