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#quaternions

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Alex Nelson<p>Another Thursday project idea for formalizing stuff in Mizar: The Icosians!</p><p>The Icosian group is isomorphic to the binary icosahedral group, but built out of quaternions.</p><p>We can use them to form a ring, also (confusingly) called the Icosians.</p><p>You can then form a lattice out of them, and it&#39;s isomorphic to the root lattice for the E8. It&#39;s really quite amazingly beautiful!</p><p><a href="https://mathstodon.xyz/tags/Mizar" class="mention hashtag" rel="tag">#<span>Mizar</span></a> <a href="https://mathstodon.xyz/tags/Quaternions" class="mention hashtag" rel="tag">#<span>Quaternions</span></a> <a href="https://mathstodon.xyz/tags/Icosians" class="mention hashtag" rel="tag">#<span>Icosians</span></a> <a href="https://mathstodon.xyz/tags/ProofAssistant" class="mention hashtag" rel="tag">#<span>ProofAssistant</span></a> <a href="https://mathstodon.xyz/tags/E8" class="mention hashtag" rel="tag">#<span>E8</span></a> <a href="https://mathstodon.xyz/tags/Lattice" class="mention hashtag" rel="tag">#<span>Lattice</span></a> </p><p><a href="https://thmprover.wordpress.com/2025/01/02/icosians-in-mizar/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">thmprover.wordpress.com/2025/0</span><span class="invisible">1/02/icosians-in-mizar/</span></a></p>
dbat :godot:<p><a href="https://mastodon.gamedev.place/tags/GodotEngine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GodotEngine</span></a> <a href="https://mastodon.gamedev.place/tags/Quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Quaternions</span></a> <a href="https://mastodon.gamedev.place/tags/PleaseHelp" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PleaseHelp</span></a> </p><p>Added another simpler version to the forum post:</p><p><a href="https://forum.godotengine.org/t/quaternion-rotates-but-then-reverses/73642/2" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">forum.godotengine.org/t/quater</span><span class="invisible">nion-rotates-but-then-reverses/73642/2</span></a></p><p>🦇</p>
dbat :godot:<p><a href="https://mastodon.gamedev.place/tags/GodotEngine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GodotEngine</span></a> <a href="https://mastodon.gamedev.place/tags/Quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Quaternions</span></a> <a href="https://mastodon.gamedev.place/tags/help" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>help</span></a> </p><p>I have posted a question on the forums. Anyone feeling brain enough to help?</p><p><a href="https://forum.godotengine.org/t/quaternion-rotates-but-then-reverses/73642" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">forum.godotengine.org/t/quater</span><span class="invisible">nion-rotates-but-then-reverses/73642</span></a></p><p>🦇</p>
dbat :godot:<p><a href="https://mastodon.gamedev.place/tags/GodotEngine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GodotEngine</span></a> <a href="https://mastodon.gamedev.place/tags/Quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Quaternions</span></a> </p><p>Hey! I'm getting the hang of this Quaternion thang! Look at it rotate!</p><p>0 degrees.<br>90 degrees. WhoooO!<br>180 degrees! Man, the excite!</p><p>90 degrees? Huh?</p><p>It's now oscillating. I don't even oscillate any more. I'm too old!<br>Please stop.</p><p>&lt;Imaginary Error: Quaternions are allergic to 2/PI+PI. Please report this to the Lovecraft hotline. Good luck in hell&gt;</p><p>🦇</p>
∞ 𝕁uan ℂarlos<p>Rotating rings now in @threejs <br /><a href="https://www.dynamicmath.xyz/threejs/rings-rotating/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">dynamicmath.xyz/threejs/rings-</span><span class="invisible">rotating/</span></a><br />using <a href="https://mathstodon.xyz/tags/quaternions" class="mention hashtag" rel="tag">#<span>quaternions</span></a> 🤯😃</p><p>Adapted from<br /><a href="https://threejs.org/examples/#webgl_lights_rectarealight" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">threejs.org/examples/#webgl_li</span><span class="invisible">ghts_rectarealight</span></a> by Abel Allison <a href="https://github.com/abelnation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">github.com/abelnation</span><span class="invisible"></span></a></p><p>Inspired by <a href="https://www.geogebra.org/m/xsy4fy25" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="">geogebra.org/m/xsy4fy25</span><span class="invisible"></span></a></p><p><a href="https://mathstodon.xyz/tags/threejsJourney" class="mention hashtag" rel="tag">#<span>threejsJourney</span></a></p>
Kevin Moerman 🔓🦿:julia:<p>This is a fantastic article on rotations and <a href="https://fosstodon.org/tags/quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quaternions</span></a> by <span class="h-card" translate="no"><a href="https://mastodon.gamedev.place/@TheNumbat" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>TheNumbat</span></a></span> based on lecture notes by <span class="h-card" translate="no"><a href="https://mathstodon.xyz/@keenancrane" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>keenancrane</span></a></span> </p><p><a href="http://thenumb.at/Exponential-Rotations/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">http://</span><span class="ellipsis">thenumb.at/Exponential-Rotatio</span><span class="invisible">ns/</span></a></p><p>My son saw the test model there "Spot the cow", and we just had to <a href="https://fosstodon.org/tags/3dprint" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>3dprint</span></a> one and color it in :) </p><p>Get yours over at Keenan's model repository: <br><a href="https://www.cs.cmu.edu/~kmcrane/Projects/ModelRepository/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">cs.cmu.edu/~kmcrane/Projects/M</span><span class="invisible">odelRepository/</span></a></p><p><a href="https://fosstodon.org/tags/GeometryProcessing" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GeometryProcessing</span></a></p>
Prof. Sally Keely<p>Happy St. Paddy&#39;s Day! </p><p>&quot;On October 16, 1843, the great Irish mathematician William Rowan Hamilton was walking along the Royal Canal in Dublin. He had been pondering for a long time whether complex numbers could be extended to higher dimensions. During his perambulation, he realized the answer was “yes”, and carved his solution on the Brougham Bridge. The plaque shown [below] commemorates the discovery.&quot; <a href="https://mathstodon.xyz/tags/ComplexNumbers" class="mention hashtag" rel="tag">#<span>ComplexNumbers</span></a> <a href="https://mathstodon.xyz/tags/quaternions" class="mention hashtag" rel="tag">#<span>quaternions</span></a> </p><p><a href="https://galileospendulum.org/2013/03/17/irish-mathematics-for-st-patricks-day/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">galileospendulum.org/2013/03/1</span><span class="invisible">7/irish-mathematics-for-st-patricks-day/</span></a></p>
Bríd McGrath<p><span class="h-card" translate="no"><a href="https://mastodon.social/@gutenberg_org" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>gutenberg_org</span></a></span> same with Rowan Hamilton’s discovery of <a href="https://mastodon.ie/tags/quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quaternions</span></a></p>
Eugene Alvin Villar 🇵🇭<p><span class="h-card" translate="no"><a href="https://mastodon.social/@acegikmo" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>acegikmo</span></a></span> excellent lecture! My frustration is that I still do not have an intuitive grasp of <a href="https://en.osm.town/tags/quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quaternions</span></a> the way I do with complex numbers and the complex plane.</p>
Tacitus 🇮🇪 :godot: :linux:<p>Phenomenal video by <span class="h-card" translate="no"><a href="https://mastodon.social/@acegikmo" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>acegikmo</span></a></span> giving a deep explanation on developing a vector product equation from first principles, visualising and explaining what the result means. Great explanation of the various rules and procedures surrounding vectors too.</p><p><a href="https://www.youtube.com/watch?v=htYh-Tq7ZBI" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">youtube.com/watch?v=htYh-Tq7ZB</span><span class="invisible">I</span></a></p><p><a href="https://mastodon.gamedev.place/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Maths</span></a> <a href="https://mastodon.gamedev.place/tags/LinearAlgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>LinearAlgebra</span></a> <a href="https://mastodon.gamedev.place/tags/GeometricAlgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GeometricAlgebra</span></a> <a href="https://mastodon.gamedev.place/tags/Quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Quaternions</span></a> <a href="https://mastodon.gamedev.place/tags/GameDev" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>GameDev</span></a></p>
nope<p>Computer Graphics and Geometric Modeling<br>(2004) : Agoston, Max K.<br>DOI: <a href="https://doi.org/10.1007/b138805" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="">doi.org/10.1007/b138805</span><span class="invisible"></span></a><br><a href="https://mastodon.social/tags/graphics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>graphics</span></a> <a href="https://mastodon.social/tags/pipeline" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>pipeline</span></a> <a href="https://mastodon.social/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>geometry</span></a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://mastodon.social/tags/colour" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>colour</span></a> <a href="https://mastodon.social/tags/text_book" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>text_book</span></a> <a href="https://mastodon.social/tags/quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quaternions</span></a> <a href="https://mastodon.social/tags/my_bibtex" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>my_bibtex</span></a></p>
Quincy<p>have you ever used <a href="https://chaos.social/tags/quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quaternions</span></a>?</p>
nope<p>Learn Vertex and Pixel Shader Programming with DirectX 9<br>(2004) : Leiterman, James C.<br>isbn: 1-55622-287-4<br><a href="https://mastodon.social/tags/direct_x" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>direct_x</span></a> <a href="https://mastodon.social/tags/quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quaternions</span></a> <a href="https://mastodon.social/tags/vertex_shaders" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>vertex_shaders</span></a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://mastodon.social/tags/matrix_match" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>matrix_match</span></a> <a href="https://mastodon.social/tags/shaders" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>shaders</span></a> <a href="https://mastodon.social/tags/fragment_shaders" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>fragment_shaders</span></a> <a href="https://mastodon.social/tags/my_bibtex" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>my_bibtex</span></a></p>
Ricardo<p>Quaternions are Amazing and so is William Rowan Hamilton! | Kathy Loves Physics &amp; History <br> <br><a href="https://www.youtube.com/watch?v=CdwxpSInhvU" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">youtube.com/watch?v=CdwxpSInhv</span><span class="invisible">U</span></a> <br> <br><a href="https://mastodon.social/tags/William_Rowan_Hamilton" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>William_Rowan_Hamilton</span></a> <a href="https://mastodon.social/tags/quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quaternions</span></a> <a href="https://mastodon.social/tags/history" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>history</span></a> <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathematics</span></a> <a href="https://mastodon.social/tags/science" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>science</span></a></p>
cos<p>3D graphics programmers know this too well. </p><p><a href="https://nitter.nl/grapefrukt/status/1618517709767016450" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">nitter.nl/grapefrukt/status/16</span><span class="invisible">18517709767016450</span></a></p><p><a href="https://fosstodon.org/tags/quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quaternions</span></a> <a href="https://fosstodon.org/tags/gamedev" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>gamedev</span></a></p>
Kenneth<p>I need a <a href="https://social.linux.pizza/tags/VennDiagram" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>VennDiagram</span></a> of Home, Local, and Federal. I strongly suspect that one of these is orthogonal to the others. <a href="https://social.linux.pizza/tags/Quaternions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Quaternions</span></a> may be involved.</p>
Arnoud Buzing<p>Interesting post on <a href="https://mathstodon.xyz/tags/wolfram" class="mention hashtag" rel="tag">#<span>wolfram</span></a> about <a href="https://mathstodon.xyz/tags/hypercomplex" class="mention hashtag" rel="tag">#<span>hypercomplex</span></a> numbers (<a href="https://mathstodon.xyz/tags/quaternions" class="mention hashtag" rel="tag">#<span>quaternions</span></a>, <a href="https://mathstodon.xyz/tags/octonions" class="mention hashtag" rel="tag">#<span>octonions</span></a>) using <a href="https://mathstodon.xyz/tags/cayleydickson" class="mention hashtag" rel="tag">#<span>cayleydickson</span></a> construction: </p><p><a href="https://community.wolfram.com/groups/-/m/t/1730287" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">community.wolfram.com/groups/-</span><span class="invisible">/m/t/1730287</span></a></p>
Simon Koch :monotile_spectre:<p>Calculating <a href="https://mathstodon.xyz/tags/quaternions" class="mention hashtag" rel="tag">#<span>quaternions</span></a> by hand is very tedious yet very satisfying.</p><p>I calculated that the point (1|2|3) when rotated by 56° around the axis \(\begin{pmatrix}1\\3\\1\end{pmatrix}\) gets moved to approximately (2.71|1.82|1.83).</p><p>Calculating took around 20 minutes. Checked with <a href="https://mathstodon.xyz/tags/wolframalpha" class="mention hashtag" rel="tag">#<span>wolframalpha</span></a> in seconds.</p>
Simon Koch :monotile_spectre:<p><a href="https://eater.net/quaternions" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">eater.net/quaternions</span><span class="invisible"></span></a></p><p>A beautiful interactive experience by <a href="https://mathstodon.xyz/tags/3blue1brown" class="mention hashtag" rel="tag">#<span>3blue1brown</span></a> and Ben Eater, which does a wonderful job at visualizing <a href="https://mathstodon.xyz/tags/quaternions" class="mention hashtag" rel="tag">#<span>quaternions</span></a> multiplication and how it can be used to model 3d rotations.</p>
Jon Awbrey<p><span class="h-card" translate="no"><a href="https://mathstodon.xyz/@johncarlosbaez" class="u-url mention">@<span>johncarlosbaez</span></a></span> </p><p>I remember <a href="https://mathstodon.xyz/tags/Eddington" class="mention hashtag" rel="tag">#<span>Eddington</span></a> was real big on the use of <a href="https://mathstodon.xyz/tags/Quaternions" class="mention hashtag" rel="tag">#<span>Quaternions</span></a> in <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="tag">#<span>Physics</span></a>.</p><p>Cursory search turns up this —<br />• <a href="https://www.jstor.org/stable/3609461" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="">jstor.org/stable/3609461</span><span class="invisible"></span></a></p>
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