Oxford University Mathematician REACTS to "Animation vs. Math"

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Oxford Mathematician Dr Tom Crawford watches @alanbecker's "Animation vs. Math" for the very first time. Watch the original video here: • Animation vs. Math
*The copyright of the original video is the property of Alan Becker. The footage is shown here under a fair usage policy.
The "Gamma Function" video can be found here: • What is the Gamma Func...
Watch Tom take a variety of high school maths exams from around the world on the designated playlist here: • Exams
Watch Tom on 'Numberphile' here: • Parabolic Mirrors - Nu...
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow in Mathematics at St Edmund Hall: www.seh.ox.ac.uk/people/tom-c...
For more maths content check out Tom's website tomrocksmaths.com/
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collec...

Опубликовано:

22 май 2024

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Комментарии : 2,5 тыс.

@TomRocksMaths 10 месяцев назад

Watch the original video by Alan Becker here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-B1J6Ou4q8vE.html

@gavros9636 10 месяцев назад

The infinite series at the end with the gamma function was summing up the areas of all even hyperspheres from 0 to infinity with radius 1.

@themathhatter5290 10 месяцев назад

Most of the rest of the channel is actually the series "Animator vs Animation", and concurrently "Animation vs Minecraft". There's an actual storyline involving the orange stick and friends.

@NinjaOnANinja 10 месяцев назад

Important math question. Very serious. You would agree, 100%. What kinda wine do you drink? I need a new flavor

@TheSpacePlaceYT 10 месяцев назад

By the way, Aleph is also at the end, similar to Aleph Nol (min infinity)

@lukasnullmeier7819 10 месяцев назад

@@TheSpacePlaceYT It has a lot of dinosaur vibes.

@raeludiansa3654 10 месяцев назад

Orange learned math in 20 minutes and yet i cant even understand half of the things he learned after 12 years

@ralexcraft990 10 месяцев назад

I mean, Orange is a being literally made of math (he’s vector animation as opposed to raster)

@CPU_99 10 месяцев назад

His name is "The Second Coming" or "TSC"

@THE_KIWI213 10 месяцев назад

#relatable

@ralexcraft990 10 месяцев назад

@@CPU_99 we still call him orange, we know he’s called the second coming, but we’ll still call him orange.

@tinkeringtim7999 10 месяцев назад

Perhaps you need to enter an existential maths duel.

@WRSomsky 10 месяцев назад

Did you notice when stick-man was "talking" to e^i\pi, he pulled out a multiplication and put it between the e and the i\pi, and was leaning over the end of the pi covering it up a bit... it spelled out "exit"... 😁

@arinasultana6437 10 месяцев назад

Genius. TSC is so smart

@jsutbule 10 месяцев назад

exip.

@janmamu8721 10 месяцев назад

@@jsutbuleexiτ

@procybit 10 месяцев назад

@@janmamu8721 exiт

@SackbotNinja03 10 месяцев назад

Yes, that was the point

@pillgrimm 6 месяцев назад

Seeing this dude get excited about numbers makes me so happy for some reason

@kelisegenti6887 6 месяцев назад

Barely numbers at that point 😭

@eldust 6 месяцев назад

the same for me, it makes me happy, don't know why, but it makes me happy

@BLOOD_AND_INK 5 месяцев назад

Same *and I don’t know why*

@ethansanchez6267 5 месяцев назад

It's just nice seeing someone geek out about the things they're passionate about when it's represented in a fun and interesting way.

@user-sh4jb2zf6r 5 месяцев назад

This is exactly what i thought the same thing. But i saw the original video (animation vs maths). What i loved about the video was that it brought a huge number of reactions and comments. The highest i have seen in recent times. i think i saw 45 M views. This shows that there are still plenty of humans who care about actual things that matter. That are not just pure entertainment

@hotshot2457 9 месяцев назад

I think this is what students who struggle with math need. Interactive math thats fun and makes something thats hard be more fun to keep people motivated and entertained so that they can pay attention and learn in the process

@ringding1000 7 месяцев назад

As a former math tutor who worked with students who were behind the curve, math is always far more fun when you teach it with fun practical applications. The math becomes real for them. I would have shown this animation to them in a heartbeat to show the playfulness that is math.

@sargentgullible2794 6 месяцев назад

@@ringding1000 I would like to mention that showing off some little video-game function that uses real-world math could be an effective way too, not a math teacher or teacher in general by any means. Like, I can just see these kids question how the actual heck that game pulled it out of their ass. Folks, real math at work here, not magic tech haha.

@amadeux5471 5 месяцев назад

It’s going to be so fun trying to figure out how the fight makes sense lol

@nolifeprobably Месяц назад

@TheTrueBongoKnight 10 месяцев назад

What impresses me as a non-mathematician is that all of the mathematicians say every single thing in the video is correct (In terms of the equations and such)

@sidsdabest2416 10 месяцев назад

That's cos alans team had a math nerd I don't remember who

@quackin12152 10 месяцев назад

@@sidsdabest2416lead animator?

@paper2222 10 месяцев назад

not really, in 10:50, he actually disagrees* that θr represents the circle, and that it should've been re^iθ *he meant that he's not sure if it's 'mathematically correct', to put in his own words

@TableTurner921 10 месяцев назад

@@paper2222 he didn't say it was wrong... just said he didnt know for sure

@rajkayne2516 10 месяцев назад

@@TableTurner921damn u just sent that a few minutes ago i and when I clicked on this comment that was sent 49 seconds ago I didn’t even notice

@marosynth6434 10 месяцев назад

Alan said in the comments of the animation that his lead animator is "the math nerd behind all this" so big props to him too

@danieljoybaguio7975 10 месяцев назад

His name is Terkoiz, fyi.

@marosynth6434 10 месяцев назад

@@danieljoybaguio7975 thanks! I was looking to see if I could find it but I couldn't, maybe I just missed it

@vanne-necashionofbread9095 10 месяцев назад

@@danieljoybaguio7975wait THE Terkoiz from the Shock series?

@Shuriken255 10 месяцев назад

@@vanne-necashionofbread9095 Yes, the animator who animated shock series works for Alan Becker full-time. :)

@darkerrex1442 10 месяцев назад

@@Shuriken255 Wait SHURIKEN?! How are you here, and happy to see ya!

@shinypikagaming 7 месяцев назад

I love how you can always see the exact moment he goes from lecturing about mathematical principles to remembering he’s talking about a stickman fighting the personification of these principles…

@omegaschatterbox8366 7 месяцев назад

i have not understood a single word this entire video but i enjoyed every minute of it, watching him get excited for each new part of it iconic

@MrBarun1981 5 месяцев назад

The word ok?

@edwinlevin7959 3 месяца назад

@@MrBarun1981 what?

@Varksterable Месяц назад

@@MrBarun1981 He starts "Hello Maths fans". I'm sure OP understood that, too. And yet he said he has 'not understood a single word...' and you feel you have to point out to him that's logically incorrect. People generally communicate using natural language. (Barely that on in the internet.) Not formal mathematical logic. And guess which came first, BTW? Only an almost psychotically pedantic person would bother to point out a logical flaw in what is a totally acceptable and well understood idiom. And yes, I'm an utterly pedantic mathematician too. Otherwise I wouldn't have bothered to point this out to you either. I only do so because such comments as yours simply add to the pointless tedium of the general grey-noise that is the internet, and I feel you should be made aware of this.

@lainothefirst 10 месяцев назад

My favorite part of this animation is when Orange shoots his infinity function gun at the big mech, and the mech uses a Limit on its right hand to turn the infinity blast into an Integral as its main weapon. Like, the final boss having an integral as its weapon hits me particularly hard cause when I was learning them for the first time, it definitely felt like a boss fight

@username-jb2wp 10 месяцев назад

his name is second coming

@lailenobtea6415 10 месяцев назад

@@username-jb2wp you forgot the "the"

@andrewr8461 10 месяцев назад

this feels like it should be a troll comment like “my favorite part was when morbius said it was morbin time then morbed all over the place”

@lightning_11 10 месяцев назад

I agree, all of Calculus felt like a boss fight, but especially integrals!

@sherisehung4594 10 месяцев назад

At what grade do you guys learn integrals? I have already learned somewhat basic differentiation like the chain rule, quotient rule, multiplication, etc and i just started 10th grade last week edit: yall i just learned integration, its a real challenge. i need to cover kinematics by this semester too cuz i have IGCSE on June :') wish me luck

@mr.random4647 10 месяцев назад

17:06 “That is one badass orange stick figure.” Buddy,, you have no idea how right you are

@jimmyg3835 9 месяцев назад

yea

@DAVV1D 9 месяцев назад

his name is the second coming

@sandrinecestmoi892 9 месяцев назад

@@DAVV1Dhere is an undetailed description of TFC: an orange stick figure

@EthanYZX 9 месяцев назад

*The second coming casually killing a red stickman who wanted to destroy all RU-vid*

@curious.8 9 месяцев назад

@@DAVV1Dyeah but we would just call him orange normally as a nickname

@boomaletslearntogether 8 месяцев назад

As a mathematics teacher, I always dream of explaining math concepts in an interesting and amazing way. Let me say, Alan Becker have done wonderful work in this regard, even though words are not enough to express my feelings. In my review/reaction video (animation vs math in Urdu Hindi), I tried to explain this masterpiece in Urdu/Hindi for roughly 1 billion people in Pakistan and India!

@BEASTangel130-gg8ph 7 месяцев назад

I am so sorry to be that guy, but it’s Alan Becker*

@boomaletslearntogether 7 месяцев назад

@@BEASTangel130-gg8ph my mistake thanks for highlighting

@EliteCameraBuddy 4 месяца назад

same i thought math was boring but Alan Becker proved me wrong

@safiyaarif5112 4 месяца назад

Oh my God I need to watch it in urdu now because I don't know math at all( like complex one) would love to see a reaction in urdu ❤

@loganator3565 8 месяцев назад

16:12 I just noticed this here! The function gun that TSC made is f(x)=9tan(πx). If you plug in e^iπ or e^-iπ as x, it cancels out to 0! This is beyond clever!

@erenyeager6251 17 дней назад

Bro can u be my math tutor I beg u me in class 9

@Lorlic1138 10 месяцев назад

Alan Becker did a commentary on this. According to him, one of his team members is a math guy and pitched this idea to him. He said that he had to just trust that the guy knew the maths because he had no idea what any of these equations meant. Also the white zone is the imaginary plain, thats why it rotates 90 degrees when they enter it. *edit* After much deliberation in the comments, I have decided that the white zone is in fact "the place where the numbers that aren't numbers but we use them anyway."

10 месяцев назад

complex plane* Edit: he said imaginary plain and I corrected it into complex plane

@pirilon78 10 месяцев назад

@imaginary*....

10 месяцев назад

@@pirilon78 there's no such thing as an imaginary plane

@hologrammaster2468 10 месяцев назад

@ hilarious.

10 месяцев назад

@@hologrammaster2468 it wasn't supposed to be funny

@Unconventionalway739 10 месяцев назад

He condensed 6000 years of civilization into 15 minutes😂

@jennyfisher3765 10 месяцев назад

Or 13 years of school

@GoofyAhhBoxy 10 месяцев назад

@@jennyfisher376513 years of pain 😢

@WisidX 10 месяцев назад

@@GoofyAhhBoxy Pretty much the best years of your life lol

@komet011 10 месяцев назад

@@WisidX depends for who

@roeital5504 10 месяцев назад

@@jennyfisher3765you mean 12

@haydencarn8737 8 месяцев назад

He was like "Hello math fans" and I felt very un-addressed.

@nighton8223 7 месяцев назад

Although this is the only math related animation on Alan’s channel, he is arguably one of the most creative animators in the world; using nothing but stick figures who don’t speak no less. This franchise began back in 2006 when Alan was only 17 years old and made a video called “Animator vs. Animation” on Newgrounds just for fun. Now the series as a whole has over five billion views on RU-vid and is still going strong with 24+ million subscribers. Alan Becker is the living embodiment of hard work always pays off for those who pursue their passion with all of their being.

@internetgas3263 5 месяцев назад

Yes, getting a reaction video from one, who is in the Matter, helps very mutch. -i is a bixxx 😂

@vitaliitomas8121 5 месяцев назад

There are physics now too

@nighton8223 2 месяца назад

@vitaliitomas8121 His animators are surprisingly knowledgeable about math and physics. They could've gone on to become physicists and engineers but chose to help Alan animate his stick figures and their fun adventures. Respect.

@endernightblade1958 10 месяцев назад

one thing that’s very easy to miss: 24:11 in the background, alongside zeta, phi, and delta, there is Aleph. hard to see, but it’s there! (tip: it’s huge)

@KunalKumar-pc4vg 10 месяцев назад

I thought it was pretty easy to see. Seems like it wasn't to everyone

@kidredglow2060 10 месяцев назад

yea i noticed it, sad that he didnt notice it though

@clearyhorizon 10 месяцев назад

It is Aleph number

@KunalKumar-pc4vg 10 месяцев назад

@yyattt yeah i watched it on a laptop so it seemed clearer i guess

@Josh72769 10 месяцев назад

Aleph 0 animation made by optie is cool

@Nitram4392 10 месяцев назад

I used this video as an example to explain to why in fantasy settings with learnable magic (D&D for example) not all people are wizards. Technically everyone can use math, you don't have to be born with it, but most people would do not be able to do it fast and accurate enought to fight with it.

@nevi5158 10 месяцев назад

That's so cool

@pepsy3085 10 месяцев назад

makes sense

@somerandomdude7815 10 месяцев назад

yea, most people can dabble in it (like the magic initiate feat) but not a lot a people can make it their job

@typhoonzebra 10 месяцев назад

Another reason is that maths is usually taught to anyone willing to listen. It has no practical or ethical considerations when choosing to take a student. Wizardry is like if maths was a weapon. People would be very cautious when choosing apprentices.

@britishneko3906 10 месяцев назад

nukes

@keddidastinky 7 месяцев назад

21:06 the reason why he put the mult. sign there cause it spelled "exit", he wanted to get back to his normal world.

@davidcrs3043 4 месяца назад

The fact that the way e dealt with the infinity gun is by using a limit and making an integral out of it is such a small but incredible detail

@percivul1786 10 месяцев назад

Actually, the function gun is firing the equivalent 1 of the prime series or just "1". When it's hitting the various Euler's Identity targets, they have their values changed from -1 to 0, which cancels them out. This is why you see a 0 form above the targets that Orange hits with the function gun.

@dread_nought 10 месяцев назад

shut up

@megauser8512 10 месяцев назад

Actually no, it is firing f(pi) = 9 tan(pi) = 0 at all of the series.

@percivul1786 10 месяцев назад

@@megauser8512 Re read what I wrote. ;) I said it's firing the EQUIVALENT of 1, which is what you'd need to cancel out the -1 from the Euler entities. I could have perhaps worded it differently, but the outcome is the same. Zero.

@pocarski 9 месяцев назад

@@percivul1786 Orange took a gamble with the function gun, there was no way of knowing if its result will be added to the target or multiplied by it. Had it been additive, he'd be shooting blanks

@kirbylover_6 9 месяцев назад

@@pocarskihis point was it WAS additive, adding one and changing the -1 that e^i(pi) is, to a 0. At least, I think so

@niello5944 10 месяцев назад

10:50 The θr here is supposed to represent the arc length, not necessarily the whole circle.

@nanamacapagal8342 10 месяцев назад

THAT'S WHAT IT WAS??

@RadeticDaniel 10 месяцев назад

Also circle points in polar coordinates, the line integral expression for the circumference and the base f(r, theta) for circle area in polars.

@Kernel15 10 месяцев назад

@@nanamacapagal8342 yeah, s = rθ

@melon_zombie_on_fire 8 месяцев назад

@@Kernel15∅ø how to write?

@Kernel15 8 месяцев назад

@@melon_zombie_on_fire just google "theta"

@NickAndriadze 8 месяцев назад

The amount of tiny details and maths Easter Eggs, be it simple or compex maths, present in this 12 minute long animation is genuinely insane and this video made me realize just how much I missed from my initial watch.

@adampatterson2195 7 месяцев назад

I just like how he's smiling the entire time. He's really enjoying this video and I delight in how happy he is.

@rikschaaf 10 месяцев назад

It's interesting that the video explained math without the x variable from algebra. The only variable used was theta, to be able to find pi and describe circle angles.

@TheSourovAqib 10 месяцев назад

Also r for the circle and n for series

@roeital5504 10 месяцев назад

@@TheSourovAqibunlike r, x is used for any value, r is only for radius

@aquaregia5948 10 месяцев назад

Well yeah, but you won't be able to use any of it unless you use actually math variables like x,y , a ,b ( not sure if that's what you're trying to say but oh well)😊

@zachrodan7543 10 месяцев назад

@@aquaregia5948 the thing about variables is that they are completely arbitrary. arguably, the only reason why we use x instead of 🙂 is because emoji didn't exist yet when variables were first introduced.

@aquaregia5948 10 месяцев назад

@@zachrodan7543 No because x is easier to draw that, no way in hell am I drawing an emoji

@daniellemurnett2534 10 месяцев назад

Alan has a bit of a tendency to reinvent the genre of stick-fight animations. Going all the way back to the original Animator Vs. Animation, the concept was a really novel idea. Then AVA 4 expanded the scope to a ludicrous degree, and AVA 5 was just an all-out spectacle. But every now and then him and his team play more within their bounds and still come up with *really* creative and imaginative representations of the sticks fighting with various things. Videogames, RU-vid, now even math itself. A very impressive series in my opinion, especially given how quite old it is.

@skethy2333 8 месяцев назад

20:53 this spells "exit" orange is covering a part of pie so that it looks like a "T"

@ChocoCookieXI 9 месяцев назад

12:35 a split second of n=0 but it fired 2 things and went to n=2

@erauirusu5658 8 месяцев назад

I notice that 2

@wannacry6586 8 месяцев назад

The things it fires are the result of the series at the respective n

@lazarussevy2777 10 месяцев назад

θr is the arc length, so by adjusting θ, Orange can choose what point on the circle to land at. Also, as a math and music nerd, I haven't noticed enough attention to the epic masterpiece of a soundtrack to the animation! Just listen to the tension rising in the music as Orange divides by zero! Awesome!

@mite3959 10 месяцев назад

*TSC

@harnageaa 10 месяцев назад

yeah the music was god tier, made the animation shine. without the music it would not be as special

@AlexFha_29 5 месяцев назад

Orange is not his name, his name is "The Second Coming" but it's "TSC" so ok

@tyronorxy5646 10 месяцев назад

After Orange has befriended e^iπ, he tried explaining to e^iπ that he wanted to know how to leave "Mathland". Orange tried to draw a door, but e^iπ didn't understand, so Orange spelled "exit" by putting the multiplication sign into e^iπ spelling: exiπ . The complicated math at the end was e^iπ helping Orange leave, as Orange can't jump between dimensions just by multiplying himself by i.

@statelyelms 9 месяцев назад

I think the coolest thing about the Animation vs. Math video, aside from recognizing some of the functions etc thanks to the hellish courses (thanks calc. 2, for being required for my diploma..), is that it will DEFINITELY be the definitive starting point for many, many careers into math. It made it seem like a world of infinite complexity and coolness instead of what school shows typically, which is drier. It literally puts animation into the world of mathematics. That's just awesome to think about.

@Voidbear_FNaF_and_Undertale 9 месяцев назад

I thought I was decent at math but Alan's video showed me otherwise, so I'm watching people who actually understand what's going on's reaction

@phoenixbugg7199 5 месяцев назад

Dude I was lost after basic math. 😅 Hope you got further than me. If not we both liked it.

@aguyontheinternet8436 10 месяцев назад

10:42 that isn't representing the circle. It's just taking the radius of the circle and multiplying by the angle of the line. It is strange, but it seems to be a useful way to play with properties of the circle and it's angles at the same time. You set r to 1 and you can see the angle, you set theta to 0 and just see what happens when you vary the size of the circle.

@nmr975 10 месяцев назад

I think this is supposed to be a representation of the circumference of a (partial) circle. This means that theta is to be understood in radian.

@mr.bacteria7148 10 месяцев назад

As niklasreich3959 said , (θ/2π = Partial Circumference/2πr)-> (Partial Circmference = θr)

@mikeschieffer2644 10 месяцев назад

s = r*theta where s = arc length, r = radius of a circle, and theta is the central angle measured in radians.

@frimi8593 10 месяцев назад

I figured fit was meant to be polar coordinates, but in the wrong order for some reason

@ppremnaikk 10 месяцев назад

It is using the l/r = theta property for an arc of a circle. You can see how if he puts different values for rtheta, different arcs form around the circle, rtheta is not representing the circle but if we give it a value, it represents an arc around the circle

@tobenamed610 10 месяцев назад

Love his determination to not see how e uses i to turn itself into an imaginary number and go to an imaginary dimension, and all the cool tricks they did with that concept

@lettucep1ay 10 месяцев назад

also love the determination to ignore all the instances of TSC and e getting negatived

@tobenamed610 10 месяцев назад

@@lettucep1ay FR, this man has determination like no other

@NoriMori1992 8 месяцев назад

Where? Looked like he figured it out just fine to me.

@simhadrig1552 7 месяцев назад

And the function gun shoots out graph of tan(x)

@onnaest3542 5 месяцев назад

What are yall so pressed about it for😭

@ballerbeau 9 месяцев назад

Dantdm if he stopped gaming in 2012

@melon_zombie_on_fire 8 месяцев назад

I love the way TSC draws the circle "⭕" like this. And also that scene where the Gamma function (all of them) use different ammunitions.

@TheScorpion0081 10 месяцев назад

Something interesting Alan's team did was the hammers. The Second Coming (orange stick figure) split pi into 2 hammers and there was some confusion about that. To be fair, looking at it strickly like that, it doesn't make sense. But looking at how he created those waves, it makes more sense to look at the broken halves of pi as the letter "T" instead. So, as given, it would be "COS over T(ime)" and "SIN over T(ime)."

@jonouyang 10 месяцев назад

i thought it was tau, given its ties to pi already

10 месяцев назад

@@jonouyangsame i thought it was tou

@aquaregia5948 10 месяцев назад

I think it being tau makes more sense but also less of sense, it's kinda weird, because whereas it would connect tau and pi, the two heated sides of the tau vs pi debate, but it also makes it look like tau=pi/2, which simply isn't true.

10 месяцев назад

@@aquaregia5948 tau + pi + pau

@NeoTher_ 10 месяцев назад

To me he was just splitting the pi symbol in two lmao

@stellatedhexahedron6985 10 месяцев назад

For the record, the math nerd who spearheaded this was terkoiz, a lead animator on Alan Becker's team.

@typhoonzebra 10 месяцев назад

Whoa really? Terkoiz is still animating? He's more than just a team member, he's a veteran. He ran Stickpage with Shock and Failed Containment while Alan was still working on AvA 2.

@mickmockedmack 7 месяцев назад

11:30 I'm not sure if this has yet to be said, but rθ is by definition the arc length of a circle. It was showing the perimeter of the circle at the same time.

@abdamit 7 месяцев назад

I like to listen to intelligent/educated people talk. I don't understand pretty much any of this, but it seems amazing to me, that there are people out there, that can see these *magical glyphs* and say: "Ah yes, I know that!" seems really mind blowing to me

@warriorsabe1792 10 месяцев назад

At the very end, iirc I saw something about that final formula being for a 2n-dimensional hypersphere, so it started as a point at 0d, then a circle at 2d, and added dimensions until it had infinite dimensions, then was turned to -1 to send him home like a portal of some kind. Also, did you catch the enormous aleph made of the complex plane at the end?

@Bentley23Playz 10 месяцев назад

It is a symbol

@gravitysalad7891 10 месяцев назад

Animation vs math makes me so happy, I loved stick animation videos as a kid and I'm willing to bet there are going to be a lot of kids today that were bored taking algebra or geometry that now might want to learn more about mathematics just to understand what's going on in the video. It's a great way to spark interest in math. Also I love how the progression of the video starts at simple arithmetic and builds up through algebra, geometry, trig, calculus and a small peak into the further beyond at the end. Even the sound design is amazing!

@SupYB 8 месяцев назад

indeed but alan becker is most well-known for his animation vs minecraft videos i just wanna say that if i may pls

@painlesskun3959 8 месяцев назад

@@SupYBand animation vs animator series (cant forget that)

@hoyitsmiguel 5 месяцев назад

They just uploaded an "Animation vs Physics" video an hour ago!

@Bodyknock Месяц назад

23:38 One bit that's easy to overlook here is that the infinite sum eventually becomes a sum from 2n=∞ to ∞ , which is really the taking the limit of 2n= k as k approaches infinity. So ultimately that is a double limit: lim k → ∞ (lim N → ∞ ( Σ from 2n = k to 2n = N of ...) .

@paulsmith410 10 месяцев назад

I love that moment you start talking about the unit circle right before TSC discovers and starts to play with it. This has so many blink and you miss it moments. The expansions does start at n = 0 but quickly increases each time Euler's monster shoots out a term.

@kurankeikun 9 месяцев назад

Yes, had to rewind as well just to make sure and it was there, n=0

@melon_zombie_on_fire 8 месяцев назад

Yes, n=0 is actually there, it increases for =n for how many times it shoots it. Ex: 2 terms shot= n=2

@lordgiacomos2551 10 месяцев назад

Yeah, I don't know if I would recommend this animation as a way to teach math (though some of the visuals would be very good standalone), but for math and animation lovers, the visual representations and how they are being manipulated are very interesting, as there is a forced creativity through constraint by having to tell a story purely through interaction with numbers. This forced creativity also explains why e^(i*pi) comes up so early. Good storytelling needs a conflict of some sort, and rather than just having orange aimlessly messing around for the entire length, Becker creates a conflict through mystery early on in the animation which becomes a recurring antagonistic force that Orange has to figure out and overcome through further experimentation.

@bruhmcbro2704 9 месяцев назад

I love seeing someone so clearly passionate about math find joy in this

@Heramb_Pathak5879 8 месяцев назад

21:28 it is saying exit

@mariaeterna. 10 месяцев назад

First time for me watching it, as well! As a non-mathematician, it made it me glad that you explained the more complex concepts! Super fun, plus amazing animation! 👏

@spanishchair 9 месяцев назад

I think a misunderstanding I've seen from a lot of mathematicians about the θ r with the circle at 10:45 of this video is they assume that the equation is θr = the circle but later in the animation when they show the θ / r = π I think it shows that the θ and r are properties OF the circle not that they are equal to the circle so I think it's still sort of mathematically correct.

@iz723 2 месяца назад

Or, arc length

@SubduedRadical 2 дня назад

@@iz723 Ark length (in radians) was my thought as well.

@ChromeTectonics 24 дня назад

I love how this video can give you just an immense sense of accomplishment - taking pride in understanding what concepts are being utilized in Orange's fights the further on the video gets. Even if you don't understand a lot of the insane math ideas that are used here (like me), even that can give you a "bruh moment" kind of discovery. I can only imagine the amount of people who have watched this and said "WOW, WHAT?!"

@zcustard 7 месяцев назад

Glad you reviewed this, I wouldn't have stood a chance without you. It started to just look like random symbols near the end. I'm amazed you could spot the concepts in fractions of a second.

@archivist17 10 месяцев назад

My 10yo son (who was already an Alan Becker fan) showed me this. I definitely missed a few things on the first view, and i appreciate your reactions to explain things new and forgotten (I don't believe I've even given the Gamma Function a single thought since 1984 😆)

@DAVV1D 9 месяцев назад

didn't ask

@scratch-agunner 9 месяцев назад

@@DAVV1Dyou are 5. you have the name thunderbeast. the world doesnt revolve around you. what does revolve around you is these: 🖕

@Raishi688 9 месяцев назад

and who asked you? @@DAVV1D

@erikpasquale9902 9 месяцев назад

u aint the man bruh@@DAVV1D

@Qwerty-ky4ek 9 месяцев назад

@@DAVV1D get better at maths nub

@hypertec650 10 месяцев назад

For (theta)r part, I think the relation it had with the circle is meant to be the arc length, since as he was turning the little bar in theta, it was giving values of the arc length

@diamondxmen 5 месяцев назад

I don’t know if you noticed but at the end there was also the Aleph symbol!

@AlbedoisAll 8 месяцев назад

I barely understood the math you explained but I loved seeing your gleeful reactions and it made the rewatch of AvM so much better! 😂

@SquareWaveHeaven 9 месяцев назад

17:19 I like how the waves from the "infinity gun" wrap around from positive to negative infinity, shown by them wrapping around vertically!

@pranavkarthik9250 10 месяцев назад

yoo i just realised this detail at 20:50 he adds an multiplication sign which makes the euilers formula look like "exit" !!!!

@Eukleides89 9 месяцев назад

The cheeky infinities adding dimension was VERY cool. Sneaky linear stuff in there (that class, which also had differential equations, kicked my ass too hard not to remember it).

@isuapig6705 8 месяцев назад

I love this guy! I understand literally everything and none of what he’s saying at the exact same time

@nathanrock9269 10 месяцев назад

Did anyone notice the big aleph null at the end :o?

@EllishGD 9 месяцев назад

For example me

@eqmalabdullah4054 8 месяцев назад

Which one?? (i'm 16 and really bad at math so idk which one that was)

@nathanrock9269 8 месяцев назад

@@eqmalabdullah4054 א

@melon_zombie_on_fire 8 месяцев назад

@@eqmalabdullah4054the one that looks like N

@EndlessScaling 8 месяцев назад

@@eqmalabdullah4054it's a big N

@RED-sl2le 10 месяцев назад

This is what I’ve been looking for for so long, genuine first impressions reaction from a professional in the field of the subject in question

@spirit5923 4 месяца назад

It's amazing to me that people are still finding his channel, i used to watch his stuff ages ago and it feels like he's the only RU-vidr left from that era of people i watched

@witherr 9 месяцев назад

This was really cool! Thanks for explaining all this!

@Princess-xv8dd 10 месяцев назад

With the power series of e^iPi it did start at n=0. It’s just that when you paused it was n=2 because it had already fired 3 times. The ammo its using are the expressions in the power series of e^iPi

@user-vs6vd1xt3p 10 месяцев назад

He already realised that at 13:49

@pauldavies7746 10 месяцев назад

This was the first time I'd seen the animation. Very clever and a great reaction to help digest the detail.

@Resetium 5 месяцев назад

The little detail of Aleph walking off in the background at the end is very neat.

@abhay45452 6 месяцев назад

Every time they hit with minus direction changes It's crazy detailing 😳👏👏

@nification7883 9 месяцев назад

As a more tactile, "throw stuff at wall type," this kind of thing I think would have helped me to "feel" maths more, and thus could have sparked an interest if I had been exposed to it when younger. Even now just watching this quick video I can feel neurons trying to make connections, unfortunately a lack of prerequisite knowledge is limiting what I could get form this but, such is life.

@erikpasquale9902 9 месяцев назад

looks like someone majored in english

@CommentPositionInformer 5 месяцев назад

@@erikpasquale9902 Wut?

@raiisleep 5 месяцев назад

@@CommentPositionInformer I'm assuming it's because they used the word prerequisite.

@Joshua-jk1om 10 месяцев назад

Im so impressed in your ability to mentally see these complex math principles in your head and rationalize them. Even the Factorials. That threw me off, even trying to solve for why n=2 was a thing.

@thecomputerguy6335 7 месяцев назад

It did start at n = 0, it then sent off two shots at the stickman meaning it went from 0 to 1 to 2 before he paused, it didn't start there but enumerated to there

@johnswolter 8 месяцев назад

You've started a visualizing math and arithmetic adventure. It could easily go back in time to counting boards and forward to explain today's and the future's unanswered questions. All visually presented to be quickly reflected upon, understood, and made of use by the youngest or oldest interested. I wish you a long and productive career. -- JSW

@RigoVids 2 месяца назад

11:00 theta r represents the arc length. So in this case it’s supposed to mean the length of a full circles arc is theta (constant value of 2pi) times r.

@riceeater112_ 9 месяцев назад

At 13:30 the summation shown starts at n=2 because the original n=0 summation "shot out" the n=0 and n=1 terms already.

@samwilde8311 10 месяцев назад

My favorite thing about the animation is that I like to think of Euler's identity as Euler himself existing as a mathmatical god in this universe

@Skupin27 8 месяцев назад

Just saying that when the eiπ becomes its power series it starts at zero it shoots two times before he stops it 12:47

@bass2564 5 месяцев назад

13:03 This one happens so fast you don't even have to blink to miss it, but the (initially complete, with n=0) Taylor expansion fires its first two terms away as projectiles, which explains why it is showing n=2 at the paused frame.

@bass2564 5 месяцев назад

Oh, watched a couple of seconds ahead. Of course you immediately got it 🙂

@Grakalor 9 месяцев назад

The reaction vids that double the length of the original video are always the greatest

@thewierdsquad7584 10 месяцев назад

I would absolutely love to see this guy react to more of alan’s animations

@ChrisMMaster0 5 месяцев назад

16:28 something else to note, when shooting the Function Gun it makes the graph of tan(x) since that was the function he used for f(x) it is more noticeable when it puts infinity inside it.

@Santiago160 5 месяцев назад

Dude youre such a math nerd and i love it... I havent touch anything math related for years and it was really interesting seeing someone who knows ton more than me to explain the later parts of the video

@mechaboy95 10 месяцев назад

Euler's identity is sometimes referred to as 'the little monster', hence why e^i(pi) is the angry little trouble-maker in the animation when the corner adds up and the little monster jumps through, thats moving between the real and complex worlds, you see this further as at 20:00 they jump back to the real world, but -roots cannot exist in the real world, so it all breaks. then multiply's by i, shifting back into the complex world the series starts at 2 because he gets hit by the 4 from and character when he grabs the infinity sign it's like grabbing the infinity 'stone', giving him ultimate power

@OskarCzechowicz-OmniMusician 9 месяцев назад

7:30 love how the lil guy was hit with a minus sign and all it just reversed him

@garethchampion8406 8 месяцев назад

11:19 rθ is what you use to fine the arc length of a circle (given that θ is in radians). You can find it in the MF19 formula sheet

@esuolaayomide6565 Месяц назад

11:25 The product of theta and radius affects the length of the arc of the circle. As theta increases,the arc's length increases and vice versa

@samuelofosu2051 9 месяцев назад

At the 11:36 minute.... I think the formula there is on circular motion in Physics where you calculate the duration in meter(s)

@hernsonhazel5953 10 месяцев назад

13:07 it WAS starting at n=0, e just shot numbers that increase the n

@jplikesmaths 10 месяцев назад

Had to pause the video to see this, great find

@gamedevlooper411 6 месяцев назад

At 10:36 , (theta x r) is the arc length formula, which can be the circumference of the circle when theta = 2π But at 10:38 he turns the circle into a unit circle, hence r = 1 Later, we can se he turns the equation into theta / r , which is just equal to theta as value of r = 1. Thus when the line rotates by 180° the value of equation is π/1 = π The digram was maybe a bit off but the values were technically correct

@paulkepshire5056 8 месяцев назад

I feel that the "little devil" (e^iπ) pops up so quickly because: 1) the devil is in the details, and 2) e is nearly omnipresent in maths.

@thorinteague989 10 месяцев назад

Alan Becker, we've been watching him for a decade+ in the animation community (he's totally brilliant). I was expecting some physical fighting by 3:24, but we'll see what develops.

@thorinteague989 10 месяцев назад

7:01 there's the Alan Becker I know and love!

@bungercolumbus 10 месяцев назад

His entire team is amazing. He's got a lot of dudes from the stickman community working with him on these master pieces.

@omidtarabavar2576 10 месяцев назад

It was so much fun watching you explain the math in the video, thank you!

@circuitgamer7759 5 месяцев назад

Just in case you haven't seen it yet, he recently released Animation vs. Physics, which is also quite fun :)

@Deerra 9 месяцев назад

If you notice at 3:20 where e add i behind meaning ie he can go to higher dimensions with it

@The_dragon_Wolf 9 месяцев назад

13:20 thats because when you paused it, it had already fired off TWO shots, so thats why n=2 at the time you paused it

@stevepowell6234 10 месяцев назад

\theta r is not a 'peculiar way to represent a complex number' but is, of course, the arc length. So altering theta makes you end up at a different place of the circle, and altering r increases the radius. The animation draws the arc (in the direction of positive arc length) as these are adjusted. I suppose it would have been easier to interpret if written r\theta, but then \pi r might not have been recognised. Conventions! Love this.

@adcgdsin9320 6 месяцев назад

That staff that the Taylor series of e^(ipi) (transformer) was holding was actually an integral from 0 to infinity. Pretty sick detail.

@Kalanioccc 4 месяца назад

my 4 year old son and i watched that animation for the first time last night. more of a science guy but i thought it was really fun and well done. i enjoyed your take on it as well!

@jackedmondson1373 10 месяцев назад

The specific function he makes is one that takes what he is shooting to 0, in the world of this fight defeating it

@iamthemouse4483 9 месяцев назад

Thanks for making this, and for making your channel. I genuinely feel like I've learned a lot about mathematics thanks to this video.

@The21stGamer 7 месяцев назад

The amount of thematic interpretations the video can have is honestly incredible, especially ironic given it's meant to be cold, absolute calculations and yet can be analysed like any other text.