3blue1brown sphere

Sphere thanks — 3Blue1Brow

If you enjoyed this video on the surface area of a sphere, join me in saying a special thanks to these wonderful viewers: 1stViewMaths. Adam Miels. Adrian Robinson. Alan Stein. Alex Dodge. Alex Frieder. Alexis Olson. Ali Yahya Visualizing high-dimensional spheres to understand a surprising puzzle.Help fund future projects: https://www.patreon.com/3blue1brownThis video was sponsored..

Thinking outside the 10-dimensional box - YouTub

Join the discussion. If you want to ask questions, share interesting math, or discuss videos, take a look at the 3blue1brown subreddit. People have also shared projects they're working on here, like their own videos, animations, and interactive lessons. When relevant, these will often be added to 3blue1brown video descriptions as additional. I just watched 3Blue1Brown's excellent video about the following problem: Four points are chosen independently and at random on the surface of a sphere (using the uniform distribution). What is the probability that the center of the sphere lies inside the resulting tetrahedron? My first idea was that it looks like the center won't be in the tetrahedron if all 4 points can be contained in a. The region on a sphere between two great circles is called a lune. Let's figure out the surface area of a lune bounded by Also the inimitable 3blue1brown has a great video on the polyhedron formula, as well as a video about the surface area of a sphere. Thanks for reading the proof! Take a look at the code if you're interested in how this was made. GitHub Projects: prideout/euler; google. Manim is an engine for precise programmatic animations, designed for creating explanatory math videos. Note, there are two versions of manim. This repository began as a personal project by the author of 3Blue1Brown for the purpose of animating those videos, with video-specific code available here.In 2020 a group of developers forked it into what is now the community edition, with a goal of. Project the points from the sphere onto an infinite plane using a stereographic projection [9]. This maps the northern hemisphere onto points inside the unit circle, and the southern hemisphere onto points outside the unit circle. There's a proof that this projection produces a correct Delaunay Triangulation on a sphere; links at the end of the page. Run the unmodified Delaunay triangulation.


  1. Ellipse from lines (inspired by a 3blue1brown video) Modulo multiplication (inspired by a Mathologer video) Orbits of planets (inspired by a John Carlos Baez blog post) Noisy edges using shaders. Car blind spots [8] Bacterial cell animation. Conveyor belt editor (inspired by Factorio) Tiling a sphere with diagonal squares. Tiling a sphere with hexagons. Tiling a sphere with Voronoi. Tiling a.
  2. Sphere and other Orbiforms: pi day special post- volumes of constant width made from solid brass. These shapes have constant diameter no matter their orientation and will roll like spheres between two planes- note how the acrylic plate stays parallel to the table as the sphere and other orbiforms roll underneath. The first orbiform is based on the Reuleaux triangle and the second on a Reuleaux.
  3. Mehr von 3blue1brown auf Facebook anzeigen. Anmelden. ode
  4. I was trying to learn to calculate are and volume of a sphere. (For a 20 radius fireball in Dungeons and Dragons) I couldn't find a formula for volume using Tau, so I augmented the formula for area. Area= Radius to the 2nd power, divided by 2, then times Tau (6.283185) Volume= Radius to the 3rd power, divided by 3, then times 2Tau (12.56623706
  5. It's easiest to start understanding this idea in a lower dimensional context, like mapping the surface of a sphere onto 2d plane. The geography enthusiasts among you will know that there are many different tactics for displaying the surface of the earth on a 2d plane. Here's what it would look like using a stereographic projection: By Strebe CC BY-SA 3.0, from Wikimedia Commons. In.

Q&A Questions : 3Blue1Brow

Euler's Polyhedron Formula - The Little Grasshoppe

3Blue1Brown. What you will learn from this course? - The hardest problem on the hardest test - But what is a Neural Network? - Exponential growth and epidemics - The most unexpected answer to a counting puzzle - But what is the Fourier Transform? A visual introduction. - But how does bitcoin actually work? - Simulating an epidemic - The Essence of Calculus - Vectors, what ev Mathematica Demonstration of the 3Blue1Brown Video on Ellipses as Conic Sections (Dandelin Spheres) The goal of these videos, as well as this post, is to understand why the definition of an ellipse as a conic section (the intersection of a certain plane with a cone) is the same as the sum of distances definition (the locus of points, the sum of whose distances to two points (foci. (And a 1-dimensional sphere = circle right?) $\endgroup$ - kennytm Aug 2 '10 at 14:01 $\begingroup$ @KennyTM: The circle is the two dimensional sphere, I think. Otherwise the answer would be 0. $\endgroup$ - Jens Aug 2 '10 at 14:0

• Solution: Embed 2-sphere in 3D - Interpolate 3D points on the 2-sphere along great circles - When done interpolating, convert the point back to angles • Use slerp for uniform velocity & to stay on sphere - Note that it's still a 1D problem along the great circle - q 0 and q 1 are now 3D points (2-DOF Orientation) q0 q1 1 Dandelin Spheres https://www.physicsfunshop.com/search?keywords=dandelin Slicing a cone with a plane can produce an ellipse, and two spheres..

GitHub - 3b1b/manim: Animation engine for explanatory math

Boolean Modifier ¶. Boolean Modifier. The Boolean modifier performs operations on meshes that are otherwise too complex to achieve with as few steps by editing meshes manually. It uses one of the three available Boolean operations to create a single mesh out of two mesh objects: This modifier needs a second mesh object, or collection of mesh. 3blue1brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective 3Blue1Brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective.\\n\\nFor more information, other projects, FAQs, and inquiries see the website: www.3blue1brown.co In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1 / 2.Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers If you believe Banach and Tarski, you can take a sphere, cut it into a handful of pieces, move them around, and put them back together into two complete spheres of the same size. 1. The accountants and engineers may be a bit angry about magically doubling a sphere but the proof that you can double a sphere does almost nothing questionable. In fact, the most questionable thing we have to do.

Radius of sphere = 4 Render method= Write. Read more about Create Spherical Zone With Manim; Add new comment; Create a Partial Cylindrical Surface With Manim . Submitted by Jhun Vert on Mon, 11/02/2020 - 01:42. A cylindrical surface of radius radius 4 and axis on the xz-plane and at a distance of 1.5 units from the xy-plane. The thickness of the cylinder is 4 units and the curvilinear length. Probability that a random tetrahedron over a sphere contains its center. Nicolás Guarín-Zapata. 2017-12-13 15:24. Comments. Also available in: Español. I got interested in this problem watching the YouTube channel 3Blue1Brown, by Grant Sanderson, where he explains a way to tackle the problem that is just elegant! I can't emphasize enough how much I like this channel. For example, his. On the other hand, there is no homeomorphism from the torus to, for instance, the sphere, signifying that these represent two topologically distinct spaces.Part of topology is concerned with studying homeomorphism-invariants of topological spaces (topological properties) which allow to detect by means of algebraic manipulations whether two topological spaces are homeomorphic (or more. 3Blue1Brown creator Grant Sanderson '15 talks engaging with math using stories and visuals Grant Sanderson '15, creator of YouTube channel 3Blue1Brown, discusses how storytelling and visuals.


Bloch Sphere. Hadamard Gate, Paulli Gates, Toffoli Gate. Quantum Cryptography. Course content. 8 sections • 33 lectures • 2h 2m total length. Expand all sections. Introduction to Quantum Computing 4 lectures • 13min. Course Introduction. Preview 03:58. Classical Computing Vs. Quantum Computing. Preview 01:15. Quantum Computing and Its Applications. Preview 04:16. Classical Computing.

Delaunay+Voronoi on a sphere - Red Blob Game

3Blue1Brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective Kernel density estimation is a really useful statistical tool with an intimidating name. Often shortened to KDE, it's a technique that let's you create a smooth curve given a set of data.. This can be useful if you want to visualize just the shape of some data, as a kind of continuous replacement for the discrete histogram Verdict: This series of videos by 3Blue1Brown was created in 2017, which is a relatively long time for a technical topic. However, to this date, they are still one of the most informative deep learning videos out there. If you haven't yet checked out 3Blue1Brown's channel on YouTube, then we highly recommend you do so. 8. Deep Learning: Recurrent Neural Networks in Python. View on Udemy. Assume the sphere is centered at the origin, and that the first point P 0 is located at the north pole of the sphere, with the three remaining points then located at random locations on the sphere. We can assume that these remaining points are chosen in a two-step process: first a diameter P i 1 P i 2 ( i Î {1,2,3}) is fixed and then one of the two end-points { P i 1 , P i 2 } is selected as.

Red Blob Game

Imagine that you had to compute the double integral. (1) ∬ D g ( x, y) d A. where g ( x, y) = x 2 + y 2 and D is the disk of radius 6 centered at the origin. In terms of the standard rectangular (or Cartesian) coordinates x and y, the disk is given by. − 6 ≤ x ≤ 6 − 36 − x 2 ≤ y ≤ 36 − x 2. We could start to calculate the. Conic section (3Blue1Brown) A beautiful proof of why slicing a cone gives an ellipse (Dandelin spheres (1822)). 3Blue1Brown. Written on August 23, 2018 math blog video 3blue1brown. If you are doing that on a sphere, like an airplane, the shortest distance is a great curve. But under the effects of gravity, what is the (For a great video on the subject, please see the video The Brachistochrone, with Stephen Strogatz on the 3Blue1Brown YouTube channel.) Johann Bernoulli solved the problem using: Fermat's principle, also known as the principle of least time.

Dandelin Spheres: Slicing a cone with a plane can produce an ellipse, and two spheres encapsulated by the same cone will always have the small sphere touching one focus and the large sphere contacting the plane at the other focus. This beautiful acrylic model shows this geometry for one choice of cone width and dissecting plane angle- but it is always true. This geometric construction is named. 3Blue1Brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective. For more information, other projects, FAQs, and inquiries see the website: https://www.3blue1brown.co For those of you (like me) who can't, a video by 3Blue1Brown on YouTube provides a pretty elegant explanation of the analytical solution. The word random in the problem, however, sparked off an alternate train of thought in my mind that eventually led to the solution that I'm going to present. I considered the possibility of obtaining the solution through random sampling. The idea. 3Blue1Brown. Related Artist. MinutePhysics Artist Info; PBS Space Time Artist Info; Stand-up Maths Artist Info; Kurzgesagt - In a Nutshell Artist Info; VSauce Artist Info; Exponential growth and epidemics. This problem seems hard, then it doesn't, but it really is. Simulating an epidemic. But how does bitcoin actually work? The most unexpected answer to a counting puzzle. Why do prime.

Math Toys physicsfun sho

  1. Compass Labels on Polar Axes. This example shows how to plot data in polar coordinates. Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands. Choose a web site to get translated content where available and see local events and offers
  2. Brilliant - Build quantitative skills in math, science, and computer science with fun and challenging interactive explorations
  3. Random variables and their distributions are the best tools we have for quantifying and understanding unpredictability. This course covers their essential concepts as well as a range of topics aimed to help you master the fundamental mathematics of chance. Upon completing this course, you'll have the means to extract useful information from the randomness pervading the world around us
  4. 3Blue1Brown. Related Artist. MinutePhysics Artist Info; PBS Space Time Artist Info; Stand-up Maths Artist Info; Kurzgesagt - In a Nutshell Artist Info; VSauce Artist Info; Exponential growth and epidemics. This problem seems hard, then it doesn't, but it really is. But how does bitcoin actually work? Simulating an epidemic . The most unexpected answer to a counting puzzle. Why do prime.

3blue1brown - New video! But WHY is a sphere's surface

Stokes theorem says that ∫F·dr = ∬curl (F)·n ds. If you think about fluid in 3D space, it could be swirling in any direction, the curl (F) is a vector that points in the direction of the AXIS OF ROTATION of the swirling fluid. curl (F)·n picks out the curl who's axis of rotation is normal/perpendicular to the surface The medical test paradox: Can redesigning Bayes rule help? | 3Blue1Brown. @k_o_t • A simple and intuitive breakdown of Sphere Eversion method(s) in topology. @k_o_t • rreusser.github.io • 1Y; 2 Comments. @k_o_t • citeseerx.ist.psu.edu • 10M; Search for the Wreckage of Air FranceFlight AF 447. 0 Comments. 1. 1. Search for the Wreckage of Air FranceFlight AF 447. @k_o_t. Python. The one extra thing that you'll need to do to get the script to run is type: import.bpy. Python. At the top of the file, so that it can read Blender Python. It's also helpful to switch on the three buttons for line numbers, word wrap, and syntax highlighting in the Text Editor's header

r/3Blue1Brown - Michael Atiyah on Dirac and Spinors

Binary counting can solve the towers of Hanoi puzzle, and if this isn't surprising enough, it can lead to a method for finding a curve that fills Sierpinski's triangle (which I get to in part 2) Yup! It turns out that making choices is more controversial than it seems it should be. 2 In fact, the Axiom of Choice is perhaps the most discussed and most controversial axiom in all of mathematics. 3. To convince you that choosing is hard, let's look at simple example, picking a number between 0 and 1. Go ahead, pick one 3blue1brown is always incredible, and this is a lovely demonstration of how definitions work and how ellipses are defined. math is amazing dandelin spheres This video presents one idea. Using number lines to represent axes, we can plot a certain point on a shape regardless of how many dimensions its in. From there, 3Blue1Brown explains how this idea.

Inspired by YouTubers like 3Blue1Brown... and various Twitter users, I decided to write my own library in Python from scratch, If the rays indeed to hit a (an) object(s), say a sphere is hit first, then we paint that pixel with the color of that sphere. Raytraced Spheres in low and high resolutions. I was not using my GPU for this, which is why the simulation is laggy for higher resolution. Visualizing quaternions, an explorable video series. While your browser seems to support WebGL, it is disabled or unavailable. There may be a setting in your browser you need to turn on. You may find this page useful to help you get WebGL working. If all else fails, it may be easiest to try a different computer From Raval to the infamous BitConnect gang, this sphere is seemingly populated by Canterbury Tales-style cozeners, and I personally can't wait until it fades into oblivion. In short, Raval's actions not only amount to a lie to his audience, but it hurts the actual researchers doing real work in his fields. This includes the researchers he plagiarized. However, Raval doesn't seem to care. Mathematische Aprilscherze. Von Thilo / 1. April 2017 / 6 Kommentare / Seite 1 von 2 / Auf einer Seite lesen. Dass Aprilscherze nicht immer subtil sein müssen, bewies Martin Gardner im April 1975: die Relativitätstheorie ist widerlegt, Leonardo da Vinci hat die Wasserspülung erfunden, im Schach gewinnt 1.h4 mit 100%iger Sicherheit, ist eine.

Picking a point uniformly on a sphere (of radius 1, say) can be done in several ways. My two favorite methods are: Pick z uniformly between -1 and 1, then pick an angle at random to determine x and y. This really does work!! Pick three numbers from a Gaussian distribution, then normalize the resulting vector Qt5 Installationsanleitung OpenGL 3 Qt Example Sphere Flake Example: 2. Display-Technik 2: Raster- und Vektor-Graphik, der Frame-Buffer, Video-Controller und Videosignale, color lookup table, Buffering-Varianten (double buffering, triple buffering), Synchronisation-Verfahren (VSYNC, GSYNC et al.), PDF: Blatt 2: Matrix: 3. Display-Technik 3: Critical Flicker Frequency, Gammakorrektur Geometrie.

By 3blue1brown. Another 3blue1brown series, this time on another mathematical construct that is commonly used in 3D graphics applications to make it easier to deal with rotations. How to walk through walls using the 4th Dimension [Miegakure: a 4D game]. By Marc ten Bosch. Why stop at three dimensions? Marc ten Bosch is developing a video game set in a four-dimensional world. If you are. The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.-Galileo Galilei I've always loved this quote

Resources. This is a list of some free to use resources for developers to help them in learning and enhancing their skills. The list contains YouTube channels, websites, cheatsheets, hosting services, tools, etc. The list may not contains all the best resources, but I tried to add almost all the resources I have used As all other 3Blue1Brown videos it is not only fascinating but also exceptionally well made. Warning: You might fall down a math rabbit hole. Answer: Pretty secure. Bruce Schneier used the physical limits of computation to put this number into perspective: even if we could build an optimal computer, which would use any provided energy to flip bits perfectly, build a Dyson sphere around our su

Yes and no. It's actually a very subtle question. Much like waves on a circle, atoms are also standing waves subject to some interesting geometrical symmetries. However, the symmetries of atoms, even Hydrogen, the very simplest atom, are much more.. You can try to visualize it by considering what happens to the unit sphere in your vector space as it's being transformed by the matrix \(A\). First, we apply some transformation \(V^T\), which is essentially a rotation, since it's a matrix with orthonormal rows. (A matrix with orthonormal rows just changes the coordinate axes via some rotation or reflection but does no scaling.) Next, we.

Final Velocity of sphere - YouTube

Visualizing quaternions, an explorable video serie

Sphere surface == four times its shadow (3Blue1Brown) December 03, 2018 Quaternions (3Blue1Brown) September 07, 2018 Quasirandom sequence August 30, 2018 Conic section (3Blue1Brown) August 23, 2018 Strength Reduction (Fastware - Andrei) July 15, 201 Susan Johnsey April 28, 2020 1 Precalculus. 3blue1brown, cosine, identities, imaginary numbers, LOCKDOWNmath, rotations, sine. The complex number system is comprised of real numbers and the imaginary numbers. 3+4i or i√2 or . Read More Start at the origin. Then begin to draw a sequence of connected line segments of length 1 by using your function. For example, if you have chosen x³, your first line segment will be along direction 1³=1. At the end of this, you will draw another line segment along direction 2³=8, and you will continue in this fashion

A matrix times matrix multiplication (eg 3x3 times 3x3) is just projecting the axis of one matrix onto the other: expressing the coordinate system in terms of a different coordinate system. The 4x3 (or 4x4) matrix is needed for translation and 3d projection for a 3d triangle onto a 2d plane (screen pixels) sphere. Technically, we are discussing tangent vectors that lie in the tangent space of the manifold at each point. For example, a sphere may be embedded in a three-dimensional Euclidean space intowhich may beplaced aplanetangent tothesphere atapoint. A two-dimensional vector space exists at the point of tangency. However, such an embedding is not required to define the tangent space of a. The Sun is almost a perfect sphere with a radius of 432,170 mi 695,700 km. The Earth's shape resembles an ellipsoid with an average radius of 3958.8 mi 6371 km. As such, the radius of the Sun is 109 times larger than that of the Earth. Naturally, the Sun doesn't look that large in the sky, but that's because the Sun is quite far away from the Earth. Before we see how far away the Sun is. Mathematician Grant Sanderson, who is behind the YouTube channel 3Blue1Brown, told ABC News that there's a one in 23,541 chance of a consecutive sequence like Tuesday's draw winning. Which, it.

Darts in Higher Dimensions — Numberphil

Check out the 3Blue1Brown video segment below for some helpful visualizations for spans of vectors in three-dimensional space. Continue. Span is closely related to linear dependence, which we will discuss in the next section. To reveal more content, you have to complete all the activities and exercises above. Are you stuck? Skip to the next step or reveal all steps. Next up: Linear. Before we go any further, I recommend checking out 3Blue1Brown's video Thinking outside the 10-dimensional box. In our case, we are looking for the surface area of a sphere with 3N dimensions and radius of the square root of 2mU. Hyperspheres. There are many ways to find the surface area of an n-dimensional sphere. I'd rather not do the direct integral in this derivation since I'd have. Case 4: When the object is a sphere (S=1) and red (R=1) The SUM>0 which means the output is 1. Et Voila! Our perceptron says it is a cricket ball. This is the most rudimentary idea behind a neural network. We connect lot of these perceptrons in a particular manner and what we get is a neural network. I've oversimplified the idea a little bit but it still captures the essence of a perceptron.

the sphere.) B-1 Let S be a set of n distinct real numbers. Let A S be the set of numbers that occur as averages of two distinct elements of S. For a given n 2, what is the smallest possible number of elements in A S? B-2 For nonnegative integers n and k, define Q(n;k) to be the coefficient of xk in the expansion of (1+x+x2 + x3)n. Prove that Q(n;k)= k å j=0 n j n k 2j ; where a b is. [X,Y,Z] = sphere(10); [U,V,W] = surfnorm(X,Y,Z); quiver3(X,Y,Z,U,V,W,0) axis equal. For comparison, create the plot with automatic scaling. Note that the arrows are shorter and do not overlap. figure quiver3(X,Y,Z,U,V,W) axis equal. Plot Vectors Normal to Surface. Open Live Script. Plot vectors that are normal to the surface defined by the function z = x e-x 2-y 2. Use the quiver3 function to. You can watch a short fun primer video on group theory from 3Blue1Brown here. A group is a general object in mathematics. A group is a set of elements that can be combined in a binary operation whose output is another member of the group. The most common example are the integers. If you combine two integers in a binary operation, the output is another integer. Of course, it depends on the.

The #$%! of Dimensionality

  1. 21.12.2017 - Jean Piaget gilt als einer der wichtigsten Entwicklungspsychologen überhaupt. Noch heute wird nach seinen Theorien und Konzepten gelehrt und erzogen. Einige.
  2. 3Blue1Brown also explains the idea of p-adic numbers, using the example of 2-adics, in this video. The p-adic absolute value has some interesting properties the normal one doesn't
  3. Volume of a cylinder in which a sphere of radius 1 can be inscribed. - Omar E. Pol, Sep 25 2013. 2*Pi is also the surface area of a sphere whose diameter equals the square root of 2. More generally, x*Pi is also the surface area of a sphere whose diameter equals the square root of x. - Omar E. Pol, Dec 18 2013. From Bernard Schott, Jan 31 2020.
  4. 3Blue1Brown: Fractals are typically not self-similar. Evening 1. Students work to create their own fractals: Van Koch Snowflake and Sierpinski Carpet DAY SESSION TOPIC COVERED/WORK DONE. 9 Wednesday Morning 1. Trigonometry basic definition, functions and identities 2. Complex number, basic operartions absolute value and argument of a complex number 3. Definition of Mandelbrot set fractal, a.
  5. GameDev.net is your resource for game development with forums, tutorials, blogs, projects, portfolios, news, and more
  6. Manim also has a TexTemplateLibrary containing the TeX templates used by 3Blue1Brown. One example is the ctex template, used for typesetting Chinese. For this to work, the ctex LaTeX package must be installed on your system. Furthermore, if you are only typesetting Text, you probably do not nee
  7. OFFSET: 1,1; COMMENTS: Numbers of divisors: A174601(n) = A000005(a(n)); squarefree kernels: A174848(n) = A007947(a(n)). - Reinhard Zumkeller, Apr 02 2010 By historical convention, the Tits group is often excluded from the list of sporadic simple groups. It could be inserted as a(7) = 17971200 giving this sequence 27 rather than 26 elements
Math 8 - 10Red Blob Games

Issues · 3b1b/manim · GitHu

Sphere packings, rational curves, and Coxeter graphs - Arthur Baragar, University of Nevada Las Vegas: 11th Floor Lecture Hall: 11:30 - 12:15pm EDT: Galaxy Leggings, Truth Serum, & the Visibility Cloak - Olena Shmahalo, Quanta Magazine: 11th Floor Lecture Hall: 12:30 - 2:30pm EDT: Break for Lunch / Free Time : 2:30 - 3:15pm ED Anyway, knots in the 3-sphere with complete finite volume hyperbolic metrics on their complements play a Von Thilo / 5. Februar 2016 / 16 Kommentare / Weiterlesen. Abonnieren Abonnieren mit: RSS2; Atom; Mit einem Feedreader abonnieren Anzeige. Mathlog. 퀘 스 너 틸 로 wohnt nicht mehr in Seoul, sondern jetzt in Augsburg. Er ist Mathematiker mit Schwerpunkt in der Geometrischen Topologie.

Volumes - YouTuberevolve examples - YouTube
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