- 1 Matrix_transpose.gif
- 2 Parabéns
- 3 Exponential.png
- 4 Request
- 5 Flaw in Image:Light dispersion conceptual waves.gif
- 6 Periodic functions in WZGrapher
- 7 Light dispersion image
- 8 Sources for your POVray images
- 9 SVD
- 10 Rotating point on a sphere-like degenerate torus
- 11 What software
- 12 Multi-Variable Animation Request
- 13 Surprise, surprise
- 14 FP Promotion
- 15 Regarding your gif work
- 16 File:Multiplication as scaling integers.gif
- 17 Awesome work
- 18 Qual programa
- 19 Your profile on Commons:Meet our illustrators
- 20 Picture of the Year voting round 1 open
- 21 A barnstar for you!
- 22 File:Eigenvectors-extended.gif
- 23 Tau instead?
- 24 information
- 25 Radians animated gif
- 26 Fourier transform animated graphic
- 27 Told ya so
- 28 small request for improvement of your "Newtons_proof_of_Keplers_second_law.gif"
- 29 Question about one of your graphs.
- 30 Would like to discuss some animations / visualisations ... please make contact
- 31 HiRes request
- 32 Picture of the Year 2013 R1 Announcement
- 33 Scalar field 3D
- 34 Pendulum 60deg.gif
- 35 The Affine Map
- 36 Fourier transform image
Hello! I'm curious: which software did you use to generate the animation illustrating matrix transposition so beautifully?
Bem vindo ao Commons:Featured picture candidates e parabéns pela sua animação (se vai ou não ser promovida a FP é outra história...). Precisamos de gente como você e de mais animações com conteúdo técnico e científico. Eu próprio tenho tentado fazer algumas pequenas coisas (craveira, sextante, quadrado desaparecido), mas sinto-me muito sozinho e não tenho nem suas ferramentas nem o seu talento. Convido-o a participar mais activamente naquele fórum, apresentando os seus trabalhos e contribuindo com a suas opiniões para melhorar o dos outros. Entretanto, que tal começar por nomear um dos seus giroscópios? - Alvesgaspar 22:52, 21 January 2007 (UTC)
- Opa, obrigado! :) Eu venho contribuindo com animações e imagens técnicas ou científicas já faz um tempo, e pretendo continuar contribuindo. Agora, por mais que eu goste de minhas imagens e animações (especialmente a do giroscópio e a dos circulos de Villarceau, que é FP na Wikipedia em inglês), eu não me sinto impelido em me auto-nomear à FP. Acho que se as imagens forem realmente de boa qualidade, elas serão eventualmente reconhecidas por mérito próprio entre a comunidade. Sinta-se livre para nomeá-las, se você realmente acha que elas merecem o status de FP... Agora, eu não costumo me envolver muito com a comunidade Commons. Geralmente eu invisto meu tempo e atenção na Wikipedia em inglês mesmo. — Kieff | KieffWikipedia | Talk 23:39, 21 January 2007 (UTC)
Hey, I saw this file you uploaded and liked it - Image:Hyperbolic triangle.svg. Would you be willing to make a similar image to describe en:Elliptic geometry? This page has no graphics whatsoever, and something like that is very helpful to picture the concept. Thanks - Sarregouset 20:55, 5 September 2007 (UTC)
Flaw in Image:Light dispersion conceptual waves.gif
Hi. I should have dropped a note to you about this before: Image:Light dispersion conceptual waves.gif has a serious flaw. The red waves are clearly moving faster than the violet waves outside the prism, which is unphysical (neglecting the dispersion of air. This image should not be used as-is. --Srleffler 00:09, 17 February 2008 (UTC)
- Crap, you're right! I did have that coded, but apparently it didn't run. I'll get it fixed as soon as I find some time. Sorry. 22.214.171.124 00:15, 17 February 2008 (UTC)
Periodic functions in WZGrapher
I have one simple question: how do you plot i.e. a sawtooth-wave function in WZGrapher? I saw your image called Periodic_identity and I would like to know how to achieve that.
April 11, 2008
Light dispersion image
The latest version of File:Light dispersion conceptual waves.gif looks better aesthetically, but has problems displaying in thumbnail form: An error message is generated saying: "Error creating thumbnail: Invalid thumbnail parameters or PNG file with more than 12.5 million pixels" I am going to revert it to your previous image which still works. ~ Kalki (talk) 17:06, 6 April 2010 (UTC)
- Oh well — I tried that, and that didn't work either — there seems to be some glitch in the current software preventing a proper display of the image in thumbnail, even when I reverted it to the previous version — I reverted it back to your latest, but the problem remains. ~ Kalki (talk) 17:11, 6 April 2010 (UTC)
Sources for your POVray images
Hi, could you please upload sources with your POVray images? It will make them easier to modify and adapt. Especially, I'm interested in the sources for this image — I'm going to create illustration for the article ru:Граф Риба based on it.
Hi, I enjoyed your animation on the singular value decomposition featured on Wikipedia. However, if possible I would suggest to change the Sigma matrix entries from what is currently shown (Sigma_11, Sigma_12, Sigma_21, Sigma_22) to (sigma_1, 0, 0, sigma_2) to reflect the diagonality of that matrix and the connection to the illustrated singular values. Cheers, Philip
Hi, I don't understand your change  in description of File:Singular-Value-Decomposition.svg. I chose the unit vectors as in x-direction (pink and horizontal right) resp. in y-direction (yellow and vertical up). Obviously M sends to and to which is true for the original version but false after your change. --Georg-Johann (talk) 20:04, 16 September 2010 (UTC)
- Well, when I used that matrix for the animation based on that image, it didn't match the transformation depicted. So I thought it was just an error you did when inputting the matrix. I see now that I just accidentally flipped things in my code: I used a row matrix instead of a column matrix for the coordinates. My bad. — Kieff | KieffWikipedia | Talk 20:29, 16 September 2010 (UTC)
Thanks. I saw the animation and was wondering why the basic transformations get further decomposed into mappings that do no more have the properties of svd components?
For example orthogonal U is decomposed into two shearings again (whereas the svd decomposes the shearing into a orthogonal-scaling-orthogonal sequence). The decompositions of U are no more orthogonal so that the indicators for σ are no more orthogonal in the intermediate frames. The overall animation leads (at least for me) to the impression of 6 transformations rather than 3 and tend to make things more complicated rather than to work out an example as easy as possible (without being trivial).
The intermediate frames could be as follows, which would reduce the number of trafos perceived to 3: 1. V is just a rotation in order to preseve orthogonality:
2. Σ is a scaling that "generates" (the absolute value of) the determinant of M, i.e. the size of the blue area is preserved because det M=1. So intermediate frames would fade in the σs and the trafo would be generated by means of
3. U ditto V
- I thought about it, but it seemed to be more interesting to show the effect of each column, as described in the article. In the context of the article, it seemed better to me. It says:
- The columns of V form a set of orthonormal "input" or "analysing" basis vector directions for M. These are the eigenvectors of M*M.
- The columns of U form a set of orthonormal "output" basis vector directions for M. These are the eigenvectors of MM*.
- The diagonal values in matrix Σ are the singular values, which can be thought of as scalar "gain controls" by which each corresponding input is multiplied to give a corresponding output. These are the square roots of the eigenvalues of MM* and M*M that correspond with the same columns in U and V.
- That way, you can see the effects of each column of the matrix, and how each represents an orthogonal transform, hence why each column is highlighted individually. If one thinks the entire matrix is acting upon in the intermediate frame, the problem you described would arise, but I didn't think it would be misleading. A quick edit in the description could solve this issue, I think. Or, maybe adding the orthogonal lines in those intermediate transforms, with arrows showing that the intermediate steps are still orthogonal to their original orientation.
- Also, from experience, most people don't understand these matrix transforms because they can't see how two shearings can result in a rotation. A straight, full-matrix transform animation that results in a rotation also has the effect of the shape "squeezing" as both shearings are in their intermediate steps, which always looked rather misleading too. This was supposed to help in that respect too.
- Either way, I can easily make an animation without the per-column transforms. I'll render it and upload shortly. If you think it's wiser, use that version instead. Cheers! — Kieff | KieffWikipedia | Talk 15:46, 17 September 2010 (UTC)
Rotating point on a sphere-like degenerate torus
First off, I love your image of a sphere like degenerate torus!
Secondly, I request that you please make a gif of a rotating point on the circle that when rotated about the torus's axis, creates the torus. This rotating point would inscribe a spiral upon the surface of the torus. Add to this the degenerate and regenerate functions of the image, bringing the torus into and out of singularity, and you got it.
I feel this motion represents consciousness and the reality of existence to a very high degree, as it includes the regeneration of singular unity and the degeneration of separate division, all within a cyclical storyline that needs both.
Thank you in advance for the honor of inviting such a request.
All the best, Matthew
Hi! Some very nice graphics! In your gallery you stated what you used for the 3D images, but what about the rest? What softwares have you been using for the different images? Thanks. -- Ekborg
- It depends on the image. this old revision of the page has some detailed information on the old images. The new ones I've made recently all used a PHP toolkit I'm writing called GDCanvas. I hope to release it soon enoug. — Kieff | KieffWikipedia | Talk 15:13, 31 July 2012 (UTC)
Multi-Variable Animation Request
My colleague and I are building a multi-variable calculus course for gifted high school students, and we were hoping you'd be able to create an animation for us. We absolutely loved your animation for scalar and vector line integrals; they truly captured the fundamental concepts of what's going on behind all the notation.
We're trying to explain the concept of a unit normal vector field (essentially a choice of orientation) on a surface, and how it induces a direction on its boundary. The text book we have chosen for the students does not do a very good job of explaining this concept, so we tried to explain ourselves, in terms of "gears". Below is a portion from our explanation:
- Let be an orientable surface with boundary curve , and pick a unit normal vector field on . We say that is traversed -positively if the direction along gives it a right-handed relation to the field near the boundary.
- Recall that in a right-handed coordinate system, a counter-clockwise rotation is associated to a normal vector. Then we would say a boundary is traversed -positively if the direction matches up with the counter-clockwise rotation of normal vectors near the boundary. Think of the base of a normal vector as a gear, which is turning counter-clockwise, and think of the boundary as a conveyor belt being moved by the gears near it. The direction the belt travels depends on how the gears near it are turning. Parts of the boundary near the edge the surface, and parts of the boundary around a hole in the surface will be traversed in opposite directions. The image below should help to make this clearer:
The animation we had in mind would go something like this:
- Opens with a surface embedded in . Something simple, like a warped sheet should be fine. The surface should have a boundary and a "hole".
- Next, a unit normal vector field appears on the surface.
- All but one vector fades away.
- A tiny "gear" appears at the base of the normal vector, spinning counter-clockwise.
- The normal vector and gear move to the edge of the surface, where small "teeth" appear on the boundary, and interlock with the gear.
- The boundary begins to move along, like a conveyor belt, with the proper "induced" direction from the gear. Blue arrows appear on the boundary to show the direction of travel.
- The normal vector and gear now move away from the edge and approach the boundary along the hole in the surface. The teeth and arrows disappear from the outside boundary.
- Teeth now appear on the portion of the boundary along the hole.
- Again, the gear locks into place with the boundary (now along the hole) and the "conveyor belt" begins to move in the correct direction. Note: this will be reversed from the direction on the outside boundary.
- Red arrows appear along the boundary of the hole to show the direction traveled.
- The gear, teeth, and normal vector all fade away and the original normal vector field returns. The arrows along all portions of the boundary reappear to indicate the orientation along the entire boundary (perhaps there could be a second hole that we ignore in the first part of the animation, and only add the direction-arrows to at the end).
Please let me know if this sounds like something you'd be willing and able to make for us. You would of course:
- be fully credited for the animation in our course, and
- have exclusive access to all of the original files (we only want the animated GIF, after it's been uploaded to Wikimedia.)
Feel free to contact me at firstname.lastname@example.org, or my colleague at email@example.com
- Obrigado! Só não entendi o seu comentário. Tem algo matematicamente errado que preciso corrigir? — Kieff | KieffWikipedia | Talk 18:28, 14 August 2012 (UTC)
- Isso é apenas artefato da projeção 3D. Não dá pra corrigir isso. Eu tentei inserir o plano ali no meio, partindo a superfície em 2, e também tentei fazer a "cortina" aparecer aos poucos, mas me pareceu excessivamente didático, visualmente complicado e a animação ficaria acima dos 12.5 megapixels, que é o limite máximo para o MediaWiki gerar miniaturas animadas. Nessas horas, eu conto com o conhecimento básico do assunto que o leitor usará para entender a animação. Uma pessoa totalmente leiga ficaria perdida. Não dá pra ser perfeito. — Kieff | KieffWikipedia | Talk 13:01, 15 August 2012 (UTC)
The image File:Line integral of scalar field.gif, that you nominated on Commons:Featured picture candidates/File:Line integral of scalar field.gif has been promoted. Thank you for your contribution. If you would like to nominate another image, please do so.
Regarding your gif work
I recently saw your graphical depiction of a line integral through a scalar field and was astonished! The power in these types of demonstrations cannot be overstated, and I would have thoroughly enjoyed these references as an undergraduate mathematics major. I'm writing to you because I feel there are lots of concepts whose comprehension would be greatly aided by visuals such as yours. I saw that you take requests, but instead I'd like to ask for advice or pointers. Where did you learn to make these animations, what software do you use, and what are some good references and tutorials on how to use it? Any extra information is immensely appreciated, as is your time and attention.
Sincerely, thank you for your response
- Hey, David. Thanks for the kind words. Answering your questions:
- Where did you learn to make these animations
- On my own. I don't think anyone has ever written about this sort of thing. I'm just unifying whatever mathematics intuition I have with whatever artistic intuition I have. So far so good.
- what software do you use
- My setup is far from optimal. I actually use PHP and its built-in graphic library, GD. I have a handful of scripts that I coded to help me with some abstractions, like drawing shapes, polygons, blending of colors, 3D and 2D rotations, etc. I just generate a bunch of PNG frames and assemble into a GIF later.
- You could probably do these things faster tapping some computer algebra system or some prototyping tool like Processing. I'm very used to PHP, so to me it works fine. It's also free and lightweight. But it's not meant for this.
- The thing is, I like to work on this sort of thing at a low level. The graphing capabilities of most programs frustrate me, as they usually look ugly, and you can't script it to animate just how you want. Making everything from the ground up using geometric primitives lets me do anything I desire, however I want it to look, at the cost of being more time consuming.
- I also just recently found out about MathBox, and the author shares these principles. It's worth looking into. — Kieff | KieffWikipedia | Talk 12:43, 20 November 2012 (UTC)
could you redo the animation with a larger dot? this dot is hard to detect so the idea of scaling is not recognised. so please make the dot larger. thanks.
Awesome adjective 1. inspiring awe: an awesome sight.
This definitely describes your work. In a few frames of a .gif you have condensed entire months of lectures of mathematics and physics. You really have a talent!
- I second that compliment. I'm visiting your page just to say "thanks" for the simple eigenvector animation you added to wikipedia, but now I see that's kid stuff compared to the work you're capable of. Animations like that help make wikipedia a special resource, and we have people like you to thank for it. So thanks! Superbatfish (talk) 16:22, 16 December 2012 (UTC) [Washington, DC]
Olá, eu gostaria muito de saber qual programa ou programa você usa para fazer os gif animados... se puder responder ou me enviar email (capu3d gmail) agradeceria bastante! Obrigado. -- 126.96.36.199
- POV-Ray e PHP com GD, usando uma biblioteca que eu mesmo escrevi. — Kieff | KieffWikipedia | Talk 06:15, 27 December 2012 (UTC)
Your profile on Commons:Meet our illustrators
In August, you raised a question on Commons talk:Meet our illustrators regarding adding you profile albeit you did not fully meet the number of required illustrations. You never got a reply back then, and I guess you then added your profile because noone objected in good faith.
I am sorry nobody answered you back then, but I really think you should wait until you have the required five FPs (I actually thought it was ten, when I wrote the reply). Am I correct, that now, currently, you have four featured illustrations on Commons? I have therefore removed your profile for the time being. But in case I have overlooked some FP(s), please do reinstate it, or reinstate it whenever, you get the fifth one. I am sure it will not be long.
On the sister page Commons:Meet our photographers, where 10 FPs are required, I am not familiar with anyne having mitigated the minimum requirement for inclusion. In contrast, many with more than 10 photographic FPs are not listed there. --Slaunger (talk) 17:48, 28 December 2012 (UTC)
Picture of the Year voting round 1 open
Wikimedia Commons is happy to announce that the 2012 Picture of the Year competition is now open. We're interested in your opinion as to which images qualify to be the Picture of the Year for 2012. Voting is open to established Wikimedia users who meet the following criteria:
- Users must have an account, at any Wikimedia project, which was registered before Tue, 01 Jan 2013 00:00:00 +0000 [UTC].
- This user account must have more than 75 edits on any single Wikimedia project before Tue, 01 Jan 2013 00:00:00 +0000 [UTC]. Please check your account eligibility at the POTY 2012 Contest Eligibility tool.
- Users must vote with an account meeting the above requirements either on Commons or another SUL-related Wikimedia project (for other Wikimedia projects, the account must be attached to the user's Commons account through SUL).
Hundreds of images that have been rated Featured Pictures by the international Wikimedia Commons community in the past year are all entered in this competition. From professional animal and plant shots to breathtaking panoramas and skylines, restorations of historically relevant images, images portraying the world's best architecture, maps, emblems, diagrams created with the most modern technology, and impressive human portraits, Commons features pictures of all flavors.
For your convenience, we have sorted the images into topic categories. Two rounds of voting will be held: In the first round, you can vote for as many images as you like. The first round category winners and the top ten overall will then make it to the final. In the final round, when a limited number of images are left, you must decide on the one image that you want to become the Picture of the Year.
To see the candidate images just go to the POTY 2012 page on Wikimedia Commons
Wikimedia Commons celebrates our featured images of 2012 with this contest. Your votes decide the Picture of the Year, so remember to vote in the first round by January 30, 2013.
the Wikimedia Commons Picture of the Year committee
A barnstar for you!
|The Original Barnstar|
|I present you, Sir, this original barnstar as a token of my respect. KodamPuli (talk) 09:49, 14 February 2013 (UTC)|
I think the graphic File:Eigenvectors-extended.gif is misleading, because the blue arrows are not actually eigenvectors. They are actually pairs of vectors, and the identity of the vector space is the origin of the grid - hence all characterizations of vectors as arrows are supposing every arrow is drawn from the origin to the point. So, that transformation does not simply scale the vectors in the blue arrows that aren't on the central line of the stretched rectangle. So, the vectors [3,1] and [4,2] form a blue arrow in the image, but multiplying by the matrix given in en:Eigenvalues and eigenvectors#An example, you would not get a scalar multiple of either vector. LokiClock (talk) 02:53, 6 March 2013 (UTC)
- Vectors aren't stuck to the origin. They're like an equivalence class: displacement and position vectors represent the same relation, but in different context. This is actually one of the main important ideas a lot of people end up forgetting, which is key to understanding how vectors don't depend on a choice of reference in physics, for instance. They end up thinking vectors "have their tail" at the origin. The beauty of vectors is precisely that they can represent a thing and relations between these things in the same package. It's a very important idea that needs to get across. Also, vectors in the animation are separated mostly in order to clearly show them. Having them all at the origin would cause a lot of overlap and confusion. — — LucasVB | LucasVBWikipedia | Talk 11:00, 6 March 2013 (UTC)
I was looking at File:Circle_radians.gif and wondering if you would not mind making another one, but without stopping for pi and instead stopping with tau, where tau := 2pi. Reddwarf2956 (talk) 13:20, 14 March 2013 (UTC)
- I was planning on it. I will do it when I have the time (probably this weekend). — LucasVB | LucasVBWikipedia | Talk 14:04, 14 March 2013 (UTC)
- Thanks. I see it done and place in Turn (geometry).
hi, Lucas, sorry. I want to know which is the program that you use to do these animations?
- Hi. I address this topic on my tumblr FAQ. If you have any other questions, let me know. Cheers! — LucasVB | LucasVBWikipedia | Talk 01:54, 18 March 2013 (UTC)
Radians animated gif
I noticed your nice animated gif for the Wikipedia Radians page, and wondered how do you make such a thing?
If you can educate me a bit, maybe I could make such things too.
- Hi. I address this topic on my tumblr FAQ. You'll probably be fine with something like Processing. I'm just nitpicky. Cheers! — LucasVB | LucasVBWikipedia | Talk 01:54, 18 March 2013 (UTC)
Fourier transform animated graphic
I was just reading up on recent changes to the FLAC format and digressed to your Fourier/time/frequency domains graphic (https://en.wikipedia.org/wiki/File:Fourier_transform_time_and_frequency_domains_(small).gif). I have to say it's fucking fantastic. Well done. —188.8.131.52 10:51, 11 June 2013 (UTC)
Told ya so
And of course, now everyone starts to copy it from there: http://csirouniverseblog.com/2013/06/28/tgi-tau-day/ --Joseph Lindenberg (talk) 11:34, 28 June 2013 (UTC)
- Lucas, have you considered switching the tau animation from yellow to green, like you did with the pi animation? I might be able to get it into the Pi article where tau is discussed, but only if I can shrink it to a small size. The yellow becomes unreadable when I do that now. --Joseph Lindenberg (talk) 02:19, 29 June 2013 (UTC)
small request for improvement of your "Newtons_proof_of_Keplers_second_law.gif"
Hi I am requesting that on your graphic found here: http://en.wikipedia.org/wiki/File:Newtons_proof_of_Keplers_second_law.gif that you include an ellipse in the background for relatability. Your graphic is not helping me if I cant see the elipse for perspective and reference. The sun and planet reference was fine but then I got lost as the animation progressed. thanks
Question about one of your graphs.
Could you explain how the tan function on the trig. wikipedia page works (The graph)? I don't understand the orange line that comes up.
- The tangent function's value is the length of the vertical line segment on the right of the unit circle, starting from the point (1,0) to (1,tan x). See image on the right. — LucasVB | LucasVBWikipedia | Talk 01:02, 11 November 2013 (UTC)
Would like to discuss some animations / visualisations ... please make contact
Nice work - crisp and clear and clean !
I would like to chat to you about some animations/visualisations I am doing for a physics paper.
Your wikipedia contributions are beautiful, and clear ... and I'm hoping you might be able to assist me and give me some guidance about the images I need to produce.
I'm based in South Africa.
Thanks ! Rich
I really enjoyed your Fourier animated gif. It captures the essence of the transform. I'm planning on using it in a lecture, to introduce the Fourier transform. I was wondering if you could make available a higher resolution version, e.g., 1024x768. Also could you make one available with a black background (or transparent background)? I'd ask for code by reading the response above, I gather the code used to generate this sequence is not easily portable at the current time.
Picture of the Year 2013 R1 Announcement
Round 1 of Picture of the Year 2013 is open!
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Wikimedia Commons is happy to announce that the 2013 Picture of the Year competition is now open. This year will be the eighth edition of the annual Wikimedia Commons photo competition, which recognizes exceptional contributions by users on Wikimedia Commons. Wikimedia users are invited to vote for their favorite images featured on Commons during the last year (2013) to produce a single Picture of the Year.
Hundreds of images that have been rated Featured Pictures by the international Wikimedia Commons community in the past year are all entered in this competition. These images include professional animal and plant shots, breathtaking panoramas and skylines, restorations of historical images, photographs portraying the world's best architecture, impressive human portraits, and so much more.
For your convenience, we have sorted the images into topical categories. Two rounds of voting will be held: In the first round, you may vote for as many images as you like. The top 30 overall and the most popular image in each category will continue to the final. In the final round, you may vote for just one image to become the Picture of the Year.
Round 1 will end on .
the Wikimedia Commons Picture of the Year committee
You are receiving this message because you voted in the 2012 Picture of the Year contest.
Scalar field 3D
What program/software did you use to render https://en.wikipedia.org/wiki/File:Scalar_field_3D.png? It's beautiful.
- Thanks! You won't like the answer, though: it's a custom graphics library on top of GD coded in PHP (yeah yeah, but it's a long story). — LucasVB | LucasVBWikipedia | Talk 22:27, 19 April 2014 (UTC)
Hey LucasVB. I was just wondering exactly how you have defined your axes in this gif My guess is that it's angle and momentum (mass times velocity) but I'm not quite sure. — Inc 17:39, 9 July 2014 (UTC)
The Affine Map
That was very cool and I noted VB! Is that true?! You did that in VB? It was the one program that forced me to use Firefox so that is sort of ironic. I'm thinking of doing a website where I just start at a math point - affine maps - and see where it goes, I'm looking at a - what I think is bogus - data analytics...I mean people could use their critical thinking skills and maybe DEDUCE something instead of data analytics, but it is interesting and cool math - and cool graphs!
Fourier transform image
Hello there. This is my first time trying to edit something and I do not know if I am doing the right thing talking to the creator, so plz show mercy.
I was reading the fourier transform page and I was impressed by your animation of the red function decomposing to six individual sines. Very demonstrative.
I noticed though that when you display the frequencies of each component you assign the higher frequency to the first sine (the one with the highest amplitude) the second higher to the second sine etc.
My opinion is that this order should be reversed. The component with the higher frequency is the last (the one with the smallest amplitude) and not the first since in the same time period has the most oscillations of the six. The second higher is the 5th component etc.
Also in the text below the animation you write: "In other words, the original function can be thought of as being "amplitude given time", and the Fourier transform of the function is "amplitude given frequency"..." IMO the amplitude should not be confused with frequency. Frequency is nothing more than oscillations per second and has nothing to do with the magnitude of the pulse of a wave.
I am looking forward for your opinion on this. Regards!