Every Complex Geometry Shape Explained

[@ThoughtThrill365]

Let me know if there's a topic you'd like me to cover next. 😊

[@mono6198]

all infinities explained

[@ak-ee7zq]

hiHi

[@Martan2010]

an explanation why is 6=9 (a higher dimensional calculation or whatever) edit: is it even true tho?

[@soulsofspirit9729]

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.

[@isavenewspapers8890]

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.

[@MrTicky4]

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.

[@TheAdriyaman]

@@isavenewspapers8890 In computer science a function can also take nothing as input

[@soulsofspirit9729]

@@isavenewspapers8890 I did not know that, I’m not that deep into mathematics.

[@minirop]

In "Benoit B. Mandelbrot, the B. stands for Benoit B. Mandelbrot"

[@daniel_77.]

It took me a while to realize what you did

[@CosmicHase]

Benoit Benoit B. Mandelbrot Mandelbrot?

[@josephjohnson313]

@@CosmicHase Benoit Benoit Benoit B. Mandelbrot Mandelbrot Mandelbrot

[@DhoklaAboveVadapav]

f(B)= benoit B Mandelbrot fof(B)= ?

[@rayzhao491]

@@josephjohnson313 Benoit Benoit Benoit Benoit B. Mandelbrot Mandelbrot Mandelbrot Mandelbrot

[@davidhopkins6946]

Mathematician: Yay! I proved it! Weierstrauss: No you didn't.

[@Are3.14]

Weierstrass* :)

[@jerometeor]

I can't help but be amazed at how original the ideas of German mathematicians from 19-20th centuries were.

[@lijauju]

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

[@suhnih4076]

“log😄 😅 = 💧” 💀

[@cosmax1448]

😂😂

[@Yarik_X]

He's not wrong tho

[@AzarinthUnknown]

i hate i understood that

[@scarletevans4474]

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! ♥

[@RishwanaHoque]

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-

[@HermesKhadivar-n5l]

11:34 now watch the video again and take a shot every time he says "german mathematician"

[@rutterj2]

I like a challenge

[@borisslavchev1328]

Ight bet

[@borisslavchev1328]

its 5 shots weak

[@Tayhay]

thought this has way more views, just realized its below 1k, awesome quality

[@LearnWithPaint]

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!

[@TheMiguelHuey]

Sierspińky*

[@emmanuelsimaurio6078]

The Legend of Zelda fans on the first one: ITS THE TRIFORCE

[@shaquille6566]

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

[@damarzrealm7731]

You forgot my blanket at 3am

[@jsalsman]

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.

[@raccoonmellows1243]

6:12 ALL HAIL THE ∞

[@noonesknight]

when your youtube feed is so cooked that you watch "every geometric shape explained"

[@lukatolstov5598]

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.

[@testname420]

The surnames give it away

[@mrakat_27]

Cool

[@4.0.4]

Fun fact the Sierpinski Triangle, and also the similarly constructed 3D shape the Menger Sponge, technically have no area/volume.

[@scottydu81]

Your mother has no real area/volume

[@MadScientyst]

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 🤔

[@MrSerbianOrthodox]

I have nothing to do with maths and science but I just like watching your videos!

[@ForgottenInForest]

The music matches your video so well😊

[@AustinTheWeenieTickler]

i have absolutely no idea what this video just said but i love it

[@santipiola2752]

"Aparment complex? I find it quite simple"

[@84bombsjetpack23]

My favorite is the Menger sponge. Bob SquarePants. 😂

[@rayzhao491]

ohhhhhhh, who lives in a pinapple under the sea? SPUNCH BOP SQUER PANCE!

[@DanialTarki]

The Tesseract will always be favorite of these.

[@matthewpollock9685]

0:00 Oh, this should be cool, I like science stuff. 1:50 Oh crap. What have I gotten myself into?

[@floretion]

Note the Sierpiński triangle is connected directly to quaternions via floretions.

[@fullestegg]

you are reading this

[@Shack283]

Yes I'm reading

[@Gimmickvr]

No, I’m not

[@SanityInAnAmazonBoxShorts]

I might be reading

[@rapallayahuma9417]

And this

[@AMig-ht8nw]

And?

[@glennlaroche1524]

Either I'm waayyy smarter than I thought, OR you are VERY good at explaining this stuff lmaoooo.

[@fishy398]

My absolute favorite, fractals

[@dinoeebastian]

I did a presentation for my highschool speech and debate class a few years ago about fractal geometry

[@SpidermansSymbiote]

I just barely passed high school math and youtube recommended this

[@Evgeni_Aleksandrov]

The only time where calculus is useful in life: making videos like this one

[@kingofawesomeness5375]

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

[@isavenewspapers8890]

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.

[@targuscinco]

Thats a triforce. Just a really festive one. Its the triforce of fun summery colors

[@damedanedameyodamenanoyo2594]

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

[@JustSomeoneHi]

I have no reason to be watching this but I'll do so either way education is nice

[@anaisnintuition]

Please please please do statistics videos!! Im a psych student and want to learn more from you ahout cool statistics things

[@zolv]

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]

The Sierpiński triangle has multiple equivalent definitions.

[@RibusPQR]

You could say it has three equivalent definitions.

[@zolv]

@@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.

[@isavenewspapers8890]

@@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.

[@Justchillingstrangers2012]

Me watching this: This is incomprehensible but I like this-

[@Mhebsandstuff0]

0:05 IS THAT THE LEGEND OF ZELDA??

[@emory5533]

I understood some of this video

[@aetheralmeowstic2392]

Sierpiński Triforce

[@x88.berkay]

Couldve added that shape of how a sphere needs to form to turn inside out without sharp edges

[@Be_a_znig]

Mandelbrot is my favorite.

[@Yukicutiepatotie]

I had a stroke trying to understand this video

[@Shack283]

The tesseract one is the hardest thing to understand in my life☠️☠️☠️

[@thatrobloxguy]

penteract💀💀💀💀💀

[@enoyna1001]

Women

[@Shack283]

@@enoyna1001 no question☠️

[@iimuffinsaur]

Is this how I finally learn what a derivative is???

[@matthewboire6843]

I find fractals so cool

[@yackawaytube]

Great!

[@Swagatronofcybertron]

0:05 bros got the complete triforce

[@JohnSmith-zw8vp]

0:05 -- Triforce!

[@The_PavaExplainer]

Nice video

[@crispbacon-wx8qu]

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

[@Bcokjwdbc]

1:05 wait 2,4,8 SO 4D TESSERACT IS 16

[@argf-ur3ib]

0:05 zelda refrence

[@Theos-zj3ys]

I didnt understand anythig but it was interesting to watch'

[@Lunar994]

Huh, so that's what that Yume 2kki world is about.

[@rjkrkkj]

Love these

[@modlich_303]

oh wow, first time seeing someone pronounce a Polish name and Last name properly, whilst not being Polish themselves

[@Garfield_Minecraft]

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

[@tukan1652]

What is the background music?

[@_4pplePen6]

The first song is Minute Waltz by Chopin and the second is Badinerie by Bach

[@reformajulesrowald9998]

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-

[@gamingdiamond168]

0:05 the triforce

[@LordShrek420]

0:08 IS THAT THE TRIFORCE?!

[@isavenewspapers8890]

11:06 Wait a second, that's a Seifert surface of a trefoil knot, not a Hopf link.

[@Phrogsage]

IS THAT A TRIFORCE REFERENCE???🤺

[@sheepyisthecutest]

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?

[@RibusPQR]

Scale up by 2 means make it larger. Multiply the height by 2, and multiply the width by 2.

[@sheepyisthecutest]

@@RibusPQRohhhh, but why does that triangle become 3 times larger if scaled up by 2, not 4 times larger?

[@RibusPQR]

@@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.

[@MdDulal-t3g]

/\/\/\ this is the only complexity i need know

[@Hiljaa_]

Fly high Michigun 🕊️/\/\/\

[@santumi2298]

5:20 too much for zblock

[@lordtachanka80]

"ADMIN HE'S DOING IT SIDEWAYS" 🗣🔊🔥🔥🔥

[@12baumarobi]

Is the Sierpinski Triangle considerd to be a type of Mandelbrot?

[@isavenewspapers8890]

Depends on what "a type of Mandelbrot" is.

[@RibusPQR]

The Mandelbrot set produces a fractal. The Sierpinski triangle is also a fractal.

[@thigmotrope]

"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?

[@akkiaddizone6889]

He's talking about dimensions, so ofcourse it's area. How else would we measure the "largeness" of a 2d shape?

[@The_Trident_Master]

How is a definitionally 2D shape roughly 1.6D?

[@strawberrymilk9767]

Rename this video to "how to fall asleep easily tutorial"

[@cocomier]

0:07 “Triforce”

[@Mizai]

pretty cool

[@JuicyJam]

Well, now I know where fallout new vegas: old world blues got their character names from.

[@Ggman854]

I think this broke my brain

[@CMDNPLYZ]

Im in middle school and yet i still get it

[@GlitchPloit]

Bro I imagined a tesseract before I even learned about it????????

[@marcelob.5300]

You're excellent, at least.

[@Yabba_yabba_do]

KLEIN BOTTLE FROM TEAM ROOM 125 AGAIN IS THAT YOU😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱

[@aleksanderagiurre29]

You get a like for all the classic memes, 🥹 so nostalgic

[@nilsgensert5814]

Lots of German names here today.

[@x88.berkay]

nice

[@KaleidoscopeGalaxy]

What would a 3d model of a human look like in 4d with the tesseract thing

[@Dark_Dragon1337]

I think I broke my brain Hjalp

[@jasonromans3016]

6:10 AND BEYOND!

[@Olliee709]

where is geometry dash?

[@Lizz-o4k]

YUME 2KKI?!?!?!?!?!?!? Note: theres a actual world called sierpinski maze

[@jerrylou9285]

Benoit Benoit Benoit Benoit..... Mandelbrot

[@pedrocruz4409]

Lolols I’m a “closet” nerd. I got the feels at about 3:20 after closing concept of the tesseract, then it goes into my favorite: the möbius strip/Klein bottle!! Ufff I got a Maths boner… 😳😬😅

[@SomeTouhouPlayer]

Yooo i just realised illusion ultimate in elemental battlegrounds(a roblox game) is a tesseract

[@TheWingus]

No calabi-yau manifold? That shape doesn’t have enough dimensions to exist in the reality we can observe!

[@Snake-l4g]

lmao me watching these at 3 am

[@Quizlz]

i want more

[@SuperiorStego]

Fractal, fractal, fractal, and ummm fractal

[@scarletevans4474]

3:38 but we clearly can see that it is counterclockwise?? How can these two be indistinguishable??

[@isavenewspapers8890]

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.

[@drakecalvingoingco498]

How about the Menger Sponge?