The secret behind constants

[@andrebarrett4112]

In 4:49, you have an indefinite integral without a +C. Unforgivable!

[@Thechillilover]

Exactly what i was gonna say

[@R0mm3n]

He is an omnipotent god remember, so he already knows it’ll be zero

[@deleted-something]

@R0mm3nwhat if the +C is tau

[@m9l0m6nmelkior7]

yeah it would have been more logical to have a definite integral starting at 1

[@TruthNerds]

@@m9l0m6nmelkior7 and the way he explains it (area under the curve) suggests that he's taking the definite integral starting at 0, which doesn't exist though (the area is infinite)

[@nathanaelhahn]

The log's flipped to the other side so it's not ambiguous where the summation notation ends :)

[@MAKiTHappen]

That... actually makes a lot of sense

[@isavenewspapers8890]

This is why we don't skimp on the parenthesis budget.

[@tgm7531]

also why H_n is better notation for harmonic series

[@creeper6530]

Just add parentheses

[@Thechillilover]

Yup

[@isavenewspapers8890]

14:42 A constant is a quantity that doesn't vary. It stays... you know, constant. I know mathematicians have a habit of giving terrible names, but I think they were pretty spot-on with this one. Would anyone actually be confused by this?

[@hueheeuuehueuheuheuhueheeu1245]

why terrible names ?

[@andreyhenriquethomas9554]

​@@hueheeuuehueuheuheuhueheeu1245 look at a course of Analysis and you will understand the frustation (increacing funcions and "non-decreacing" functions are different things) besides incosistent notation (f²(x) for any non trigonometric function means compounding the function like in f(f(x)) while for trigonometric it means "square the content of the function" as like cos²(x) ≠ cos(cos(x)) but cos²(x)=(cos(x))², and like 3-6 names and notation for the same thing.

[@peepee8925]

MakIT you’re doing great these videos are always so fun to watch and the work you put in and CONTINUE to put in is very impressive I hope soon you start getting an influx of views cause it’s kinda insane to me how it’s working out BUT YOURE STILL PUSHING AND FULL TIME NOW so hell yeah massive respect

[@JamesRedekop]

The last segment is a good argument for the τ fans -- with π, you *do* need to scale to get one rotation...

[@angeldude101]

It was fairly abrupt since they were previously talking about π as the area of the unit circle, and in that context π really is a full rotation. It's only at the end where π is suddenly half a rotation even though the circumference / perimeter weren't mentioned at all prior. I have found reasons for respecting π as the area of the unit circle, and fractions of a circle have areas that are the corresponding fraction of π. These reasons mostly come from analysing hyperbolas, where the arc-length of a hyperbola is very hard to calculate and also pretty useless. Hyperbolic angle is instead defined as twice the area of the corresponding sector. Circles can work in the same way, though the usual definition of elliptic angles doesn't work for hyperbolas. There's also the third option of a vertical line at x = 1, which actually works with both definitions as well. (Together these form the unit... shapes? of the complex/elliptic/spinny numbers, split-complex/hyperbolic numbers, and dual numbers respectively.)

[@StefanKoran]

τ for the win!

[@JamesRedekop]

@@angeldude101 Yeah, π works for the area of the unit circle... But if π is showing up in my work it's in the context of rotations, where having to constantly account for it being a half-revolution and not a full one is mildly irritating. Of course, I could just start using τ in my code...

[@lucassrandomations4084]

These videos are awesome! Your teaching style really helps make complicated ideas seem simple. Please keep making these :D

[@Planetarium963]

Minor error at 6:20 The limit variable should be n and the ln(k) should be ln(n), like at 1:05 The error is you used k as both the variable for the summand and the limit variable, and also n isn't defined here.

[@nacholibre5173]

You’re for sure the most underrated education KZbin channel out there

[@DanielFackrell]

At about 16:10, you say pi is a whole circle, but that's only true if we measure angles based on the diameter. Since we measure them in radians, which is based on the radius, or half the diameter, pi is only half of the way around a circle. Thank you for making the point that 2pi is actually the circle constant, and that pi is the half-circle constant.

[@McDonalds-Empty-Cup]

τ, the much better and more useful number, as it is the amount of radians in a circle, 2π

[@angeldude101]

π _is_ a whole circle when measuring angles in terms of _area._ (diameter doesn't exist) π is the area of the unit circle. Any sector spanning a fraction f of a unit circle has an area of fπ. The way π was first brought up in this video was in terms of the area of a unit circle, and comparing it to the area of a square with radius 1.

[@giorgosmergiannis8782]

Amazing video, I never thought of constants in any particular way other than a lookup table that slowly drills itself into your brain as you solve more and more problems in calculus. Thank you

[@inutamer3658]

I have a math major and couldn't tell you the second digit of e

[@winnablebtw459]

​@@inutamer3658 Why? e starts with a few digits that repeat and you can get 10 significant figures essentially for free.

[@tgm7531]

you didn’t mention the most interesting thing about eulers constant, we don’t know if it’s irrational, and efforts have been made. it’s imo the most interesting constant i know

[@snytty]

This video sent me onto a binge of your videos .. instantly one of my favorite creators

[@yuvrajbanerjee8578]

This is genuinely some of the best educational content I've seen on youtube, from math to quantum physics. I really hope you blow up some day, this is easily on par with channels like 3blue1brown and veritasium.

[@CalculusReviser]

You explain these concepts so well! The animations are so clear, please keep making these :)

[@aurora8orialis]

The way this video slowly worked into subjects of math I more clearly understand made me realize just how well put together these videos are. If only your explanations of advanced topics didnt completely overwhelm me because you explain them so well ;-;

[@fetch7312]

6:07 i think you got your wires crossed here. n should be the variable we take the limit of and it should be ln(n) instead of ln(k)

[@Dr.ScoobyDooDoo]

You beautifully captured my struggle with unit vectors and explained it like a champ Great video as always😁

[@Fangamer1254]

Since the video from addition to quantum physics, I'm your frequent watcher. You're really good at explaining which is a very good skill.

[@gagelucas6036]

I’ve gotta say, the effort you put into this channel really is awesome. Each video has such care and heart, the animations and explanations work together so well. Thank you for making these videos! The upload schedule you have is breakneck, I can’t imagine how often you must be at work! I appreciate what you do, thank you.

[@Thaaa.PleaseBeAvailable]

Love your videos, the quality and humor is unmatched

[@yarikzhiga]

wake up baby, new MAKiT video just dropped (awesome as always, keep it up! you ABSOLUTELY deserve way more recognition and it's a shame that youtube's algorithms are kind of ignoring you)

[@ibi_DoesAlot]

these are some of the best videos i have watched on the platform i really hope you are able to continue this and get the recognition you deserve i wish i could help out even if a little through patreon but i am a kid

[@vindi167]

7:47 personally i call it "tesseracted" so that the 5th power i can call "hypertesseracted"

[@the_lord_2610]

really nice video, like always. my one suggestion is that when you are doing the LaTeX you include “\” before the “ln”.

[@Ema9ine]

Love your content! Commenting to support and keep you from starving!

[@sspaghet4080]

the new backgrounds are amazing btw i just wanna appreciate it

[@rohankopuchetti]

Hey MakIT, you are one of the best animators and explainers i ever knew about. Good luck on all your future endeavours bro You will get famous. Trust me, but remember me when you get there😊

[@bonitageorge6410]

You deserve so many more subscribers man, underrated fr

[@phagon7487]

Good video Just a bit funny that "eulers numbers" is called "oilless number" in the subtitles. x)

[@mani_mincraft]

Great video as always. Your truly amazing

[@victorlgteskov3128]

hell yeah goated video i really loved it. also the part with e is nice since im doing a physics degree and it keeps poping up in physics all the time

[@Akronymus_]

Why is the ln taken for k and not n, when it isnt part of the sum, in eulers constant?

[@MAKiTHappen]

That's because when I started scripting the video I was drunk, when I got around to animating I was high, and when I ended up editing I was both, so the consistency of variables became... varied and unconsistent

[@altair-tf8fp]

@@MAKiTHappen average mathmetician lmao

[@isavenewspapers8890]

@@MAKiTHappen Oh dear.

[@vinod-cf2jl]

​@@MAKiTHappenLesson learned: Never drink and Animate.

[@TimonK404]

I think this was your best video yet. To be fair, it's not a surprise, since you started these types of videos not so long ago. But if anything, this deserves to blow up! (also, I died in fanboy panic at the end, tho I should have seen it coming)

[@AlanHernandez-jg1xv]

Your animation is amazing

[@fleefie]

I'm not a big fan of the intuition for pi here. You're removing squares, so you will always have a "rough" surface, so you'll have a fractal whose surface approaches pi but it won't be pi. Going with the infinitely thin pizza slices is just as intuitive and more accurate

[@isavenewspapers8890]

Okay, let's untangle this. What we have here is a sequence of regions, the boundaries of which form a sequence of polygons. These boundaries are "rough" because, roughly speaking, you can see sharp corners when you zoom in close. The sequence of regions approaches a disk. The sequence of boundaries approaches a circle. It does not, in any sense, approach a fractal; the limit is simply a genuine circle. What we want here is to find the area of the disk-the disk being the interior of the circle. This area is πr^2, as stated in the video. Indeed, the sequence of regions in the video corresponds to a sequence of areas of those regions, and those areas approach πr^2. This is a legitimate method of obtaining the area of a figure. Another method is to approximate the disk as a many-sided regular polygon with circumradius r, sliced into triangles, and then take the limit of the area as the number of sides approaches infinity. (This is the "infinitely thin pizza slices" method.) This gives the same πr^2 quantity. Intuitiveness is subjective, so Iw won't speak on that. This method is no more accurate than the other method-both have equal, perfect accuracy. Let's go back to our sequence of boundaries. Though the boundaries approach a circle, the length of the boundaries do not approach the circumference of the circle, that being 2πr. Instead, the length of the boundaries is a constant value of 8r. This demonstrates that the length of the limit of some curves need not equal the limit of the length of those curves. This is called the staircase paradox. This problem does not occur with our regular polygon method, where the regular polygon's perimeter does converge to the circle's circumference. I imagine this is what you were trying to get at, but you failed to communicate it properly. That, or there was some kind of genuine misunderstanding about how area works. If so, that's understandable. It happens. Incidentally, I am *also* not a big fan of the intuition for π here. However, that's simply because it seems like kind of a bizarre and confusing way to conceptualize the idea, particularly because I would never start with area instead of circumference. It is not because I think it is straight-up wrong. .

[@isavenewspapers8890]

3:08 Apparently infinity, if you chose the lower bound x = 0. 4:26 I really wish you'd have simply written lower and upper bounds of 1 and x, respectively, then renamed the 1/x dx to 1/t dt or something. Then the equality would actually be correct, and we'd understand exactly what area we're supposed to be calculating here. More correct and less confusing; it's a win-win! No, wait, weren't we supposed to be using n as our variable tending to infinity? Yeah, use n as the upper bound, and then change the right hand side to ln n. Perfect. 5:11 Missed opportunity to replace each of the n's with the number of steps you've taken to the right, since that's literally what n means here. But without having written the integral properly, you couldn't have done that anyway.

[@freakingannonymouspanda1766]

6:20, I think they put the negative term first because, when you put a function of K after the summation sign , people might include that IN the summation, so to avoid that kind of confusion, they put the negative sign first, I think....

[@VikasBhardwaj-kt8gi]

I love you man your videos make my day

[@sashagornostay2188]

12:10 uhmm actually Euler was to argue one of the greatest influencers for the usage of pi as a constant soooo...

[@andreyhenriquethomas9554]

As a avid Pi fan, Euler used it all over the place to fit what he needed, creating some trully bizare "identities" pi=pi/2, pi=2pi, etc. So he kinda used the number as a placeholder for "the thing i need that is about circles" and not so much as "constant" in the mathematical sense. (You could get for what he was using based on context)

[@isavenewspapers8890]

@@andreyhenriquethomas9554 I was of the understanding that this "context" consisted of an explicit definition. Am I wrong?

[@yousifalzaidi2570]

You have swapped the numerator and the denominator with each other at 14:23 😊

[@isavenewspapers8890]

Yeah, the equality 4 = (π / 4) * π is definitely false.

[@arysword]

lim n -> infty ( sum_{k=1}^{n} 1/k - ln(n)) you used k instead of n at 6:30 yes its a nitpick, the animations are gorgeous

[@hamsturinn]

The reason why they flip the log is probably so people don't think it is in the sigma.

[@aosidh]

I've loved the Euler-Mascheroni constant gamma ever since it was featured on an irrational number clock my grandparents gave me

[@chandeepec]

please explain about non euclidean space + covariant and contravariant tensors

[@spacepython_]

10:44 absolutely blew my mind. That doesn't happen very often to me.

[@Frddy_-sh8so]

they are constantly mathing

[@gabrielribeiro222]

To me im always so happy wen you upload even if its somethig i already know you always make these hard concepts so fun.

[@paper5959]

oil up is truly my favourite mathematician

[@MrBlaze2126]

Wow! I can't believe thats how they were made. I have seen so many explanations for pi but yours was the best. (also anti - disintegrator😂)​

[@MegaTitan64]

The negative sign on the left triggers me, too. I felt so vindicated by your comments. XD

[@experimentingalgorithm1546]

I can't imagine it man using green screen on these kind of videos, It's like a new discovery to me

[@ManiaAlive]

Honestly, you are very underrated. How does this video have less than a thousand views???

[@DjSapsan]

What is the blur method on minute 7? It looks insane

[@collin6526]

1:42 I have a suggestion for the visual presentation. Fade out the dark grey layer that the text is on when you start using the 3D environment for explaining. It will shift the viewer's focus to the visual. Also it just looks wrong to me that this isn't happening. Actually now that I look again, there isn't a grey layer, it's just darker than I expected.

[@ramitisking]

Makit... I dont want to sound like a nerd but... I loved the video but it missed on example. The limit 0 times infinity is often described as an unstoppable force meets an immovable object. The limit e is the maximum amount of compound interest you get in a year if it compounds n times a year, at a rate of 1/n Still great video honestly. PS: Makit if and only if you're reading this HAPPY BIRTHDAY WOOOOO🎉🎉🎉🎉

[@hafixion]

I know someone already mentioned it, but the ln being on the left is actually the most sensible notation. I've seen an error like this before in one of your chemistry videos (iirc it was something to do with the meth- prefix) and commented on it before. It's not major nor that important in any way, but you should get someone to double-check your videos before uploading.

[@mike-q2f4f]

I came for meaning. Thank you!

[@TannerJ07]

I'm so glad I subscribed so I could be 15 hours late for a video

[@Richard_Ingalls]

12:17 So true

[@F-15EXEAGLE2]

This video is very underrated

[@BeepImasheep460]

please do a video about the how eulers constant is useful

[@SayandipRoy-n7j]

You gonna be 3blue1brown 2.0 soon !! So fascinating and Amazing explanation

[@phoenixbr4747]

I am a simple person. I see MakIT video, I click and like

[@friedrichmyers]

Damn. Ran across a Goldmine of educational content and it isn't even a million views yet?

[@ClaudeSpeed32]

I thought i was alone using the term "hypercubed"

[@isavenewspapers8890]

A hypercube could be a square, a cube, a tesseract-it's not specific. That's why I prefer the term "tesseracted".

[@nightglide_]

0:04 Half-Life jumpscare

[@isavenewspapers8890]

5:21 More like a limit? What are you trying to say here? I thought the inaccuracy requiring a technicality was that this was only an approximation, but it sounds like you had something else in mind.

[@collin6526]

Yet another great video

[@TruthNerds]

6:23 You messed up with the variable names here, it should be ln _n_ and not ln _k_ and the limit for _n_ to infinity.

[@Gokuk-oq3uk]

Nice vid 👍👍👍

[@tomkerruish2982]

6:22 The limit should involve n, not k, and you should have ln n, not ln k.

[@shrodinger3844]

1:00 he made THAT joke

[@CC1.unposted]

your saying ln(n) = log n / log e and ln is use in Eulers number (idk symbol) and e is also a random non polynomial equation to find N I've only found one use e is used for Eulers number it's like Euler is branding his constant it's Maths you can do anything

[@radzel-u2f]

15:50 isnt pi a half rotation and tau a full rotation?

[@angeldude101]

If you're talking about angles or arc-length, then yes. If you're talking about area, as the video was when introducing π, then no. π is the area of the unit circle, and I'd argue that this is just as important as τ being the perimeter of the unit circle. Diameter doesn't exist.

[@isavenewspapers8890]

@@angeldude101 ​​⁠​⁠The difference is, radians are extremely important and useful. We use arc length divided by radius all over the place because of how natural it is. We hardly use sector area divided by radius squared; I don't think that's even got a name. Besides, sectors themselves are an example of the usefulness of radians: the area of a sector with central angle radian measure θ and radius r can be found by integrating θr' with respect to r' from 0 to r to get (1/2)θr^2, which is where that factor of 1/2 comes from in the first place.

[@mr.littleman2263]

yo ts actually fire

[@joosvanloo5405]

Wait but is the euylers principle not just infinite? Or why is it not infinite?

[@isavenewspapers8890]

Euler's constant γ can be represented as the area of an unbounded region, as seen in the video, but an unbounded region can have finite area. An easy way to see this is if you imagine shifting all the little pieces horizontally to the left so that they all sit in a vertical arrangement, one on top of the other. There's no overlap, and they fit neatly into a square with a side length of 1, with plenty of room to spare. Since the square has an area of 1^2 = 1, this shows that the value of γ is less than 1.

[@Richard_Ingalls]

7:50 😂 thats hilarious

[@TheEliteMan723]

Great video

[@randomjazzpicture5108]

I love your videos and I would keep watching them. However, unfortunately I am human so I do have to sleep.

[@suryamgangwal8315]

Gamma is the Euler mascheroni constant

[@thelittlemaster5311]

Can anyone know how to made exactly this type of 3D math video.... One i know is manim python library others software you tell me in reply...

[@Frddy_-sh8so]

4:15 Ba dum sch

[@C8H13O5N]

Leaving a comment to boost the algorithm

[@isavenewspapers8890]

15:51 Really, the full rotation? No, I'm pretty sure it's only halfway. Gee, someone should give a name to the number that actually represents a full rotation, just to avoid this kind of confusion. That would be cool, I think.

[@Wither_AnimationsTCO]

Tau

[@N3rd-s1h]

MAKiT I’m never gonna give you up

[@piogwit]

certified banger

[@Skyhighjettalone]

Not gonna even give a special mention to Tau? Pi's little brother?

[@isavenewspapers8890]

Little?

[@cimitechcimitech9114]

What are logs? I don't think you mean the ones from trees

[@isavenewspapers8890]

They're logarithms, the inverse of exponentials. For example: 2 to the 3rd power is 8, so the logarithm base 2 of 8 is 3.

[@anodarai4393]

It's Euler-Mascheroni constant. Also, log(1)=0, any number taken to power 0 gives 1. Your starting box in animation should be just a line. Also, you forgot +C and the absolute value for x in the integral of 1/x. Yes, I am a mathematician, how did you know :)

[@isavenewspapers8890]

1) γ is variously termed either Euler's constant or the Euler-Mascheroni constant. I prefer the latter to avoid confusion, but the former is also used. 2) Really, the underlying problem with the integral situation was that it should've been a definite integral in this context. We were looking to represent the natural logarithm of n, which can be done by integrating 1/x with respect to x from 1 to n. You knew the rules, but I don't think you applied them correctly. 3) *Technically*, your given solution does not give the antiderivative class of 1/x in fullest generality. The true answer is ln|x| + C_0 for x < 0, and ln|x| + C_1 for x > 0. Each piece can have a different constant added, and the derivative is still 1/x. Yeah, people use ln|x| + C as shorthand anyway, but if we're gonna nitpick, we might as well go all in. Just out of curiosity, what do you mean when you call yourself a mathematician?

[@yjovian]

awesome

[@epicstar86]

cooking

[@Omar._e]

The explanation in the video is full of randomness.

[@gamma_02]

im a constant :3

[@lucahermann3040]

14:40 that's actually Legendre's constant 𝐥. It's the limit of ln(n)-n/π(n), with π(n) being the prime-counting function. There's an entire Wikipedia article about it. You should check it out!

[@abdul-muqeet]

14:36:Looks wrong

[@romibob.5932]

If you included the constants i and zero, you could have related then all. By the way, you used the wrong limit, not k approaches infinity, n does.

[@isavenewspapers8890]

Ah, e^(2πi) = 1 + 0. Or even 1 + 0i, to put it in a + bi form.

[@Sng4]

Comment for the algorythm

[@Il_panda]

This video was done in a bathroom 😂

[@MAKSHiTHappen]

Maybe the constants were the mental illneses we got along the way

[@-_Nuke_-]

In actual Greek, "π" is not actually pronounced "pie"... It's pronounced "p". What a shocker 😮😂 Why do you guys get to have "pee" for "p" and we "pie" for "π"? Its the same letter, it makes the same sound, it takes the SAME name... It only has a different shape, but for everything else "p" = "π" - they are pronounced THE SAME. (As you might have already guessed by now, "τ" isn't pronounced "tau" either...).

[@goosemchonk]

Pi is the name of the letter. If you were actually Greek, you would know when spelling a word where the next letter to be said is π, you say "pi" not "puh".

[@SaturnMist4]

P and pi do not have the same name

[@trewajg]

The letter's name and the letter's use and pronounciation in real writing is not the same thing