I use to be a tour guide for NASA, this will be great to explain the orbit path of the ISS on a flat map

Electrician here. I'm going to share this with some apprentices. Thanks bud

Excellent example of a sine wave. Hopefully teachers start using these animations more often. I think it could be a big help.

/u/lucasvb actually has their own version on tumblr.

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OH MY GOD, FINALLY.

For the record the circle on the left can be called a phase and is used to easily depict everything from AC current and voltage in different circuits to EM waves

Goramit! Where was this when I was learning about the unit circle in high school.

/r/mildlyinteresting

Now do tangent.

That looks awesome and I feel like it brings me to the verge of understanding some cool concept but... What is that?

That made me laugh for some reason.

Polar graphs...I remember that nightmare.

I think the jar gif is a gas, so you could say fluid but not liquid, iirc

I watched the Cylindrical coordinates gif and it made them look horribly hard. Isn't it easier to just say that you can write a point as radius and angle?

Yep cylindrical coordinates are still horrible.

THAT'S WHAT THE DIRECTRIX AND FOCUS IS FOR?! Ever since algebra 2 I thought it was just some pointless bullshit designed to annoy sophomores.

So in the 19th GIF, with the spring falling, does the bottom not fall because the tension is pulling it up at 9.8ms^-2 ?

Perhaps /u/PinchieMcPinch wants this?

https://en.wikipedia.org/wiki/User:LucasVB/Gallery

Of course there is. This is most excellent. Thanks for sharing!

Cheers. subscribed!

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Some of the coolest graphics of this type I've seen were on NASAs website and were about orbital mechanics. Showing things like how the velocity changes in elliptical orbits so that the area swept by a line connecting the satellite and the nearest focus is always the same for equal periods of time.

I've never been able to find them again. Have you ever done any like that?

The idea of wild math gifs excites me.

Dude, you should make your own reddit and cross post to oddlysatisfying and interesting as fuck for the sweet sweet karma

This is, you are, awesome. Errr...How soon? Where can I find it when it's done?

Dude, your gifs are awesome! I'm sending the radian one to one of my professors to use. Please keep up the amazing work.

How do I subscribe to your work?

Thanks for your gifing

For anyone who wants to learn more, I think that what really made them click for me was watching a web series on those Harmonic Analyzers that did these calculations manually. This series from the engineer guy (https://www.youtube.com/watch?v=NAsM30MAHLg) is absolutely fantastic.

15 years ago or so I wrote a wikipedia article. A small, puny one, about a book. And it was a TON of work.

Since then, guys that contribute to WP in any way are my heroes. But you specifically are simply put, the hero of heroes. You really go way beyond of what is expected of reference material and cross the line into actually educational, which is rare even for very expensive material, not to mention free.

Also, your way of mathing speaks to me. Thank you from the bottom of my heart. I have trouble expressing how awesome you are for contributing to WP in the way you are.

Do you have a subreddit or site where people can dig into this? I've always excelled at geometry because I think with the logic and visual/spatial relationships very well, but the formulaic approach killed me for algebra and calc etc. these are brilliant for me to understand all the "Greek" in math in a way that related to things I understand.

Thank you!!!

As a physics major, I'd just like to say that your gifs are generally regarded as awesome and super useful

I'm looking forward to this, as your gif cleared up a lot of confusion I had in the beginning about FT. I've developed some neat intuitions about how the transform actually works, and I can see how it would be difficult to actually present something visual without making a mess.

Actually going this deep isn't required to pass my courses, but I feel like it pays off both in pure intuition and in being awe struck by how clever we humans actually are.

Your gifs have helped me develop this intuition, so I thank you and look forward to seing content on your youtube channel :-)

Anytime during these couple of weeks would be great, just in time for finals. :D

Try watching this series on harmonic analyzers, the machines that were created to perform these calculations manually. I feel it really made them click for me: https://www.youtube.com/watch?v=NAsM30MAHLg

I had an amazing geometry teacher who had a real passion for helping people understand geometry -- he drew almost that exact same thing on the board, and explained it the same way. He died a few years back, so this makes me smile... Thanks for making it.

We need a set of YouTube tutorials that brilliantly explain things where the average teacher fails.

I asked a few teachers if they share reliable YouTube tutorials amongst themselves and they all said no. That should change.

Thank you for your work. I too lost interest in mathematics when a teacher failed to explain how and why something worked and told me just to memorize the formula. Visualizations and logical explanations will go a long way to fixing that type of issue.

This turned a bit long and rambly.

Has our system always been broken? I don't mean a specific national education system, I mean the way math has always been taught. Was there some way in the past that math was taught better than now? One thing I especially liked about some math teachers I had was when they talked about the people that came up with the math. I had to google the name, but one that stood out was Galois, in my linear algebra class. He had done amazing things and died at an age where a lot of people are still considered children today.

How did he learn math? Are people like him flukes, and genius beyond my capability? I really feel like I'm too dumb for math. I don't lose sleep over it. The universal response to this when I tell people about my feeling, is that 'anyone can learn anything,' or 'I just needed to try harder.' I feel like that's a feel-good answer, and I don't believe it. Could I learn like Galois? Is it the system that failed me? Or did I just not try hard enough? Or can I just not be that smart in math?

Thank you so much for your dedication to helping fix things! Because of people like you, I know my daughter will have an easier time finding alternative resources to explain complicated concepts, and she'll have a better chance to understand and learn to love math instead of dreading and loathing it. The internet wouldn't be the magical resource it is without treasures like you. Love your work and looking forward to the post of the "wild" ones in February, thanks again :)

It's not just the grade-school education system, either. I had a professor in university who, when I asked for the reasoning behind some aspect of matrix calculations (don't remember what - it was a long time ago), told me "because it's the rule. You have to do it this way or you get the wrong answer."

I struggled in that class for weeks, until a programming lab instructor had me mess with the matrix calculations for a 3D animation. If you did it wrong, you'd end up moving the object to the right instead of rotating it, or turning it inside out instead of moving it forward.

My grades in that class went from 60 to 95 in the span of 10 minutes.

You are seriously really great. I ended up in a field that barely uses math at all, but for quite some time have wished to relearn what I learned in school, and more. Is there a place you would recommend starting?

Thank you.

As a parent who had no problems 20 years ago, but has a heck of a time explaining them to my teenager, thank you!

I think it's sort of telling that that gif felt like cheating because I understood it so quickly, and yet struggled with math all through middle and high school. Thanks for a mini-confidence booster first thing in the morning!

Have you sern Mathbox² ? (Google mathbox death of powerpoint) . It talks about having animations in lectures, but eith the actual math being done and not a prerendered animation. It makes it easier to understand fractals as well.

I am still waiting for project based learning to be adopted after several decades of studies repeatedly finding it better than the old way. But it will be difficult for any of these innovations to happen if we don't start taking teaching more seriously like Korea and Finland do. Right now we treat it as an expense instead of as an important investment.

Thank you so much for doing the work you do. As a major fan of the subject, I also think the way math is taught in primary and secondary schools is horrendous and hope that we can all fix it someday. Just want to express my appreciation and hope you keep it up! :)

You're awesome. Hopefully you can help make the logic of math visual for everyone who sees your work.

I don't see why these aren't used in school already. I love the simplicity of it, it's great!! This would have helped me so much when I was in school and imagine it being applied to other mathematical equations.

You can't really prove things visually though. You can give a visual motivation as to why the theorem might be true but you can never prove it visually.

Personally, I can't visualize things in my head. But that doesn't mean I don't get anything out of seeing things illustrated. If anything, I might need them more in some situations since I can't just picture it myself.

But when it comes to geometry specifically, my class was 1/2 visual and 1/2 proofs, and the heavy reliance on visuals was a little irritating to me because I much prefer just sitting down and doing math (see also: revolving solids and 3D molecular drawings, because rotating things is the worst). Yet, weirdly, when I had a class in college that went through Euclid's Elements, the completely visual proofs of everything were actually pretty awesome. It's weird how simple some of them are when you break them down to just straight lines and circles.

learning on their own

I truly believe too many people are not reading the book.

Reading is fundamental in our society but I think people have learned in the public education system especially that the job of a teacher is to be a tour guide, and to hold your hand and spoon feed you things a little at a time.

Reading is like exploring, in many other disciplines and in professional life you have to read read read, and explore.

Teachers are there to talk to you when you just can't make it work on your own and you need somebody to wave their arms around and chat with you.

Not to say everyone doesn't have different styles of learning, just saying all styles of learning are part of the whole of learning and they all should be practiced for highly effective learning.

Of course they aren't, we weed the ones who are out by only providing numerals not visuals to work with.

People learn differently. You're like me - verbal descriptions are usually enough to explain a concept. You hear, "A radian is the measure of the angle such that the arc created is equal to the length of the radius" and you can essentially draw that gif in your mind. We're not all wired the same way, so some people get lost in that word-soup and are much more easily able to understand by way of an illustration. You and I may not need that illustration, but that doesn't mean we're smarter, more talented, or better than the folks that understand better with the animation - we just learn differently.

That's not it. I'm well past getting it, but I remember having high school teachers and even a fair amount if professors that teach concepts and expect students to remember them by wrote memorization instead of explaining the reasoning behind it.

I would bet money that 180 deg = 2 pi is taught more than taking the extra 5 min to explain why, as this simple gif elegantly shows.

It is the same for sinusoidal waves and lots of other concepts. I remember Fourier transforms not clicking until I started working with spectrum analyzers in the lab almost 10 years after I struggled through them in college. I walked out of that class with an "A" and no idea how to apply it because it was all memorization and knowing just enough to get by, but not enough understanding to see the beauty of the application.

Too many teachers teach just enough to move on to the next concept, not caring to show some of the simple elegance of the concepts.

Edit: leaving my math error to show my shame

Radians are not a dumb unit! Degrees are the dumb unit! Breaking things into 360 is Babylonian garbage. This way, all you have to do to find the length of a circular arc is multiply its angle in radians by the radius of the circle!

I'm seriously confused how people are responding to this as if its new insight. Isn't this what they always teach when they introduce radians in school?

It's the difference between knowing the equation and understanding it. As an engineer radians has been an inconvenient conversion I have to do, never given it any deeper thought. Also, after years of calculus, vector math, and fluid mechanics you push things like this out of your head. Writing the Navier-Stokes equation in non-cartesian coordinates will cause a surprising mental purge.

That is a great thing to do with your life. Thank you.

I had to sign in to upvote this. Also, I needed to thank you for your work.

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you better come up with something good ^ ^ You've got 2.354 subscribers to please now.

Oh yeah deffo, you could get this outfit too

Srsly tho, I'm very impressed by your gifs, they really are some of the clearest explanations of maths I've ever seen, I really like your Fourier Analysis ones.

What kind of software do you use to make them? I've been doing still graphics for a while and have wanted to get into animation but I'm not sure what would be best to start with ^{Never mind, I found the comment where you say}

if you make one showing that a cat is homeomorphic to a coffee cup, you'd become like an internet God or something

I wouldn't go exactly as far as cooler, but thanks :)

Well, if you ever need any help with physics simulations for your YT channel, I'd be honoured to help!

Ooh. I like your Reddit username.

Ah okay, we don't really use the term or unit radians. A circle is just 2 π, that's it... At lesst in my university in germany

Ah, that's a very interesting way! I was playing around a bit and got this

Leaving the big pause at the end, and colouring the labels go match the diagram... It is the best!

DAMNIT. Well, thanks for it anyway! Helped me understand how radians work and why they're called that.

Gave up on RSS when google reader was murdered.

I think your visualizations are fantastic. I think you would find a lot of interest. You could crosspost to r/pics or other broad interest subs. r/engineeringporn would probably enjoy them as well, but it's nice to find these kind of visualizations all in one place.

You'd own it. I think you've got a real opportunity here because it's inventive thinking. The iBook would be interactive and show the animation. You'd basically have a trademark and copyright on the material.

Check out the iBooks Author conference if you're interested.

Regardless, great work.

as a (former) environment designer in video games, using phi was essential to making spaces feel right. I'm trying to impress this asthetic upon my kids.

You've written the best meta-discussion of tau I've ever read, and I agree with it. However, it's the section called "Dimensions" vs. "units" that really blew my mind. You've confirmed (and clarified) something I've long pondered.

For the past fifteen years I've been working on a philosophy I've been calling Triessentialism. I stumbled across the root concept in 2001, and my own "conceptual analysis" of it has shaped how I understand the world. Basically, there are three types of things: the Physical (the What), the Logical (the How), and the Emotional (the Why). They're fundamentally incommensurable (a word I learned thanks to you and Wikipedia), and they all play by their own rules. These concepts are imbedded in all philosophies across the millennia, usually hidden or badly grouped, but they're always there.

It's also a fractal ontology: each of the main categories has three similarly differentiated subcategories. I won't bore you with those details here, but you've just given me the key to my conceptual categorization of the physical: Mass ~= Physical (What), Time ~= Emotional (Why), Length ~= Logical (how). (Length must be measured against a standard rod, and is fundamentally rational. If this sounds like a cobbled-together explanation, I don't have space here to explain why it's not.) I'd previously matched up Mass = What and Time = Why, but not Length = How.

So, thank you for more than just the awesome animations!

Thanks :)

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Oh come on it was a fun story.

And if you're not American, the joke doesn't even work, because you pronounce lever as lee-ver.

When I worked as a camp counselor over the summer, I told this joke to each new group of campers. Some loved it. Some hated it

Edit: 1 word

And you just lost the game.

Edit: just for this one, I relish your downvotes. Thank you all sincerely, it warms my heart!

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I mean they do have projectors lol

It was certainly never in any of my textbooks as a kid.

Keep up the good fight. I did well with geometry but the "Greek" math never worked well for me, I think mostly because I couldn't understand what exactly it was accomplishing. Just plugging stuff into formulas isn't learning. Anyway, things like this would have made a huge difference for me in the classroom. Don't give up on kids like me! We are smart I swear!

I could have really used this in algebra and FST too.

And I bet they still don't pay attention. Source: used to be a high school student.

The thing is that "I wish I spent more time doing x" does mean that they wish they spent less time doing something else.

Sometimes you might find that the rocketry club (for example) is more interesting than your degree and you are doing your degree so you can keep doing that. In university sometimes the degree isn't the important bit.

That's great advice, and also learn as much as you can outside of your field. I roomed with a bunch of engineers in college, and work with them all the time in my career. It takes them a few years beyond college to realize they are not the smartest people in the world, and they they don't know everything. I'm getting a kick out of some of these responses.

Yeah your right, but it helps that I find everything except math very interesting.

Civil is the easiest one though.

Hmm shame, but yeah if you say it's necessery haha. It's still quite easy for me but I really do need to my homework because I now do it just the week before the test.

Luckily you aren't hiring.

Do you mean solidworks with sw? If so can you really trust the calculations solidworks makes? To a noob engineer like me it seems impossible that it can calculate a simulation the way it will behave in the real world.

Well I knew a circle circumference was 2* pi* r I just never thought about it like a radius was a radian.

It's like in pre-calc physics, where you're presented a whole bunch of projectile equations that you essentially have to memorize because you don't know calculus. A waste of time IMO. What's the point in teaching memorization? Just wait til you have the proper framework to understand more thoroughly and it becomes much easier.

Which unfortunately is how you can get through calc 1-3, linear algebra and diff. equations. I mean, they're supposed to be the building blocks for higher math, but only if you actually understand the material. Getting through without much understanding is entirely possible, unless your professor is very, very proof oriented.

Please continue to tell me what I know and don't know... perhaps check out /r/iamverysmart while you're at it.

I don't think you understand what he (and I) are saying. We know that a circle is 2pi radians and we can use them in math, it's more about the origin of the radian than anything else.

I felt the same way. Radians were introduced to me by this definition, and I'm surprised that it's done any other way.

Also TIL "learnt" is a word.

That's a really broad generalization. When I took engineering in college the curriculum went deeply into the theory and origins of concepts. Professors regularly took the time to show derivations in lectures (or at least tell you where to find them).

Yes I understand how radians are used, but if you watch the gif you clearly see an arc length that supplies us with that angle.

Congrats, I'm doing quite well without knowing the origin of radians thanks ;)

I have no idea, it's been nearly a decade since I first heard the word radian. I was probably told what they come from and let it slip away because it's irrelevant to your ability to use them in mathematics.

That's no way to learn maths

Which is probably fine because s/he is studying engineering.

I would argue that an engineers ability to assess stress, fatigue, shear etc. of materials does not depend on having a fundamental understanding of the chemical interactions of that material at an atomic scale. Sure it might help, but it is not essential and certainly not indicative of poor teaching.

Similarly the theory behind radians is not an essential prerequisite to using them as a tool in engineering.

In an ideal world you're right. No one explained what radians were to me until it randomly came up in my calc 2 class a few semesters ago. No one every bothered. I memorized the unit circle but no one taught me that 1 radian was just the arc length of the radius length.

Some people understand some concepts of math better than others. I agree though, and the US is actively trying to change this.

I have to agree... this is a basic concept I learned in middle school. It really is something that is easy to visualize and could give people a better insight in how the principle works, so I don't understand why some education systems or schools don't employ such tricks.

You know nothing about what I know and don't know, unless of course you are gifted with telepathy through the internet as well as your glorious 'maths' education.

English is not my primary language, so I suppose I may be wrong. What I've been taught is that comprehension, due to its Latin root, has the meaning of grasping/encompassing. Thus, to comprehend is to fully internalize a concept, compared to the perhaps shallower knowledge implied by understanding.

It's not even remotely necessary to understand the origin of the raidan to use them in calculations. More to the point, understanding this concept doesn't get you anything.

You probably learned how to use the fundamental theorem of algebra a long time ago.... can you prove it?

It's not like everybody wants to or is going to be a great success in math, science or engineering like you.

Ok.

What do you mean? How did you end up on the Calc BC track in high school without learning that circumference = 2r(pi) back in algebra or whatever?

I would never ask them to show me precisely what a radian is.

Yeah, that's exactly the problem. People get degrees that prove they know stuff they actually don't. In one year this person will be out in the wild designing bridges/electrical/mechanical systems or who knows what other things without knowing what a radian or sin is. It's dangerous to say the least.

If only I had more of these phenomenal gifs to sinc my teeth into.

Initially heliocentrism still needed epicycles to account for the fact that the orbits aren't perfect circles. Its main advantage was that it needed less of them.

I don't know, I think they make some pretty good points. I think we should teach both sides in science class, and let children come to their own conclusion.

/r/Geocentrism

Just goes to show how overkill and desperate geocentrism is.

No, it's more really the desperateness of people insisting on circular orbits. Heliocentrism itself needed epicycles as well before Kepler came along.

What a useless comment. And how fucking rude.

There are many ways of considering, visualising and using mathematical constructs, and contexts within which to apply them. To see them in a different way is just that. It doesn't make the work I've done with them so far useless or invalid. To try to belittle someone for not seeing them the way you perhaps saw them is petty and belies deep insecurity. Seriously, what value did you add to this? What is the point of anything you said? Nothing.

Take your rude, condescending and needless insult and fuck off back to your sperglord mindpalace.

Wow, I'm super excited for this youtube channel. 10/10 would watch. Subscribed already

I recognize a large portion of your illustrations from reading various Wikipedia-articles over the years. Only yesterday I saw your scalar field png! It's amazing how much a good illustration can aid the understanding of a concept, and it's so easy to forget that there is a person behind every line of text and every picture. I'm almost as star struck right now as when the guy who made solitaire for Windows showed up on reddit not long ago.

You should look at King Crocoduck's Quantum Theory Made Easy series, he goes over the history and math of duality without boring you and making it easy to understand, great videos if you want some ideas on how to structure it

Curious, but have you looked at Processing as a language to help you with your animations? It's largely designed for visual representation.

High five for POV-Ray! :D

You could start an indiegogo campaign to crowdfund a better computer setup. Ill help and i'm sure many others will be willing to help

Subbed.

This is great! I'm subscribing!

Consider myself subscribed to your channel. Hope to see your content in there soon :)

You seem like the type of guy they could really use on a temporary posting to the CTO's office in the White House. I an hoping to do one someday if I can get some money from options at a startup at some point in my career.

I need to learn more of this kind of thing, where do I start?

Can you release the source code?

As for the rest, things are a little bit trickier. For one, the animations are created using a custom library that’s ever changing, so compatibility is often broken with time. While I am trying to publish the library sometime in the future, I’m not terribly enthusiastic about it because I’m probably the only person who would use such a thing for PHP.

Do you keep your code under version control (like Git)? If not, you should.

In any case, you could just dump the code as-is to Github or something, even if nobody would use it.

And if you have both the code and the images under version control, that's already useful (it doesn't matter if the code is constantly changing if you can match each image to the source used to render part of it)

Hi, I am a math Ph.D student and a TA, and I often get ideas for animations which I think could be pedagogical and fun. Are you open to suggestions?

Did you major in anything physics related?

Oh man, OpenGL shaders are hell, the first time I dived into them I spent like 8 hours trying to dynamically change the color, I feel you man. Good luck with your project!

POVRay! Holy hell that brings back memories of ~1996, starting a render on my 386 in the morning and going to school, hoping that it might be done before bedtime that night...

Have you ever tried blender?

SUB FUCKING SCRIBED D:

More videos please!

Mike Bostock (creator of d3.js) has a whole page of amazing algorithm visualizations. If you haven't seen them, they might be good reference/inspiration. (My favorite is the maze turning into a binary tree on the bottom)

Well, i'm not in a financially stable situation to make donation, yet i'm very glad to be one of your very first subscribers. Keep it up!

This home school mom says thank you very much!

(That's because it's incorrect grammar)

A ñunit

It really bothers me when people use the wrong indefinite article. Acronyms/initialisms can be especially tricky.

No he's not.

Radians are not the only dimensionless unit.

There are all sorts of units which could be dimensionless.

I could just as easily have a single unit which is the full rotation of the circle.

The advantage of using radians is that it makes (sinx)/x =1 for very small values of x, this means that it has a gradient of 1 and a derivative of cos(x).

Other dimensionless units will not do this.

In algebra, the digits are irrelevant.

Isn't that exactly what I'm saying? Radians are dimensionless. The product of a radian by a length is obviously a length. Why doesn't it make sense?

Probably not since there aren't 360 days in a year.

The babylonians couldn't have known that. From empirical obvervations (ie seasons, etc.) it makes sense to guess a roughly 360-day cycle.

Also 60 minutes in an hour, 60 seconds in a minute, etc.

Thanks! :)

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I was never taught radians in high school hence my questions and confusion but it seems like asking things is against the spirit of /r/eli5 so nevermind.

No.