Yes, for a function on numbers, this is true. However, a function does not necessarily take a number as input. It can take in a vector, a matrix, a set, or even another function, among many other things.
Oh boy, wait until you find out about functionals (a function that takes in a FUNCTION, does something to it and spits out an answer). Mathematics is just getting started.
this made me think of how Gottlob Frege was a German mathematician from that same time period that laid out the principles for the study of logics which ended up as the basis for semantics
1:15 Dude, WTF! I think I checked like few times in past what this fractional dimension thing is and I never really grasped it, but the way you explained it is so simple!! Just consider the way it scales and you get the dimensionality! Thank you! ♥
i cant decide if my life is really good or pitiful based off of the fact that im watching a video explaining mathematical concepts that aren't in my syllabus-
1:32 The logarithmic notation of the emoji 😅to base 😄 is some next level genius explanation. Now, I'll never use the emoji without thinking about logarithms
The explanations of fractals like the Serinsky Triangle and the concept of fractal dimension blew my mind. It's amazing how mathematics can turn seemingly simple objects into something so intricate and beautiful, especially with fractals like the Mandelbrot set. Awesome content!
If you're a mathematician and you find yourself compelled to denounce a function, it's time to take a step back and re-examine all the pertinent premises.
Brilliant exposition indeed! As a Math Lecturer the content is invaluable, worthy of subscription! Many thanks for highlighting the beauty of Seifert Surfaces, which hardly get due recognition. Now whilst not entirely geometric (Differential Geom., Chaos Theory, Complex Anaysis, etc), I'd suggest: *Polytopes (link to Crystallography) *4D Fractals *Riemann Surfaces *Hilbert Curves *Lie Groups *Conformal Mappings *Bifurcation Maps *Kusudama Origami (yes it's paper-folding, but Math knowledge helps immensely) ...To be included from an advanced study point of view & also to expose the sheer beauty of Mathematics...IMO 🤔
Yeah, a 2D representation is kinda the best you can do on a 2D screen. Maybe not this 2D representation specifically if you're picky about shading, but a 2D representation regardless.
00:00 Sierpiński triangle is not defined the way it's presented. It's defined as connecting middle points creating an internatl triangle. You even do this in 00:17 . If you want to be consistent, your triangle shouldn't be "divided" but rescaled and multiplied as previously in the video.
@@isavenewspapers8890 True, not all of them are equivalent. E.g. If it's defined like in the video (by expanding), the side lenght and area go to infinity. If it's defined as original (by dividing), side and area are limited. Therefore these definitions are not the same.
Honestly most of this was jibberish not because this video is bad but because I'm a little dumb, this does not mean I did not leave without learning anything! Good work
"If you scale up the dimensions of a sapinski triangle by a factor of two, it becomes three times as large. " How are we measuring largeness though? area?
@@sheepyisthecutest That's the whole idea behind fractals. They take up a fractional dimension of space. A normal triangle is 2-dimensional, and this thing is 1.5-dimensional.
A mathematician named Klein thought the Möbius band was divine. Said he: "If you glue the edges of two, you'll get a weird bottle like mine." POEM! 10:50 bruh this is like a meme equivalent in mathematics community LOL
You ever notice how, if a rotation looks clockwise from one side, it looks counterclockwise from the other side? Well, that's similar to what's happening here. When you look at the same rotation from a different orientation, your point of view gets flipped, so the rotation seems to be going the other way.
9:54 what are these black balls placed in-between the strands of the rope? are they connecting it into some type of net? What is their function and how are they defined? What are they there for?? Anyone here who understands this weird picture? :-(
Let me know if there's a topic you'd like me to cover next. 😊
all infinities explained
hiHi
an explanation why is 6=9
(a higher dimensional calculation or whatever)
edit: is it even true tho?
5:30 Literally the best explanation of a function. It takes a number, does a bunch of stuff to it, and spits out an answer.
Yes, for a function on numbers, this is true. However, a function does not necessarily take a number as input. It can take in a vector, a matrix, a set, or even another function, among many other things.
Oh boy, wait until you find out about functionals (a function that takes in a FUNCTION, does something to it and spits out an answer). Mathematics is just getting started.
@@isavenewspapers8890 In computer science a function can also take nothing as input
@@isavenewspapers8890 I did not know that, I’m not that deep into mathematics.
how else would you explain functions???
In "Benoit B. Mandelbrot, the B. stands for Benoit B. Mandelbrot"
It took me a while to realize what you did
Benoit Benoit B. Mandelbrot Mandelbrot?
@@CosmicHase
Benoit Benoit Benoit B. Mandelbrot Mandelbrot Mandelbrot
f(B)= benoit B Mandelbrot
fof(B)= ?
@@josephjohnson313 Benoit Benoit Benoit Benoit B. Mandelbrot Mandelbrot Mandelbrot Mandelbrot
Mathematician: Yay! I proved it!
Weierstrauss: No you didn't.
Weierstrass* :)
I can't help but be amazed at how original the ideas of German mathematicians from 19-20th centuries were.
this made me think of how Gottlob Frege was a German mathematician from that same time period that laid out the principles for the study of logics which ended up as the basis for semantics
1:15 Dude, WTF! I think I checked like few times in past what this fractional dimension thing is and I never really grasped it, but the way you explained it is so simple!! Just consider the way it scales and you get the dimensionality! Thank you! ♥
i cant decide if my life is really good or pitiful based off of the fact that im watching a video explaining mathematical concepts that aren't in my syllabus-
“log😄 😅 = 💧” 💀
😂😂
He's not wrong tho
i hate i understood that
Still water😱😱😱
thought this has way more views, just realized its below 1k, awesome quality
11:34 now watch the video again and take a shot every time he says "german mathematician"
I like a challenge
Ight bet
its 5 shots
weak
1:32 The logarithmic notation of the emoji 😅to base 😄 is some next level genius explanation. Now, I'll never use the emoji without thinking about logarithms
The explanations of fractals like the Serinsky Triangle and the concept of fractal dimension blew my mind. It's amazing how mathematics can turn seemingly simple objects into something so intricate and beautiful, especially with fractals like the Mandelbrot set. Awesome content!
Sierspińky*
@@TheMiguelHuey Sierpiński*
@@lixin_9660 oops
If you're a mathematician and you find yourself compelled to denounce a function, it's time to take a step back and re-examine all the pertinent premises.
6:12 ALL HAIL THE ∞
The Legend of Zelda fans on the first one: ITS THE TRIFORCE
Forget the Quad Force theory, I wanna see the Infinite Fractal Triforce theory
link mentioned!!!!
I was looking for this comment lol real
Brilliant exposition indeed!
As a Math Lecturer the content is invaluable, worthy of subscription!
Many thanks for highlighting the beauty of Seifert Surfaces, which hardly get due recognition.
Now whilst not entirely geometric (Differential Geom., Chaos Theory, Complex Anaysis, etc), I'd suggest:
*Polytopes (link to Crystallography)
*4D Fractals
*Riemann Surfaces
*Hilbert Curves
*Lie Groups
*Conformal Mappings
*Bifurcation Maps
*Kusudama Origami (yes it's paper-folding, but Math knowledge helps immensely)
...To be included from an advanced study point of view & also to expose the sheer beauty of Mathematics...IMO 🤔
0:25 IDK he was from Poland, until I saw him in a math book. Now this video confirmed to me that he is from Poland.
The surnames give it away
Cool
Fun fact the Sierpinski Triangle, and also the similarly constructed 3D shape the Menger Sponge, technically have no area/volume.
Your mother has no real area/volume
I have nothing to do with maths and science but I just like watching your videos!
You forgot my blanket at 3am
i have absolutely no idea what this video just said but i love it
when your youtube feed is so cooked that you watch "every geometric shape explained"
and you enjoyed it because its a banger
The music matches your video so well😊
Note the Sierpiński triangle is connected directly to quaternions via floretions.
The Tesseract will always be favorite of these.
I just barely passed high school math and youtube recommended this
0:00
Oh, this should be cool, I like science stuff.
1:50
Oh crap. What have I gotten myself into?
The only time where calculus is useful in life: making videos like this one
"Aparment complex? I find it quite simple"
you are reading this
Yes I'm reading
No, I’m not
I might be reading
And this
And?
Either I'm waayyy smarter than I thought, OR you are VERY good at explaining this stuff lmaoooo.
I have no reason to be watching this but I'll do so either way
education is nice
Thats a triforce. Just a really festive one. Its the triforce of fun summery colors
My favorite is the Menger sponge. Bob SquarePants. 😂
ohhhhhhh, who lives in a pinapple under the sea? SPUNCH BOP SQUER PANCE!
2:24 I have to point out the fact that you talk about "a world with only 3 dimensions" while showing a 2d representation of Earth
Yeah, a 2D representation is kinda the best you can do on a 2D screen. Maybe not this 2D representation specifically if you're picky about shading, but a 2D representation regardless.
00:00 Sierpiński triangle is not defined the way it's presented. It's defined as connecting middle points creating an internatl triangle.
You even do this in 00:17 . If you want to be consistent, your triangle shouldn't be "divided" but rescaled and multiplied as previously in the video.
The Sierpiński triangle has multiple equivalent definitions.
You could say it has three equivalent definitions.
@@isavenewspapers8890 True, not all of them are equivalent. E.g. If it's defined like in the video (by expanding), the side lenght and area go to infinity. If it's defined as original (by dividing), side and area are limited. Therefore these definitions are not the same.
@@zolv That's not expanding; it's shrinking and copying. The length of the outer boundary of each shape in the sequence remains the same.
I did a presentation for my highschool speech and debate class a few years ago about fractal geometry
Less than two minutes in, I just wanted to see the funny shapes and my brain's already like, this shit's too complex for us bro
where is geometry dash?
0:05 IS THAT THE LEGEND OF ZELDA??
1:31 that logarithm function🤣
LOVE IT, THANKS!!! ❤❤❤
Couldve added that shape of how a sphere needs to form to turn inside out without sharp edges
Is this how I finally learn what a derivative is???
A Photoshop artist named Valdevia made an interesting horror story about a chemical leak causing a Mandlebrot (referred to as Fractal) infection
Please please please do statistics videos!! Im a psych student and want to learn more from you ahout cool statistics things
Honestly most of this was jibberish not because this video is bad but because I'm a little dumb, this does not mean I did not leave without learning anything! Good work
My absolute favorite, fractals
1:05 wait 2,4,8 SO 4D TESSERACT IS 16
I understood some of this video
oh wow, first time seeing someone pronounce a Polish name and Last name properly, whilst not being Polish themselves
0:05 zelda refrence
The tesseract one is the hardest thing to understand in my life☠️☠️☠️
penteract💀💀💀💀💀
Women
@@enoyna1001 no question☠️
5:20 too much for zblock
"ADMIN HE'S DOING IT SIDEWAYS" 🗣🔊🔥🔥🔥
Me watching this: This is incomprehensible but I like this-
Sierpiński Triforce
All my braincells are fusing together to try to understand this
Mandelbrot is my favorite.
0:05 bros got the complete triforce
I had a stroke trying to understand this video
Nice video
0:05 -- Triforce!
Great!
I find fractals so cool
I made a fractal, so if the creator of the sierpiński triangle was named sierpiński and it was a triangle.
I call mine the rowald swastik-
0:08 IS THAT THE TRIFORCE?!
I hate mathematicians
/\/\/\ this is the only complexity i need know
Fly high Michigun 🕊️/\/\/\
"If you scale up the dimensions of a sapinski triangle by a factor of two, it becomes three times as large. "
How are we measuring largeness though? area?
He's talking about dimensions, so ofcourse it's area.
How else would we measure the "largeness" of a 2d shape?
11:06 Wait a second, that's a Seifert surface of a trefoil knot, not a Hopf link.
I didnt understand anythig but it was interesting to watch'
0:05 the triforce
Love these
Lots of German names here today.
IS THAT A TRIFORCE REFERENCE???🤺
KLEIN BOTTLE FROM TEAM ROOM 125 AGAIN IS THAT YOU😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱
Im in middle school and yet i still get it
What is the background music?
The first song is Minute Waltz by Chopin and the second is Badinerie by Bach
Is the Sierpinski Triangle considerd to be a type of Mandelbrot?
Depends on what "a type of Mandelbrot" is.
The Mandelbrot set produces a fractal. The Sierpinski triangle is also a fractal.
0:07 “Triforce”
You get a like for all the classic memes, 🥹 so nostalgic
Bro I imagined a tesseract before I even learned about it????????
Huh, so that's what that Yume 2kki world is about.
can someone explain what that triangle that appears in the beginning of the video means? I still don’t understand. what is scale up by 2?
Scale up by 2 means make it larger. Multiply the height by 2, and multiply the width by 2.
@@RibusPQRohhhh, but why does that triangle become 3 times larger if scaled up by 2, not 4 times larger?
@@sheepyisthecutest That's the whole idea behind fractals. They take up a fractional dimension of space. A normal triangle is 2-dimensional, and this thing is 1.5-dimensional.
Rename this video to "how to fall asleep easily tutorial"
No calabi-yau manifold? That shape doesn’t have enough dimensions to exist in the reality we can observe!
Well, now I know where fallout new vegas: old world blues got their character names from.
Polish have atention
You're excellent, at least.
A mathematician named Klein thought the Möbius band was divine. Said he: "If you glue the edges of two, you'll get a weird bottle like mine."
POEM!
10:50 bruh this is like a meme equivalent in mathematics community LOL
YUME 2KKI?!?!?!?!?!?!?
Note: theres a actual world called sierpinski maze
I think this broke my brain
0:00 POLAND MENTIONED!!!!!!! 🇵🇱🇵🇱🇵🇱
3:38 but we clearly can see that it is counterclockwise?? How can these two be indistinguishable??
You ever notice how, if a rotation looks clockwise from one side, it looks counterclockwise from the other side? Well, that's similar to what's happening here. When you look at the same rotation from a different orientation, your point of view gets flipped, so the rotation seems to be going the other way.
pretty cool
nice
6:10 AND BEYOND!
And mobius strip?
Benoit Benoit Benoit Benoit..... Mandelbrot
9:54 what are these black balls placed in-between the strands of the rope? are they connecting it into some type of net? What is their function and how are they defined? What are they there for?? Anyone here who understands this weird picture? :-(
Yeah, the visuals in this section barely make sense. Sorry.