MetaFilter posts tagged with Math and animation
http://www.metafilter.com/tags/Math+animation
Posts tagged with 'Math' and 'animation' at MetaFilter.Sun, 11 Sep 2016 00:21:14 -0800Sun, 11 Sep 2016 00:21:14 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Animated math
http://www.metafilter.com/162201/Animated%2Dmath
<a href="https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab">Essence of linear algebra</a> - "[<a href="https://twitter.com/3blue1brown">Grant Sanderson</a> of <a href="http://www.3blue1brown.com">3Blue1Brown</a> (<a href="https://www.khanacademy.org/math/linear-algebra/eola-topic">now at Khan Academy</a>) <a href="https://twitter.com/3Blue1Brown/status/772904942365347840">animates</a>] the geometric intuitions underlying linear algebra, making the many matrix and vector operations feel less arbitrary." <ol><li><a href="https://www.youtube.com/watch?v=fNk_zzaMoSs">Vectors, what even are they?</a> - "I imagine many viewers are already familiar with vectors in some context, so this video is intended both as a quick review of vector terminology, as well as a chance to make sure we're all on the same page about how specifically to think about vectors in the context of linear algebra." (9:48)</li>
<li><a href="https://www.youtube.com/watch?v=k7RM-ot2NWY">Linear combinations, span, and basis vectors</a> - "The fundamental vector concepts of span, linear combinations, linear dependence and bases all center on one surprisingly important operation: Scaling several vectors and adding them together." (9:55)</li>
<li><a href="https://www.youtube.com/watch?v=kYB8IZa5AuE">Linear transformations and matrices</a> - "Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra." (10:54)</li>
<li><a href="https://www.youtube.com/watch?v=XkY2DOUCWMU">Matrix multiplication as composition</a> - "Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact." (9:59)
<br> fn. <a href="https://www.youtube.com/watch?v=rHLEWRxRGiM">Three-dimensional linear transformations</a> - "What do 3d linear transformations look like? Having talked about the relationship between matrices and transformations in the last two videos, this one extends those same concepts to three dimensions." (4:42)</li>
<li><a href="https://www.youtube.com/watch?v=Ip3X9LOh2dk">The determinant</a> - "The determinant of a linear transformation measures how much areas/volumes change during the transformation." (9:59)</li>
<li><a href="https://www.youtube.com/watch?v=uQhTuRlWMxw">Inverse matrices, column space and null space</a> - "How to think about linear systems of equations geometrically. The focus here is on gaining an intuition for the concepts of inverse matrices, column space, rank and null space, but the computation of those constructs is not discussed." (12:04)
<br> fn. <a href="https://www.youtube.com/watch?v=v8VSDg_WQlA">Nonsquare matrices as transformations between dimensions</a> - "Because people asked, this is a video briefly showing the geometric interpretation of non-square matrices as linear transformations that go between dimensions." (4:22)</li>
<li><a href="https://www.youtube.com/watch?v=LyGKycYT2v0">Dot products and duality</a> - "Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation." (14:07)</li>
<li><a href="https://www.youtube.com/watch?v=BaM7OCEm3G0">Cross products</a> - "Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation." (8:54)
<br> part 2. <a href="https://www.youtube.com/watch?v=eu6i7WJeinw">Cross products in the light of linear transformations</a> - "This covers the main geometric intuition behind the 2d and 3d cross products." (13:11)</li></ol>
also btw...
<a href="http://setosa.io/ev/eigenvectors-and-eigenvalues/">Eigenvectors and Eigenvalues explained visually</a> - "Eigenvalues/vectors are instrumental to understanding electrical circuits, mechanical systems, ecology and even Google's <a href="http://www.rose-hulman.edu/~bryan/googleFinalVersionFixed.pdf">Page</a><a href="http://www.metafilter.com/140141/Eigendemocracy-crowd-sourced-deliberative-democracy">Rank</a> algorithm. Let's see if visualization can make these ideas more intuitive." (<a href="http://www.epicenecyb.org/archives/date/2016/09#post-22704">via</a>) tag:metafilter.com,2016:site.162201Sun, 11 Sep 2016 00:21:14 -0800kliulessxEuclidx
http://www.metafilter.com/162142/xEuclidx
Compass-and-straightedge construction (aka Euclidean construction) is a method of drawing precise geometric figures using only a compass and a straightedge (like a ruler without the markings). <a href="http://www.mathopenref.com/tocs/constructionstoc.html">MathOpenRef maintains a catalog of many common constructions</a>, each with an explanatory animation and a proof. <a href="https://www.youtube.com/watch?v=LBgIWQcC6lM">This YouTube video</a> demonstrates how to construct almost every <a href="https://en.wikipedia.org/wiki/Constructible_polygon">polygon that can be constructed using these methods</a>. Useful in many decorative arts for laying out figures and patterns, the methods can also be fun to watch, often resulting in an "aha!" moment when one sees how a particular construction is done.
Although not animated, <a href="http://faculty.scf.edu/condorj/256/presentations/Gothic%20Constructions.pdf">this paper</a> [pdf] shows how geometric constructions can be used to create many common Gothic design elements, such as trefoils and arches. tag:metafilter.com,2016:site.162142Thu, 08 Sep 2016 10:29:57 -0800jedicusTime with class! Let's Count!
http://www.metafilter.com/150420/Time%2Dwith%2Dclass%2DLets%2DCount
<a href="https://www.youtube.com/watch?v=Q4gTV4r0zRs">I want to demonstrate how amazing combinatorial explosion is! Please don't stop me. </a> An animation about numbers that get large. It has a happy ending and possibly even a moral. About those "latest algorithmic techniques" mentioned at the end: <a href="http://www-alg.ist.hokudai.ac.jp/~thomas/TCSTR/tcstr_13_64/tcstr_13_64.pdf">Efficient Computation of the Number of Paths in a Grid Graph with Minimal Perfect Hash Functions</a> [PDF] tag:metafilter.com,2015:site.150420Fri, 12 Jun 2015 11:44:44 -0800Wolfdog3Blue1Brown: Reminding the world that math makes sense
http://www.metafilter.com/150242/3Blue1Brown%2DReminding%2Dthe%2Dworld%2Dthat%2Dmath%2Dmakes%2Dsense
<a href="https://www.youtube.com/watch?v=F_0yfvm0UoU">Understanding e to the pi i</a> - "<a href="http://www.3blue1brown.com/s/HowToThinkAboutExponentials.pdf">An intuitive explanation</a> as to why <a href="http://www.bbc.co.uk/programmes/b04hz49f" title="Melvyn Bragg and his guests discuss Euler's number, also known as e. First discovered in the seventeenth century by the Swiss mathematician Jacob Bernoulli when he was studying compound interest, e is now recognised as one of the most important and interesting numbers in mathematics. Roughly equal to 2.718, e is useful in studying many everyday situations, from personal savings to epidemics. It also features in Euler's Identity, sometimes described as the most beautiful equation ever written. With: Colva Roney-Dougal, Reader in Pure Mathematics at the University of St Andrews; June Barrow-Green, Senior Lecturer in the History of Maths at the Open University; and Vicky Neale, Whitehead Lecturer at the Mathematical Institute and Balliol College at the University of Oxford.">e</a> to the <a href="http://www.bbc.co.uk/programmes/p004y291" title="Melvyn Bragg and guests discuss the history of the most detailed number in nature. In the Bible's description of Solomon's temple it comes out as three, Archimedes calculated it to the equivalent of 14 decimal places and today's super computers have defined it with an extraordinary degree of accuracy to its first 1.4 trillion digits. It is the longest number in nature and we only need its first 32 figures to calculate the size of the known universe within the accuracy of one proton. We are talking about Pi, 3.14159 etc, the number which describes the ratio of a circle's diameter to its circumference. How has something so commonplace in nature been such a challenge for maths? And what does the oddly ubiquitous nature of Pi tell us about the hidden complexities of our world? With: Robert Kaplan, co-founder of the Maths Circle at Harvard University; Eleanor Robson, Lecturer in the Department of History and Philosophy of Science at Cambridge University; and Ian Stewart, Professor of Mathematics at the University of Warwick.">pi</a> <a href="http://www.bbc.co.uk/programmes/b00tt6b2" title="Melvyn Bragg and his guests discuss imaginary numbers. In the sixteenth century, a group of mathematicians in Bologna found a solution to a problem that had puzzled generations before them: a completely new kind of number. For more than a century this discovery was greeted with such scepticism that the great French thinker Rene Descartes dismissed it as an 'imaginary' number. The name stuck - but so did the numbers. Long dismissed as useless or even fictitious, the imaginary number i and its properties were first explored seriously in the eighteenth century. Today the imaginary numbers are in daily use by engineers, and are vital to our understanding of phenomena including electricity and radio waves. With: Marcus du Sautoy, Professor of Mathematics at Oxford University; Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick; and Caroline Series, Professor of Mathematics at the University of Warwick.">i</a> equals -1 <a href="https://www.youtube.com/watch?v=1rVHLZm5Aho">without a hint</a> of calculus. This is <a href="https://www.youtube.com/watch?v=zLzLxVeqdQg">not your usual</a> Taylor series nonsense." (<a href="https://twitter.com/stevenstrogatz/status/604653212214292481" title="''A star is born.''">via</a> <a href="https://twitter.com/Noahpinion/status/604679198259580928" title="''Best geek video I've seen all week.''">via</a>; <a href="http://www.reddit.com/r/math/comments/2xzzk0/nontaylorseries_explanation_for_eulers_formula/">reddit</a>; <a href="http://www.metafilter.com/89918/Math-is-beautiful">previously</a>) <a href="https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw">More videos from 3Blue1Brown</a>: "<a href="http://www.3blue1brown.com/">3Blue1Brown</a> is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be <a href="http://www.3blue1brown.com/about/" title="''When the tool I am building for animations becomes something besides a jumble of Python and Duct tape, I'll make it publicly available so that anyone can use it to easily illustrate their own explanations.''">driven by animations</a>, for difficult problems to be made simple with changes in perspective, and for philosophizing to be limited to the brevity and semantic constraints of silly poetry. Basically, math sits in <a href="https://plus.google.com/117663015413546257905/posts/QAhMH35LThk">an ivory tower it built itself out of</a> jargon and impossibly long sequences of (seemingly) logical steps, and I would like to take it out for a walk to <a href="http://wordplay.blogs.nytimes.com/2015/03/09/%CF%80/">meet everyone</a>." tag:metafilter.com,2015:site.150242Sat, 06 Jun 2015 11:42:18 -0800kliulessFake 3D Until You Make 3D
http://www.metafilter.com/145968/Fake%2D3D%2DUntil%2DYou%2DMake%2D3D
Louis Gorenfeld lovingly explores <a href="http://www.extentofthejam.com/pseudo/">the mathematics and techniques</a> behind early, pseudo-3D games. <blockquote>Now that every system can produce graphics consisting of a zillion polygons on the fly, why would you want to do a road the old way? Aren't polygons the exact same thing, only better? Well, no. It's true that polygons lead to less distortion, but it is the warping in these old engines that give the surreal, exhillerating sense of speed found in many pre-polygon games. Think of the view as being controlled by a camera. As you take a curve in a game which uses one of these engines, it seems to look around the curve. Then, as the road straightens, the view straightens. As you go over a blind curve, the camera would seem to peer down over the ridge. And, since these games do not use a traditional track format with perfect spatial relationships, it is possible to effortlessly create tracks large enough that the player can go at ridiculous speeds-- without worrying about an object appearing on the track faster than the player can possibly react since the physical reality of the game can easily be tailored to the gameplay style.</blockquote> tag:metafilter.com,2015:site.145968Fri, 09 Jan 2015 05:43:35 -0800gilrainAspiring Animators & Game Designers, Study Your Calculus & Combinatorics
http://www.metafilter.com/125790/Aspiring%2DAnimators%2Dandamp%2DGame%2DDesigners%2DStudy%2DYour%2DCalculus%2Dandamp%2DCombinatorics
Every film Pixar has produced has landed in the <a href="http://en.wikipedia.org/wiki/List_of_highest-grossing_animated_films">top fifty highest-grossing animated films of all time</a>. What's their secret? <a href="http://www.theverge.com/2013/3/7/4074956/pixar-senior-scientist-derose-explains-how-math-makes-movies-games">Mathematics.</a> Oh, and <a href="http://aerogrammestudio.com/2013/03/07/pixars-22-rules-of-storytelling/">22 Rules of Storytelling</a>. <a href="http://sciencefocus.com/feature/tech/pixar-animations-research-scientist">Dr. DeRose</a> has recently <a href="http://www.deseretnews.com/article/705369303/Whats-the-secret-to-Pixars-success-Math-of-course.html?pg=1">been giving lectures</a> about the Pixar formula ("story, concept art, modeling, rigging, shading and lighting") around the country.
On Youtube: <a href="http://www.youtube.com/watch?v=gXYvDYsh_CQ">Movies, Math and Making</a>.
PDFs of his <a href="http://graphics.pixar.com/library/indexAuthorDeRose.html">papers</a> are archived at Pixar's website.
Vimeo: <a href="http://vimeo.com/22094163">Math in the Movies: Making It All Add Up</a> tag:metafilter.com,2013:site.125790Fri, 08 Mar 2013 13:20:49 -0800zarqFactor Conga
http://www.metafilter.com/121460/Factor%2DConga
<a href="http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/">Animation of prime factorization of the integers</a> based on Brent Yorgey's factorization diagrams, described <a href="http://mathlesstraveled.com/2012/10/05/factorization-diagrams/">here</a>. [via <a href="http://www.datapointed.net/">Data Pointed</a>, <a href="http://www.metafilter.com/106060/Historical-Crayola-rainbow">previously</a>.] tag:metafilter.com,2012:site.121460Thu, 01 Nov 2012 08:17:09 -0800albrechtPythagasaurus
http://www.metafilter.com/109367/Pythagasaurus
<a href="http://www.youtube.com/watch?v=Q5cab4NMHsY">Pythagasaurus</a> is the fabled Tyrannosaurus practiced in the skills of trigonometry and long division. Apparently he knows all eight numbers. <small>[<a href="http://coilhouse.net/">Via</a>]</small> tag:metafilter.com,2011:site.109367Fri, 11 Nov 2011 15:18:13 -0800homunculusGrowing a hyperdodecahedron
http://www.metafilter.com/106119/Growing%2Da%2Dhyperdodecahedron
<a href="http://www.youtube.com/watch?v=MFXRRW9goTs">This short computer graphics animation</a> <em>presents the regular 120-cell: a four dimensional polytope composed of 120 dodecahedra and also known as the hyperdodecahedron or hecatonicosachoron.</em> Gian Marco Tedesco's animation was part of the <a href="http://www.mathfilm2008.de/dvd/index_en.html">MathFilm Festival 2008</a>, which also included <a href="http://motion-design.jp/dice.htm">Dice</a> - if you like it, you'll probably like <a href="http://motion-design.jp/works.htm">Hitoshi Akayama's other animations</a> - and the chilling documentary <a href="http://www.youtube.com/watch?v=08HkQ8TkKbs">Attack of the Note Sheep</a>. tag:metafilter.com,2011:site.106119Tue, 02 Aug 2011 10:44:29 -0800WolfdogQuasi-hypnotic mathematical construct
http://www.metafilter.com/94416/Quasihypnotic%2Dmathematical%2Dconstruct
<a href="http://www.afana.org/cornwell.htm">Bruce and Katharine Cornwell</a> are primarily known for a series of <a href="http://www.archive.org/details/journey_to_the_center_of_a_triangle">remarkable animated films on the subject of geometry</a>. Created on the <a href="http://www.electronixandmore.com/articles/teksystem.html">Tektronics 4051 Graphics Terminal</a>, they are brilliant short films, tracing geometric shapes to intriguing music, including the memorable 'Bach meets Third Steam Jazz' musical score in '<a href="http://www.archive.org/details/afana_congruent_triangles">Congruent Triangles</a>.' tag:metafilter.com,2010:site.94416Wed, 04 Aug 2010 13:58:01 -0800Potomac AvenuePsychemathadelica!
http://www.metafilter.com/73682/Psychemathadelica
How deep does the rabbit hole go? <a href="http://www.fractal-animation.net/ufvp.html">The Ultimate Fractal Video Project</a> features animated zooms into the famous <a href="http://en.wikipedia.org/wiki/Mandelbrot_set">Mandelbrot Set</a>. Some zoom in so far that, by the end of the dive, the first frame you had viewed would be as large as (or larger than) the known universe. | <small>The animations are offered as .zip'd WMV files; lower-quality versions are viewable on <a href="http://www.youtube.com/profile_videos?user=FractAlkemist&p=r">FractAlkemist's YouTube page.</a></small> The author explains: <small><i>"The 'Universe' viddies are so named because at a zoom depth of E+26, the original Mandelbrot is expanded to approximately the size of the known observable universe, 10-20 billion lightyears. And E+61 is the ratio of the entire visible universe to the smallest sub-atomic quantum effects. So where does E+89 take you? To the Mother of All Mandelbrot ZooM animations!
"This one took 8 months to render on 3 systems, all running 24/7. This is the Deepest Mandelbrot ZooM Animation ever made, and ever likely to be made (without frame interpolation, shortcuts, tricks or cheating). It goes all the way to a final zoom depth of E+89, and uses maximum iterations (2,100,000,000) all the way for maximum detail."</i></small>
- - - - -
Recommended uses: download a few, put them in a queue on your media player, and let them play on repeat at your next box social.
- - - - -
<a href="http://www.metafilter.com/44096/MARGE-Youre-soaking-in-it">This FPP</a> by loquacious points to another cool fractal animation site.
- - - - -
Bonus: two more cool fractal animations: one with <a href="http://www.youtube.com/watch?v=gEw8xpb1aRA">Jonathan Coulton's song "Mandelbrot Set" as the soundtrack</a>, the other with a more <a href="http://www.youtube.com/watch?v=WAJE35wX1nQ">baroque flavor</a>.
- - - - -
<small>There are many more examples of fractal animation out there; please add your favorite links in the comments section.</small> tag:metafilter.com,2008:site.73682Tue, 29 Jul 2008 15:56:40 -0800not_on_displayKlik Kandy
http://www.metafilter.com/47409/Klik%2DKandy
<a href="http://www.uncontrol.com/">Klik Kandy</a> tag:metafilter.com,2005:site.47409Thu, 08 Dec 2005 20:53:50 -0800Mr BlueskyNerd Porn
http://www.metafilter.com/46584/Nerd%2DPorn
<a href="http://faraday.physics.utoronto.ca/GeneralInterest/Harrison/Flash/">Flash Animations for Physics.</a> Animations and interactive demos available in many varieties, such as <a href="http://faraday.physics.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/Projectile/Projectile.html">classical mechanics</a>, <a href="http://faraday.physics.utoronto.ca/GeneralInterest/Harrison/Flash/Nuclear/XRayInteract/XRayInteract.html">nuclear</a>, <a href="http://www.upscale.utoronto.ca/PVB/Harrison/BohrModel/Flash/BohrModel.html">quantum</a>, and <a href="http://faraday.physics.utoronto.ca/PVB/Harrison/SpecRel/Flash/LengthContract.html">relativistic</a>. There's even a nice explanation of the forces at work in <a href="http://faraday.physics.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/Curling/Curling.html">Curling</a>. And if that doesn't wet your geek whistle, then take a peek at the patterns of <a href="http://www.miqel.com/pure-math-patterns/visual-math-varieties.html">Visual Math</a>. tag:metafilter.com,2005:site.46584Fri, 11 Nov 2005 10:01:56 -0800GamblorSimpsons math
http://www.metafilter.com/28367/Simpsons%2Dmath
<a href="http://www.mathsci.appstate.edu/~sjg/simpsonsmath/">Simpsonsmath.com:</a> a guide for teachers to engage math-o-phobes with animated fun. <em>"Mmmmmm, pi."</em> tag:metafilter.com,2003:site.28367Wed, 17 Sep 2003 11:11:06 -0800serafinapekkala