So fascinating. I can't believe this is the only math vid on this channel. We need more.
@WillyFlowerz
2 ай бұрын
THANK YOUUUUUUUUUUUUUUUUUUUUUU I've been pulling my hair out since middle school trying to understand x^x and now 15 years later FINALLY a complete and beautifully explained explanation I can finally die in peace, thank you so much
@Gromit048
7 ай бұрын
how do i download this? i tried every method and it did't work.
@a.arredondo
7 ай бұрын
Your best bet is to ask in the discord. I'm no longer up to date in the modding meta and it's changed a lot since I published these.
@Gromit048
6 ай бұрын
@@a.arredondo I have successfully downloaded this and ported it to ex-coop. Can I have it's .blend file so i can make it colorable?
@a.arredondo
6 ай бұрын
Hi Gromit. There is no .blend file for this mod, as I didn't prepare it with Blender. I just used some custom tools that I made to edit the C source files directly. Hit me up on discord if you want to discuss further.
@Gromit048
6 ай бұрын
@@a.arredondo what is your discord?
@a.arredondo
6 ай бұрын
@@Gromit048 arredondos
@MagnetoBombin
8 ай бұрын
This is running in an actual Nintendo 64 emulator or real console?
@Josuh
8 ай бұрын
HE LOOKS SO DAMN PRETTY DEAR GOD
@jotaro9305
8 ай бұрын
1:54 please what is the grapher for this part ? thk !
@hkayakh
9 ай бұрын
I’ve been looking for this video for half a year because the question in the thumbnail alone is enough to get me hooked
@Wilker_uwu
9 ай бұрын
it's been a year, i wonder if a pull request has been made for GeoGebra to include a visualization like this.
@Sonic_productions6
11 ай бұрын
I love how you made Bowser look better but at the same time, making it still look like the original design from actors\bowser
@yaitz3313
11 ай бұрын
Huh. When I wanted to see how x^x looked on the negative side, I just graphed (x^2)^(x/2), which seemed a natural extension that gave me just the continuous part of Tupper's graph.
@jeunjetta
11 ай бұрын
Nice work! Thanks. Understanding your 3d graphs intuitively is easy! It's making me revisit stats and probabilities. Dara science might be 10 times easier things are platted this way 😊
@tcoren1
Жыл бұрын
Assigning negative real numbers an argument of pi does not feel like a canonical choice, as -pi is just as valid. Values such as 3pi, 5pi etc. are incongruent with positive numbers having an angle of 0, but both pi and -pi are valid choices
@gmncnr
Жыл бұрын
Animations are so good!
@zhoutai182
Жыл бұрын
Great video! Some months ago I was looking for the X^X graph for negative numbers because of reasons (just curiosity), and I found the same 3D graph you showed on the video. I was blown away for the 3D graph with imaginary numbers, and for me is the best way to show this kind of graphs. Additional to X^X, I wanted to look at the X^(1/X) or xth root of X for negative values, but sadly I couldn't find anything on a 3D graph as the first one, so in a sleepless night I put some numbers on a calculator for negative values of X and start plotting those results on a 3D graph, and I was again blown away because of this new graph! It results that, in very small negative values of X (close to zero), the function goes to infinity in an spiral between real and imaginary axis, and when you start increasing the X value (for example, -100), the graph tends to 1 on the Y axis and to -0 on the imaginary axis. Now that I look at your video I can understand why, so thanks for the info! I'm just a nerd who is interested in this kind of nerd content, but not a mathematicians in any way
@dunsparce4prez560
Жыл бұрын
e^ia🥧 is the most imaginary number I’ve ever seen
@JoakimfromAnka
Жыл бұрын
This 3d function must be added to desmos! I want my spirals.
@MemeAnt
Жыл бұрын
WAIT NO WAY! HAHAHAHA! I WIN THE BET! For context, I came up with this kind of idea on my own, and my friend said that this was ridiculous! I WIN! HAHAHHAHDJSISGSIANAHAOANAHUANABAUAHSISNAJSH YEEEEEEEE
@ezekielbrockmann114
Жыл бұрын
This is a great video. You should post more.
@محمدحارثبھائی
Жыл бұрын
Sometimes it doubts me as if e^x is hyperbolic in shape with it's tip at where the slope is 1 ..... can you clear my doubt by rotating e^x the 45 degrees clockwise?
@a.arredondo
Жыл бұрын
No, e^x is not a rotated hyperbola. A rotated hyperbola is 1/x.
@takusek
Жыл бұрын
This man really dropped one of the most chill math videos ever and then went quiet, I would really watch more of these if you make them
@любойпользователь-я2ж
Жыл бұрын
I waaaaant low poly luigi, like Fake luigi :((
@torazis3286
Жыл бұрын
3b1b with light theme
@DEPURMateusz
Жыл бұрын
hey can you make it a bps patch with marios voice
@hvok99
Жыл бұрын
Why did this video not take all the awards, it was so simple, elegant, clear, and powerfully revealing. I was hooked from start to end. 👏👏👏
@Berry_N
Жыл бұрын
Fantastic video.
@welcometochiles6156
Жыл бұрын
3:33 I don't think mod and abs are the same thing?
@angeldude101
Жыл бұрын
They are. mod(x) = sqrt(x*conj(x)). If x is a Real number, then conj(x) = x, so mod(x) = sqrt(x²) = abs(x) In both cases, they give the Euclidean distance from the origin. (Or non-euclidean distance if you're using a non-euclidean modulus function.)
@welcometochiles6156
Жыл бұрын
@@angeldude101 I suppose I'm too familiar with modulus in programming.
@angeldude101
Жыл бұрын
@@welcometochiles6156 Oh ya. The modulus of a ℂomplex number seemingly has nothing to do with modular arithmetic. This is the main reason I almost never use the former meaning and instead say "norm" or "magnitude."
@MrSeezero
Жыл бұрын
Here's my take on this. This can be easily explained with phasor angles. First of all, 0 is 0 all the time. Positive numbers are basically magnitudes with a phasor angle of 0 degrees while negative numbers are magnitudes with a phasor angle of 180 degrees. Only regular positive (/0 degrees heading) and negative numbers (180 degrees heading) are graphable on a regular graph. To find the cube root of 27, you take 27/_0 degrees and take the regular cube root of 27 for the final magnitude and divide 0 degrees by 3. This gets you 3/_0 degrees which is graphable. To find the other 2 cube roots, you use the same resulting magnitude, but you divide 360 degrees and 720 degrees by 3 to find the headings of the other two roots which aren't graphable since those headings aren't 0 or 180 degrees. To find the cube root of -27, you take 27/_180 degrees and take the regular cube root of 27 for the final magnitude and divide 540 [180 + 360] degrees by 3. This gets you 3/_180 degrees which is also graphable. To find the other 2 cube roots, you use the same resulting magnitude, but you divide 180 degrees and 900 degrees by 3 to find the headings of the other two roots which aren't graphable since those headings aren't 0 or 180 degrees. If you take -1 and try to put it to the 2.4th power then you would have 1/_180 ^ 2.4 = 1/_432 degrees for the first possible root. Then you add 864 degrees for any succeeding roots. There is at least some possible ways to end up with at a multiple of 180 degrees if the possible heading is 432 + n * 864 in which n is any integer. If n = 2 + m*5 in which m is any integer, then (-1)^2.4 is actually graphable. I can understand why it needs to be assumed that it can't be graphable though.
@ik964
Жыл бұрын
Awesome! Those are continuous and derivative, right?
@blacksuppository
Жыл бұрын
5:23 the visualization here genuinely made me gasp, i thought it was gonna be tilting or bending into the complex plane but it was something else entirely
@Picikak03
Жыл бұрын
I'm not trying to prove you're wrong but there's something I don't get I don't think a^x × a^y = a^(x + y) is the most important thing that should apply when we consider a as negative number. From that perspective everything truly looks alright. What if we consider an imortance of this: (a^x)^y = a^(x × y) ? Let's take a = -8, x = 1 and y = 1/3. Then in the left side we should have: ((-8)^1)^(1/3) = (-8)^(1/3) = cuberoot(-8) = -2 But what would be if we took the same a = -8, but x = 2 and y = 1/6: ((-8)^2)^(1/6) = 64^(1/6) = 2 So in the left sides we have: ((-8)^1)^(1/3) = -2 ((-8)^2)^(1/6) = 2 Therefore left sides are not equal But in the right sides whe have: (-8)^(1 × 1/3) = (-8)^(1/3) (-8)^(2 × 1/6) = (-8)^(2/6) But since left sides are not eqaul, so right sides should'd be as well. So 1/3 is not equal 2/6 despite the fact they are the numbers and moreover the same number So we are coming up with conclusion: 1/3 != 2/6 Which is nonsense Did I missed a part of the video which explains why taking different representations of the same number leads us to different results?
@Picikak03
Жыл бұрын
Well, I might be wrong about the first equation be equal to -2, let it be any complex non-real number But still, the second case gives a real number So we still get: 1/3 gives complex number 2/6 gives real number But they should be equal, how're they not?
@a.arredondo
Жыл бұрын
Hello Артем. What's going on here is simply that, unlike the property a^x a^y = a^(x + y), the property (a^x)^y = a^(x y) only applies if a>0, and the examples that you give are proof that this is the case. You will never find a serious math text that indicates otherwise. I hope this clarifies things. Cheers!
@Picikak03
Жыл бұрын
@@a.arredondo so (-8)^(2/6) is not equal to 2? Kinda weird that they tried to avoid a restriction of a >= 0 and still run into the restriction of a >= 0, but alright, that makes sense now
@angeldude101
Жыл бұрын
The problem is that we're trying to pretend that exponents are functions when they're really not. I'm actually suspecting that this result here might be related to the (a^x)(a^y) = a^(x+y) law not applying when x and y are non-commutative. As in the "principal roots" don't match, but that there would be other roots that do.
@benjamingraemegorman7657
Жыл бұрын
Awesome video. You don’t often find quality like this from a channel without 400 other videos in the same style. Super inspiring, and looking forward to more!
@Enderia2
Жыл бұрын
This feels like a Lines That Connect video
@nnwslswu
Жыл бұрын
讚!
@marklangridge2734
Жыл бұрын
You have far too few subscribers for the quality of your videos. Really interesting, very well explained, and shows how beautiful mathmatics can be.
@louf7178
Жыл бұрын
When new definitions are actually differ things (so, not exactly equal).
@승준박-j9n
Жыл бұрын
minus cannot exist. only activity. however 0 exist either.
@승준박-j9n
Жыл бұрын
0 either means physics.
@renegadex2o395
Жыл бұрын
Reject 2d, Embrace x,y,Im 3d
@caramelldansen2204
Жыл бұрын
Love the video, though I'd recommend investing in a pop filter for your mic
@boredgrass
Жыл бұрын
Why hide valuable instruction about a subject that demand focus and concentration, behind a distracting music wall? Did you know that many people are effected by a hearing impairment that renders the brain unable to blend out background noises and results in a constant back and forth between noise sources? Perhaps you have heard people complaining that they can't understand anything at family gatherings or when they try to have a conversation in a cafe or bar with background music?
@angeldude101
Жыл бұрын
The exact opposite can be said for many other people; that the music helps calm them down and focus more easily. The ideal solution would be to be able to adjust the music and voice volumes independently like you can do in some video games. Without that, this video at least has actual subtitles, so if you're willing to lose the voice to avoid the music, you could mute the audio entirely and just use the subtitles. It's an imperfect solution, but the only solution I can imagine working for the widest number of people would require completely changing how KZitem stores videos.
@_AHN_
Жыл бұрын
Wow, I didn't realize it contains Euler formula
@blablabla55555
Жыл бұрын
Wow! Subscribed!!
@jlee1522
Жыл бұрын
Sees thumbnail. Ok, I think it's pretty simple. Half way through video... ...Uh, ok, I made a mistake. I'm just going to leave now and watch something dumb.
@Doubaer
Жыл бұрын
Which xkcd comic is that at 8:53?
@lemagicbaguette1917
Жыл бұрын
If it spins only once after two integer exponents go by, could it be called a spinor?
@BigyetiTechnologies
Жыл бұрын
Wouldn't it be the tenth root of x^24?
@SashaSashevich
Жыл бұрын
без тени график не понятен
@Jacobwe21
Жыл бұрын
Hey, stop stealing the music of 3Blue1Brown. But otherwise, a very good and enjoyable video.
@ferdinandkraft857
Жыл бұрын
What a great video!
@chrissch.9254
Жыл бұрын
Excellent video - I have never thought about this…
@leftysheppey
Жыл бұрын
I don't like the top left function. It feels like a set of functions. It's cool in its own right, don't get me wrong, but not really what we're going for
Пікірлер