Oxford University Mathematician REACTS to "Animation vs. Math"
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/
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Watch the original video by Alan Becker here: kzhead.info/sun/dZWDZrOta6NuqX0/bejne.html
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.
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.
Important math question. Very serious. You would agree, 100%. What kinda wine do you drink? I need a new flavor
By the way, Aleph is also at the end, similar to Aleph Nol (min infinity)
@@TheSpacePlaceYT It has a lot of dinosaur vibes.
Orange learned math in 20 minutes and yet i cant even understand half of the things he learned after 12 years
I mean, Orange is a being literally made of math (he’s vector animation as opposed to raster)
His name is "The Second Coming" or "TSC"
#relatable
@@CPU_99 we still call him orange, we know he’s called the second coming, but we’ll still call him orange.
Perhaps you need to enter an existential maths duel.
Seeing this dude get excited about numbers makes me so happy for some reason
Barely numbers at that point 😭
the same for me, it makes me happy, don't know why, but it makes me happy
Same *and I don’t know why*
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.
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
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
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.
@@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.
It’s going to be so fun trying to figure out how the fight makes sense lol
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…
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
His name is Terkoiz, fyi.
@@danieljoybaguio7975 thanks! I was looking to see if I could find it but I couldn't, maybe I just missed it
@@danieljoybaguio7975wait THE Terkoiz from the Shock series?
@@vanne-necashionofbread9095 Yes, the animator who animated shock series works for Alan Becker full-time. :)
@@Shuriken255 Wait SHURIKEN?! How are you here, and happy to see ya!
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)
That's cos alans team had a math nerd I don't remember who
@@sidsdabest2416lead animator?
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
@@paper2222 he didn't say it was wrong... just said he didnt know for sure
@@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
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
The word ok?
@@MrBarun1981 what?
@@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.
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!
I am so sorry to be that guy, but it’s Alan Becker*
@@BEASTangel130-gg8ph my mistake thanks for highlighting
same i thought math was boring but Alan Becker proved me wrong
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 ❤
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
his name is second coming
@@username-jb2wp you forgot the "the"
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”
I agree, all of Calculus felt like a boss fight, but especially integrals!
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
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"... 😁
Genius. TSC is so smart
exip.
@@jsutbuleexiτ
@@janmamu8721 exiт
Yes, that was the point
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!
I think he missed it in his reaction vid
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 KZhead 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.
Yes, getting a reaction video from one, who is in the Matter, helps very mutch. -i is a bixxx 😂
There are physics now too
@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.
17:06 “That is one badass orange stick figure.” Buddy,, you have no idea how right you are
yea
his name is the second coming
@@thunderbeast6512here is an undetailed description of TFC: an orange stick figure
*The second coming casually killing a red stickman who wanted to destroy all KZhead*
@@thunderbeast6512yeah but we would just call him orange normally as a nickname
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."
complex plane* Edit: he said imaginary plain and I corrected it into complex plane
@imaginary*....
@@pirilon78 there's no such thing as an imaginary plane
@ hilarious.
@@hologrammaster2468 it wasn't supposed to be funny
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.
He was like "Hello math fans" and I felt very un-addressed.
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)
Ah thanks! I saw it but couldn't make out the shape.
I thought it was pretty easy to see. Seems like it wasn't to everyone
yea i noticed it, sad that he didnt notice it though
It is Aleph number
@@KunalKumar-pc4vg I guess it depends on what you're watching on. I normally watch on a tv and there the boundary of the aleph is invisible. I could only see it because of the texture inside it. When I rewatched on my phone its clear.
He condensed 6000 years of civilization into 15 minutes😂
Or 13 years of school
@@jennyfisher376513 years of pain 😢
@@GoofyAhhBoxy Pretty much the best years of your life lol
@@WisidX depends for who
@@jennyfisher3765you mean 12
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
I just like how he's smiling the entire time. He's really enjoying this video and I delight in how happy he is.
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.
That's so cool
makes sense
yea, most people can dabble in it (like the magic initiate feat) but not a lot a people can make it their job
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.
nukes
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.
shut up
Actually no, it is firing f(pi) = 9 tan(pi) = 0 at all of the series.
@@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.
@@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
@@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
21:06 the reason why he put the mult. sign there cause it spelled "exit", he wanted to get back to his normal world.
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.
Or, arc length
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.
Also r for the circle and n for series
@@TheSourovAqibunlike r, x is used for any value, r is only for radius
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)😊
@@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.
@@zachrodan7543 No because x is easier to draw that, no way in hell am I drawing an emoji
10:50 The θr here is supposed to represent the arc length, not necessarily the whole circle.
THAT'S WHAT IT WAS??
Also circle points in polar coordinates, the line integral expression for the circumference and the base f(r, theta) for circle area in polars.
@@nanamacapagal8342 yeah, s = rθ
@@Kernel15∅ø how to write?
@@melon_zombie_on_fire just google "theta"
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
Dude I was lost after basic math. 😅 Hope you got further than me. If not we both liked it.
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.
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, KZhead, now even math itself. A very impressive series in my opinion, especially given how quite old it is.
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!
*TSC
yeah the music was god tier, made the animation shine. without the music it would not be as special
Orange is not his name, his name is "The Second Coming" but it's "TSC" so ok
12:35 a split second of n=0 but it fired 2 things and went to n=2
I notice that 2
The things it fires are the result of the series at the respective n
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.
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!
indeed but alan becker is most well-known for his animation vs minecraft videos i just wanna say that if i may pls
@@SupYBand animation vs animator series (cant forget that)
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
also love the determination to ignore all the instances of TSC and e getting negatived
@@lettucep1ay FR, this man has determination like no other
Where? Looked like he figured it out just fine to me.
And the function gun shoots out graph of tan(x)
What are yall so pressed about it for😭
I love the way TSC draws the circle "⭕" like this. And also that scene where the Gamma function (all of them) use different ammunitions.
Dantdm if he stopped gaming in 2012
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.
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.
As niklasreich3959 said , (θ/2π = Partial Circumference/2πr)-> (Partial Circmference = θr)
s = r*theta where s = arc length, r = radius of a circle, and theta is the central angle measured in radians.
I figured fit was meant to be polar coordinates, but in the wrong order for some reason
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
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)."
i thought it was tau, given its ties to pi already
@@jonouyangsame i thought it was tou
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.
@@aquaregia5948 tau + pi + pau
To me he was just splitting the pi symbol in two lmao
I love seeing someone so clearly passionate about math find joy in this
They just uploaded an "Animation vs Physics" video an hour ago!
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.
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.
Yes, had to rewind as well just to make sure and it was there, n=0
Yes, n=0 is actually there, it increases for =n for how many times it shoots it. Ex: 2 terms shot= n=2
7:30 love how the lil guy was hit with a minus sign and all it just reversed him
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
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! 👏
For the record, the math nerd who spearheaded this was terkoiz, a lead animator on Alan Becker's team.
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.
I don’t know if you noticed but at the end there was also the Aleph symbol!
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).
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?
It is a symbol
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 😆)
didn't ask
@@thunderbeast6512you are 5. you have the name thunderbeast. the world doesnt revolve around you. what does revolve around you is these: 🖕
and who asked you? @@thunderbeast6512
u aint the man bruh@@thunderbeast6512
@@thunderbeast6512 get better at maths nub
I barely understood the math you explained but I loved seeing your gleeful reactions and it made the rewatch of AvM so much better! 😂
I love this guy! I understand literally everything and none of what he’s saying at the exact same time
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.
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
Every time they hit with minus direction changes It's crazy detailing 😳👏👏
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.
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
This was the first time I'd seen the animation. Very clever and a great reaction to help digest the detail.
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
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 KZheadr left from that era of people i watched
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
reason why this is so well done is cause alan beckers editior ( i think ) is a massiave maths nerd so he was the one that made sure it was all done correctally
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
17:19 I like how the waves from the "infinity gun" wrap around from positive to negative infinity, shown by them wrapping around vertically!
yoo i just realised this detail at 20:50 he adds an multiplication sign which makes the euilers formula look like "exit" !!!!
This was really cool! Thanks for explaining all this!
Just in case you haven't seen it yet, he recently released Animation vs. Physics, which is also quite fun :)
I would absolutely love to see this guy react to more of alan’s animations
It was so much fun watching you explain the math in the video, thank you!
" *Pause* Has he just made a function gun?" Got me so good XD
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
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.
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
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
He already realised that at 13:49
I need this guy as my maths teacher
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
Did anyone notice the big aleph null at the end :o?
For example me
Which one?? (i'm 16 and really bad at math so idk which one that was)
@@eqmalabdullah4054 א
@@eqmalabdullah4054the one that looks like N
@@eqmalabdullah4054it's a big N
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.
looks like someone majored in english
@@erikpasquale9902 Wut?
@@CommentPositionInformer I'm assuming it's because they used the word prerequisite.
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 ...) .
If you notice at 3:20 where e add i behind meaning ie he can go to higher dimensions with it
The reaction vids that double the length of the original video are always the greatest
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.
7:01 there's the Alan Becker I know and love!
His entire team is amazing. He's got a lot of dudes from the stickman community working with him on these master pieces.
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.
My man Alan just ussually upload Animation vs Physics
Thanks for making this, and for making your channel. I genuinely feel like I've learned a lot about mathematics thanks to this video.
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.
You just gained a new subscriber pls do more of this this was fun!!! ❤
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.
Oh, watched a couple of seconds ahead. Of course you immediately got it 🙂
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
I was waiting for mathematician KZheadrs to react to this video. Thank you.
Just saying that when the eiπ becomes its power series it starts at zero it shoots two times before he stops it 12:47
Alan is just showing off his math and animation skills
\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.
Even though my basic german Abitur knowledge is not quite enough to understand all that (not even remotely actually lol), this video really is a masterpiece to me. Great reaction as well :)
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
I like the fact that when he smacked the point with both sine and cosine it started to produce a time delayed wave
Your KZhead videos have been (for some reasons) in my recommendations lately and they are amazing. Feels very genuine and enriching to watch. You are definitely my favourite 2012 Justin Bieber x Math Genius Punk crossover math channel. No seriously, great work and always a delight to watch!
I learned more from this video than any teacher at school could ever have done
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.
"One does equal one, *solid* " This is ✨ golden ✨