Rémi Eismann<p>One day, one decomposition<br>A198773: Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=y</p><p>3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A198773.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3Dgraph/A198773.</span><span class="invisible">html</span></a><br>2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A198773.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/2Dgraph500terms/</span><span class="invisible">A198773.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>javascript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/representations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>representations</span></a> <a href="https://mathstodon.xyz/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://mathstodon.xyz/tags/form" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>form</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>webGL</span></a></p>
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#quadratic
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Rémi Eismann<p>One day, one decomposition<br>A198772: Numbers having exactly one representation by the quadratic form x^2 + xy + y^2 with 0 <= x <= y</p><p>3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A198772.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3Dgraph/A198772.</span><span class="invisible">html</span></a><br>2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A198772.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/2Dgraph500terms/</span><span class="invisible">A198772.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>javascript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/representation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>representation</span></a> <a href="https://mathstodon.xyz/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>webGL</span></a></p>
NR4/Team210<p>I Cooked a reliable winding number filler for quadratic bezier curves. But now which tools edit vector graphics with quadratic bezier paths? SVG supports it, but <span class="h-card" translate="no"><a href="https://mastodon.art/@inkscape" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>inkscape</span></a></span> and the like seem to degree-elevate to cubic per se. <a href="https://abraum.social/tags/demoscene" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>demoscene</span></a> <a href="https://abraum.social/tags/svg" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>svg</span></a> <a href="https://abraum.social/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://abraum.social/tags/bezier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>bezier</span></a> <a href="https://abraum.social/tags/distance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>distance</span></a> <a href="https://abraum.social/tags/windingnumber" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>windingnumber</span></a> <a href="https://abraum.social/tags/filler" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>filler</span></a> <a href="https://abraum.social/tags/vector" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>vector</span></a> <a href="https://abraum.social/tags/vectorgraphics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>vectorgraphics</span></a> <a href="https://abraum.social/tags/graphics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>graphics</span></a> <a href="https://abraum.social/tags/illustration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>illustration</span></a></p>
Rémi Eismann<p>One day, one decomposition<br>A094619: Fundamental discriminants of real quadratic number fields with class number 2</p><p>3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A094619.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3Dgraph/A094619.</span><span class="invisible">html</span></a><br>2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A094619.html" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/2Dgraph500terms/</span><span class="invisible">A094619.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>javascript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/discriminants" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>discriminants</span></a> <a href="https://mathstodon.xyz/tags/real" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>real</span></a> <a href="https://mathstodon.xyz/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://mathstodon.xyz/tags/number" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>number</span></a> <a href="https://mathstodon.xyz/tags/fields" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>fields</span></a> <a href="https://mathstodon.xyz/tags/class" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>class</span></a></p>
:rss: Hacker News<p>Flattening Bézier Curves and Arcs<br><a href="https://minus-ze.ro/posts/flattening-bezier-curves-and-arcs/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">minus-ze.ro/posts/flattening-b</span><span class="invisible">ezier-curves-and-arcs/</span></a><br><a href="https://rss-mstdn.studiofreesia.com/tags/ycombinator" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ycombinator</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/graphics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>graphics</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/vector_graphics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>vector_graphics</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/flattening" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>flattening</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/approximation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>approximation</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/B%C3%A9zier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Bézier</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/cubic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>cubic</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/elliptical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>elliptical</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/arcs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>arcs</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/blossom" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>blossom</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/De_Casteljau" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>De_Casteljau</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/subdivision" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>subdivision</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/arc_length" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>arc_length</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/path_length" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>path_length</span></a></p>
Alexandre B A Villares<p><a href="https://pynews.com.br/tags/Processing" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Processing</span></a> <a href="https://pynews.com.br/tags/python" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>python</span></a> <a href="https://pynews.com.br/tags/py5" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>py5</span></a> <a href="https://pynews.com.br/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a></p>
illestpreacha<p>Rect + Pegs Infused</p><p><a href="https://post.lurk.org/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathart</span></a> <a href="https://post.lurk.org/tags/mathober" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathober</span></a> <a href="https://post.lurk.org/tags/mathober2023" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathober2023</span></a> <a href="https://post.lurk.org/tags/mathober11" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathober11</span></a> <a href="https://post.lurk.org/tags/mathober8" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathober8</span></a> <a href="https://post.lurk.org/tags/counting" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>counting</span></a> <a href="https://post.lurk.org/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> </p><p>Video <a href="https://youtu.be/4JyAFd7VmkQ" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="">youtu.be/4JyAFd7VmkQ</span><span class="invisible"></span></a></p><p>Blogpost: <a href="https://blog.illestpreacha.com/mathober2023countingquadratic" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">blog.illestpreacha.com/mathobe</span><span class="invisible">r2023countingquadratic</span></a></p><p>AudioVisuals coded in <a href="https://post.lurk.org/tags/livecodelab" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>livecodelab</span></a><br>Tweaked for Visuals</p><p>For this combinational prompt, I will be taking my submission for Quadratic: Rect ^ 2 and merging it with a new coded entry for Counting. The counting occurs through different iterations of assessing the time variable</p><p>Overlaid sketches that were coded in LiveCodeLab</p><p>Poem</p><p>Rectangles roaming<br>Rotating & rolling<br>Running & rimming along<br>Reciting the rhymes that belong<br>Twirling and twisting<br>Avoiding the mistakes that were tripping<br>As the angles of the others are tilting<br>Tiling and tipping<br>Tipping to the ways as the rectangles are roaming</p><p><a href="https://post.lurk.org/tags/creativecoding" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>creativecoding</span></a> <a href="https://post.lurk.org/tags/coding" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>coding</span></a><br><a href="https://post.lurk.org/tags/newmedia" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>newmedia</span></a> <a href="https://post.lurk.org/tags/scifi" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>scifi</span></a> <a href="https://post.lurk.org/tags/animation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>animation</span></a><br><a href="https://post.lurk.org/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://post.lurk.org/tags/geometricart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>geometricart</span></a> <a href="https://post.lurk.org/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>geometry</span></a> <a href="https://post.lurk.org/tags/3danimation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>3danimation</span></a></p><p><a href="https://post.lurk.org/tags/codeart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>codeart</span></a> <a href="https://post.lurk.org/tags/programming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>programming</span></a> <a href="https://post.lurk.org/tags/programmer" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>programmer</span></a> <a href="https://post.lurk.org/tags/newmediaart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>newmediaart</span></a> <a href="https://post.lurk.org/tags/creativecodeart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>creativecodeart</span></a> <br><a href="https://post.lurk.org/tags/dailyart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>dailyart</span></a> <a href="https://post.lurk.org/tags/generativeart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>generativeart</span></a> <a href="https://post.lurk.org/tags/artoftheday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>artoftheday</span></a> <a href="https://post.lurk.org/tags/instaartist" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>instaartist</span></a> <a href="https://post.lurk.org/tags/digitalart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>digitalart</span></a> <a href="https://post.lurk.org/tags/sqaures" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>sqaures</span></a><br> <a href="https://post.lurk.org/tags/scifiart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>scifiart</span></a> <a href="https://post.lurk.org/tags/worldbuilding" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>worldbuilding</span></a></p>
nilesh<p>What I find interesting is: b^2 -4ac > 0 can be rewritten to say that the arithmetic mean of roots is > geometric mean. But what even IS geometric mean for two complex numbers?</p><p><a href="https://fosstodon.org/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a> <a href="https://fosstodon.org/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathematics</span></a> <a href="https://fosstodon.org/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://fosstodon.org/tags/equations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>equations</span></a></p>
nilesh<p>This plane represents all possible <a href="https://fosstodon.org/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://fosstodon.org/tags/equations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>equations</span></a> with real coefficients. </p><p>The area in red is where both roots are real because the discriminant b^2 - 4ac is > 0. All the quadratics with imaginary roots lie inside the white region that's a parabola itself.</p><p>Interesting.</p><p><a href="https://fosstodon.org/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>maths</span></a></p>
Xavier B.<p>For me, this is the best method to solve <a href="https://mathstodon.xyz/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://mathstodon.xyz/tags/equations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>equations</span></a> (better than completing squares, general quadratics formula, factorization, ...)</p><p><a href="https://twitter.com/l_d_hodge/status/546712133732696064" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">twitter.com/l_d_hodge/status/5</span><span class="invisible">46712133732696064</span></a></p><p>(Credits from "l hodge" - @l_d_hodge on twitter)</p><p>It's easy to understand, it works with $a \neq 1$ and it has meaning.</p><p>It's based on change of variables and <a href="https://mathstodon.xyz/tags/symmetry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>symmetry</span></a></p>
Khurram Wadee ✅<p>Finally the most sophisticated of the three is Simpson’s rule in which pairs of adjacent strips use a <a href="https://mastodon.org.uk/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://mastodon.org.uk/tags/parabola" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>parabola</span></a> to interpolate between the ordinates. This even better at convergence than the trapezium rule. I’ve shown a different function here because for the function shown above the difference between the approximation and the numerical <a href="https://mastodon.org.uk/tags/approximation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>approximation</span></a> is not discernible.</p><p><a href="https://mastodon.org.uk/tags/MyWork" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MyWork</span></a> <a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mastodon.org.uk/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Maths</span></a> <a href="https://mastodon.org.uk/tags/Numerics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Numerics</span></a> <a href="https://mastodon.org.uk/tags/SimpsonsRule" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SimpsonsRule</span></a> <a href="https://mastodon.org.uk/tags/FreeSoftware" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>FreeSoftware</span></a> <a href="https://mastodon.org.uk/tags/CCBYSA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CCBYSA</span></a> <a href="https://mastodon.org.uk/tags/Wikipedia" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Wikipedia</span></a> <a href="https://mastodon.org.uk/tags/Wikimedia" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Wikimedia</span></a></p>
Michael Connor Buchan<p>Got sick of not having a <a href="https://linuxrocks.online/tags/calculator" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>calculator</span></a> that can <a href="https://linuxrocks.online/tags/solve" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>solve</span></a> <a href="https://linuxrocks.online/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://linuxrocks.online/tags/equations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>equations</span></a>, so I made one. In <a href="https://linuxrocks.online/tags/Rust" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Rust</span></a>!</p><p><a href="https://gist.github.com/mcb2003/6f6779fce0af8bd9881b63636a280f3f" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">gist.github.com/mcb2003/6f6779</span><span class="invisible">fce0af8bd9881b63636a280f3f</span></a></p>
Xavier B.<p>For me, this is the best method to solve <a href="https://scholar.social/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://scholar.social/tags/equations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>equations</span></a> (better than completing squares, general quadratics formula, factorization, ...)</p><p><a href="https://twitter.com/l_d_hodge/status/546712133732696064" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">twitter.com/l_d_hodge/status/5</span><span class="invisible">46712133732696064</span></a></p><p>(Credits from "l hodge" - @l_d_hodge on twitter)</p><p>It's easy to understand, it works with $a \neq 1$ and it has meaning.</p><p>It's based on change of variables and <a href="https://scholar.social/tags/symmetry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>symmetry</span></a></p>
Khurram Wadee ✅<p>I was explaining to my wife yesterday how <a href="https://mastodon.org.uk/tags/DifferentialCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DifferentialCalculus</span></a> gives us a way to find the <a href="https://mastodon.org.uk/tags/gradient" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>gradient</span></a> of a <a href="https://mastodon.org.uk/tags/function" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>function</span></a> at any point and to illustrate it I wrote a short routine in <a href="https://mastodon.org.uk/tags/Maxima" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Maxima</span></a> to draw the <a href="https://mastodon.org.uk/tags/tangent" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>tangent</span></a> to any point on a graph of a function. Here we see the example for the <a href="https://mastodon.org.uk/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> and <a href="https://mastodon.org.uk/tags/reciprocal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>reciprocal</span></a> functions, x^2 and 1/x i.e. a <a href="https://mastodon.org.uk/tags/parabola" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>parabola</span></a> and a <a href="https://mastodon.org.uk/tags/hyperbola" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>hyperbola</span></a> respectively.</p><p><a href="https://mastodon.org.uk/tags/MyWork" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MyWork</span></a> <a href="https://mastodon.org.uk/tags/Gif" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Gif</span></a> <a href="https://mastodon.org.uk/tags/AnimatedGif" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AnimatedGif</span></a> <a href="https://mastodon.org.uk/tags/CCBYSA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>CCBYSA</span></a> <a href="https://mastodon.org.uk/tags/WxMaxima" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>WxMaxima</span></a> <a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mastodon.org.uk/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Maths</span></a> <a href="https://mastodon.org.uk/tags/Calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Calculus</span></a> <a href="https://mastodon.org.uk/tags/Differentiation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Differentiation</span></a></p>
claude<p>I implemented Slow Mating for quadratic polynomials using the equations and hints in Chapter 5 of Wolf Jung's 2017 paper "The Thurston Algorithm for quadratic matings" <a href="https://arxiv.org/abs/1706.04177" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/1706.04177</span><span class="invisible"></span></a></p><p>My code is 145 lines of quite-straightforward C, vs 2249 lines of C++ with various state hidden in mutating objects for the code accompanying the paper (which admittedly does a lot more, working from angles to compute the complex points and (pre)periods that are the input to my code). I'll do a blog post next week once I've tested more cases to make sure I haven't done any big mistakes.</p><p>There were a couple of subtleties, 1. needing to use cproj() to normalize infinity's representation and avoid NaNs; and 2. in one place, converting (a - b) / (a - c) to (1 - b/a) / (1 - c/a) so that it still works when a is infinite.</p><p>Attached images are the north period 4 island mated with the west period 4 island (blue background), and 2/5 bulb mated with 1/2 bulb (turquoise background).</p><p><a href="https://post.lurk.org/tags/Quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Quadratic</span></a> <a href="https://post.lurk.org/tags/JuliaSets" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>JuliaSets</span></a> <a href="https://post.lurk.org/tags/SlowMating" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>SlowMating</span></a> <a href="https://post.lurk.org/tags/RationalFunction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>RationalFunction</span></a> <a href="https://post.lurk.org/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>maths</span></a> <a href="https://post.lurk.org/tags/fractals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>fractals</span></a></p>
IT News<p>The Quadratic Equation Solution a Few Thousand Years in the Making - Everyone learns (and some readers maybe still remember) the quadratic formula. It’s a pillar of alge... more: <a href="https://hackaday.com/2020/01/03/the-quadratic-equation-solution-a-few-thousand-years-in-the-making/" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">hackaday.com/2020/01/03/the-qu</span><span class="invisible">adratic-equation-solution-a-few-thousand-years-in-the-making/</span></a> <a href="https://schleuss.online/tags/polynomial" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>polynomial</span></a> <a href="https://schleuss.online/tags/mischacks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mischacks</span></a> <a href="https://schleuss.online/tags/quadratic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>quadratic</span></a> <a href="https://schleuss.online/tags/featured" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>featured</span></a> <a href="https://schleuss.online/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>math</span></a></p>
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