It might be weird, but, as a Pole, seeing a properly written polish name made me smile
@rogerkearns8094
9 сағат бұрын
Amazing. The moment you said, convert to binary, I saw it - but the effect not continuing forever, I didn't see.
@leif1075
2 сағат бұрын
But for gods sake theres no resson to think of binary..its contrived and out of nowhere rught?? No obewould rver think of that no.matter how smartbyou are
@andrasszabo1570
Сағат бұрын
@@leif1075 But you just saw that someone has thought of that and did convert it to binary. It's not about being smart. It's about having the affinity and the time to play around with numbers.
@Yulenka-
Сағат бұрын
@@leif1075When you're dealing with Fermat numbers, there's all the reason in the world to use binary haha 😅 You can easily derive binary representation of their products since each number only has bits in two positions. I'm sure the pattern will reveal itself very quickly if you continue down this path
@element54_
9 сағат бұрын
My heart broke at 9:48 "until row 33".
@RealCadde
9 сағат бұрын
For a moment, my brain heard "until rule 33" and I was like "don't you mean rule 34?"
@Testgeraeusch
8 сағат бұрын
@@RealCadde "If we mathematicians can write it down, it must exist."
@Sharxee
6 сағат бұрын
And I was thinking Parker for some reason.
@sk8pkl
4 сағат бұрын
33 degrees in free masonry. Not a coincidence.
@ArawnOfAnnwn
4 сағат бұрын
@@Testgeraeusch Calm down there, Max Tegmark.
@jayluck8047
8 сағат бұрын
I love the way she can draw triangles with so much equilaterality.
@johnjeffreys6440
8 сағат бұрын
very isosolece
@jayluck8047
8 сағат бұрын
@@johnjeffreys6440 - did you mean, isolesence? But I got you.
@johnjeffreys6440
8 сағат бұрын
@@jayluck8047 yust a yoke 🤤
@thatonedynamitecuber
10 сағат бұрын
That is the straightest triangle i have ever seen. To clarify I mean by hand not by any other means
@Ayliean
10 сағат бұрын
Pretty much the straightest thing I've ever done.
@bagelnine9
10 сағат бұрын
💀 💀💀 💀 💀 💀💀💀💀 💀 💀 💀💀 💀💀 💀 💀 💀 💀 💀💀💀💀💀💀💀💀
@thatonedynamitecuber
9 сағат бұрын
@@bagelnine9 nice italic sierpinski you got there. SKHULLLLEMOJIIIII
@catmacopter8545
9 сағат бұрын
@@bagelnine9isnt this Wolfram automaton rule 90
@cosmiccake791
9 сағат бұрын
@@thatonedynamitecuberno. No matt rose here...
@MonsieurBiga
6 сағат бұрын
Ayliean : you can timelapse this Brady : don't tell me what to do
@McLir
5 сағат бұрын
Take Pascal's Triangle and dot out all the odd numbers - that also gives a Sierpinski triangle. Seashells can also produce Sierpinski-like patterns.
@TheArizus
9 сағат бұрын
Fun side note, one of the problems on the 2023 British Algorithmic Olympiad was related to finding rows of the Sierpinski triangle when written in binary (similar to this)
@kirillsukhomlin3036
9 сағат бұрын
And if you just take Pascal triangle mod 2, there would be proper infinitely growing Sierpinski triangle.
7 сағат бұрын
Yes. I think it's utterly fascinating that people can avoid seeing that. On the other hand it's something you might have to anticipate to look for.
@happyvirus6590
7 сағат бұрын
5:08 and the length from that point to the edge of the circle is the *golden ratio*
@stickfiftyfive
7 сағат бұрын
and the length from that point to the edge of the circle *is the side length times the Golden ratio*. It's only the Golden ratio itself if the sidelength is 1. Worth clarifying.
@josephpk4878
10 сағат бұрын
Neat to see this geometry again. I just designed a 3d model based on Sierpiński's Triangle, which is a 3D rendered pyramid of the 2D fractal, but I took it a step further and actually modelled the negative space, then printed out these interesting cubes composed of negative and positive 3-sided pyramids - beautiful things, especially when printed with clear materials.
@jellorelic
9 сағат бұрын
Gonna tease us like that and not offer photos? Maaaaaan...
@genghiskhan6688
9 сағат бұрын
yeah I wanna see that too!
@winnablebtw459
6 сағат бұрын
Strictly speaking, at 3:00, you can't pick up lengths with a compass in construction problems. Doing so would allow you to trisect an angle which is famously impossible.
@PaulFisher
4 сағат бұрын
Can’t you transfer a distance between two arbitrary points by constructing a parallelogram with one edge being the distance you want to transfer and the second being the line from the source to the destination point?
@WK-5775
4 сағат бұрын
Please explain: How can one trisect an angle if one is allowed to pick up a length with a compass?
@dingus42
4 сағат бұрын
Wait why not? I thought that was one of the primary functions of the compass, to keep a set distance
@zmaj12321
4 сағат бұрын
I'm pretty sure one of the first proofs in Euclid's Elements is how to transfer a distance without being able to "store" distances on the compass.
@dingus42
4 сағат бұрын
@@zmaj12321 but you literally cannot use a compass for its normal function of drawing an arc without it being able to hold its distance
@kappasphere
10 сағат бұрын
I think an interesting way to generate an image of a sierpinski triangle is to take every pixel coordinate (x, y), and color the pixel if x & y == 0, where "&" is the bitwise and operator.
@bogdan_ostaficiuc
9 сағат бұрын
xd ur imagining it
@ulob
6 сағат бұрын
@@bogdan_ostaficiuche's not
@bogdan_ostaficiuc
6 сағат бұрын
@@ulob how? can you please explain? i'm dumbfounded
@maksymisaiev1828
5 сағат бұрын
@@bogdan_ostaficiuc it won't build exact sierpinski triangle but more like something area of sierpinski triangle. Here is easy python code to check: for i in range (0,40): for j in range(0,40): if i&j == 0: print(0, end="") else: print("_",end="") print("") You can play in numbers and still see that it is building triangles if you play with range numbers.
@maksymisaiev1828
5 сағат бұрын
@@bogdan_ostaficiuc somehow youtube removed my comment. But idea is that bitwise operator gives 1 only in case when x and y share the same binary 1 at that position (in other words, it is binary multiplication). If we look at rows only, first row will be filled with 0, second row will have flappening 0 and 1, well because we compar numbers X1 and X0 and only X1 will return non zero. The third row is also similar. We compare 10 (binary 2) with numbers like X00, X01, X10, X11 and only last 2 numbers will return non zero bitwise response. Same for further rows. But the same picture is for columns, because we just flip x and y coordinates.
@panzer1896
Сағат бұрын
You used to sell the brown papers on eBay…do you still sell the used brown papers? These ones would be pretty cool to get.
@WAMTAT
10 сағат бұрын
Heck yeah, more triangles!!!!!
@johnjeffreys6440
8 сағат бұрын
Isosceles!
@ggb3147
7 сағат бұрын
I really appreciate keeping an acute over the letter N. Greetings from Poland ;)
@xinpingdonohoe3978
7 сағат бұрын
I'm not even offered it. Just ñ.
@Bronzescorpion
8 сағат бұрын
The 15 in binary mistake was somewhat funny considering Ayliean pointed out how close it was to 16. Even without giving it much thought, one could easily conclude that it must then be a row of ones, as all the numbers that are 2^n-1 must follow this pattern, before the next number ie. the number that is a power of two rolls over and becomes a number with a 1 followed by a string of zeroes (equal to n).
@jaymanier7286
7 сағат бұрын
"Timelapse this." "...No." 😄
@ianstopher9111
4 сағат бұрын
It's not the only time we get a finite list of terms. Finite normed division algebras have dimensions 2^n for n=1,2,3,4 and that's it. The general solution in radicals of polynomial equations only applies for powers n=1,2,3,4 and that's it. Fermat primes only for n=0,1,2,3,4. I recall at least in the first two cases they are related, but no-one knows if this also applies to Fermat primes or is just a coincidence.
@waltercisneros9535
6 сағат бұрын
Good to see a old style video, without the animations instead the very draws of our favorites mathematicians
@KarolKarasiewicz
2 сағат бұрын
Wow! Two things: 1. Miss, You're great at drawing, triangles drawn by hand, double wow. 2. So mamy theorems You just mentioned by the way, just like toystory... Triple wow! Thank You, that was great.
@bkuker
8 сағат бұрын
Any chance you'll talk about why there is this relationship between odd constructible polygons and fermat primes? Is it proven, or just coincidental? Would finding another fermat number mean finding more (large) odd constructible polygons? Does the relationship tell us anything about how we can construct them?
@stephenbeck7222
5 сағат бұрын
I believe the connection is proven in Gauss’ seminal work on arithmetic (number theory), in the same book he demonstrated the construction of the 17 sided polygon. I would guess the proof is beyond the scope of this channel.
@tomkerruish2982
5 сағат бұрын
It's too much to fit in this comment (appropriate for something Fermat-related), but it boils down to algebra. A straightedge and compass allow us to add, subtract, multiply, divide, and take square roots. (This is why we can't duplicate the cube since that would require a cube root.) Constructing a polygon with Fermat-prime-many sides can be done by performing a sequence of such computations. For further details, look up 'splitting polynomial'.
@jamesknapp64
Сағат бұрын
Another Roof did a breakdown on the proof this. And yes this is proven that construcble odd factor distrinct odd fermat primes Yes finding another Fermat prime would mean there is an incredably large number of sides constructable polygon. Currently the smallest Fermat number that we don't know if its Prime or Composite is F_33 or 2^2^33 + 1 which is about *2.5 Billion DIGITS* long. However most number theorists believe that there are only 5 Fermat Primes. Yes Being a Fermat Prime tells you how to construct 17, 257 and 65537 sided polygons.
@Sylocat
8 сағат бұрын
I remembered the Fermat Primes from that earlier video series on constructable polygons.
@itioticginger9520
2 сағат бұрын
I noticed at 6:35 that either side of 2^2^X were consistently constructible, as in either side of 2^2=4 meaning 3 and 5, then 2^4=16, and 15, 17 both worked, then 2^8=256, with 255, 257, then 2^16=65536 with 65535 and 65537 working and the final one shown was 2^32-1 This is too convenient to not be a pattern, and no one has ever been wrong when thinking a pattern holds true after a few iterations Edit: I did not expect to be immediately disproven
@jamesknapp64
Сағат бұрын
it has to do with the fact that the product of all up to "nth" Fermat Numbers is 2 less than the next Fermat Number 3 x 5 = 15 = 17 - 2 3 x 5 x 17 = 255 = 257 - 2 3 x 5 x 17 x 257 = 65535 = 65537 - 2 3 x 5 x 17 x 257 x 65537 = 4294967295 = 4274967297 - 2 ; etc Note this another way to show that there are infinately many primes. Since all Fermat Numbers are odd and due to the product relationship above the only common factor could be 2 that means they all have different prime factors. Since we have infinate fermat numbers there are infinately many primes.
@volodyadykun6490
9 сағат бұрын
4:15 I wonder how many people will scream this isn't allowed (in any case, you can find the center with these rules)
@JohnDoe-ti2np
9 сағат бұрын
Alternatively, start with the center.
@esajpsasipes2822
9 сағат бұрын
You can first draw the line, choose any point on it, and draw a circle of any lenght with that point as a center. Then you end up in the starting position without "breaking rules".
@acaryadasa
6 сағат бұрын
I didn't "scream", but yeah I noticed and posted. I suggest drawing the circle, creating a chord, make a perpendicular bisector of the chord to create a diameter, then create a perpendicular bisector of the diameter for the center.
@rmsgrey
6 сағат бұрын
Technically, you needed to identify the center in order to draw the circle in the first place.
@yiannchrst
9 сағат бұрын
damn! I had accidentally discovered this some day while bored at school! I didn't go far enough to see that the pattern brakes though! Cool to see!!
@NatiNugasu
6 сағат бұрын
Ayliean: timelapse this Brady Brady: 👍 *awkward silence*
@marwynthemage
3 сағат бұрын
Interesting. However, my favorite method of constructing the Sierpiński triangle will always be using recursive quad trees: draw the upper right quadrant black, and the other quadrants as the original quad tree (with the upper right quadrants black, recursively). You obviously need to stop rendering after a while, otherwise the entire image will be black :-)
@N7492
7 сағат бұрын
The "chaos game" method also constructs the Sierpinski triangle. Counterintuitive!
@777kangiron777
10 сағат бұрын
Huh, so thats how you triforce.
@ronny332
9 сағат бұрын
My brain smoked a bit while keeping track, but hey, it makes sense 🙂Thanks for showing!
@nate8334
Сағат бұрын
My favorite Fractal. The blood type compatability chart is also a sierpinski triangle. I thought it was interesting that information about us could be Fractal in addition to the physical shapes of things like blood vessels.
@morganconnelly5734
Сағат бұрын
Ah Ayliean coming back again with the amazing content! I love seeing her come back to the channel with her incredible mathematical story telling
@losveratos
40 минут бұрын
Really like her tattoos. She has a good artist.
@AkiSan0
9 сағат бұрын
That Alien looks like an Ayliean!
@Buzk_4
10 сағат бұрын
Patterns fool ya
@Rubrickety
Сағат бұрын
How they fool ya…
@betoneiracromadarebaixada8187
2 сағат бұрын
the Sierpinski triangle really just randomly jumpscares people when it feels like it
@coulie27
2 сағат бұрын
Love the Sierpinski Triangle !
@bigsarge2085
4 сағат бұрын
Fascinating.
@RealCadde
9 сағат бұрын
Start of video. All i know is, the number in the thumbnail is 2 to the power 16, plus 1. Dealing with powers of 2 all my life has damaged me.
@esajpsasipes2822
9 сағат бұрын
someone could say it upgraded you
@timetraveler1234-m3q
8 сағат бұрын
Hey, cool golden ratio tattoo ❤
@Nawakooo0
6 сағат бұрын
It's always a delight to see Ayliean on Numberphile 💜
@machevellian79
4 сағат бұрын
Great video, fascinating! Thanks for sharing.
@David_Last_Name
55 минут бұрын
Lmao. I felt like Brady was refusing to timelapse it just to make a point. 😁
@CHAYITO-ii5pt
8 сағат бұрын
FASCINATING
@hedlund
8 сағат бұрын
Oh, that's brought back memories of CS classes.
@karlwaugh30
59 минут бұрын
Awesome episode. I wonder what properties the binary sieprisnki numbers have
@Ny0s
8 сағат бұрын
This was a really beautiful construction
@NoNeedForRandomNumbers
10 сағат бұрын
Better asmr than asmr
@ex59neo53
8 сағат бұрын
I used to find fractals beautiful ,then I had to study them 30 years ago ,before Internet ,and learned to hate the name Hausdorff :)
@EastBurningRed
7 сағат бұрын
just learned about haushorff in topology, what made you hate him?
@mathphysicsnerd
7 сағат бұрын
_"What do you MEAN represent a set of points with transcendental metric definition?!"_
@David_Last_Name
53 минут бұрын
"This is my favorite way to draw a serpinski triangle." "Great. I need 34 rows." "No."
@allwaysareup
6 сағат бұрын
Came for the maths, but staying for the surprise Ayliean.
@joysanghavi13
4 сағат бұрын
Gauss proved that Fermat's prime numbers as polygon sides are constructible, when he was around 16 years old
@xethlorien4736
9 сағат бұрын
well i wasn't expecting all of that. :D
@janTasita
34 минут бұрын
My favourite place where an unexpected Sierpinski triangle appears is the evolution of a long straight line in Conway's game of life.
@soilnrock1979
21 секунд бұрын
That game got me through school without dying from boredome.
@OneTrueBadShoe
4 сағат бұрын
I absolutely adore Ayliean. I love seeing her visual representations of the beauty of math(s). Bonus: Those fingernails are sweet.
@Trolligi
5 сағат бұрын
9:11 isn’t that basically Pascal’s triangle but in binary (where 0 is even and 1 is odd)
@acaryadasa
6 сағат бұрын
IMO, using the center hole of the compass to find the center of a circle is kind of illegal according to the rules of Euclidian constructability. It doesn't really matter for the sake of this great video explanation, but strictly speaking one should/could construct a circle, draw a chord, construct a perpendicular bisector of the cord to construct a diameter, then create a perpendicular bisector of the diameter to find the center.
@rmsgrey
6 сағат бұрын
How do you construct the circle in the first place without starting with the center?
@JohnPretty1
3 сағат бұрын
Is Ayliean dating Tom Craawford? Match made in heaven.
@PrimordialOracleOfManyWorlds
7 сағат бұрын
in the Sierpinski triangle fractal, i noticed the binary ones made up the upright triangles and the binary zeros made up the inverted triangles. suppose you do the fractal, fill binary ones in the upright triangles and binary zeros in the inverted triangles, then assemble the binary numbers, and convert to base 10 numbers. What numbers do you get?
@WK-5775
4 сағат бұрын
Fill the entire fractal? You'll get nothing at all because there are infinitely many layers of numbers. Instead, if one stops at some level, (and if I understand your question correctly), one will get exactly the products of finitely many different Fermat numbers.
@DeathlyTired
7 сағат бұрын
If you increase the tools to {compass, straight edge, can fold/unfold the paper (plane)} are all polygons then constrctible?
@redblackgaming
10 сағат бұрын
im a simple man. i see a Zelda reference, and i like a video.
@Kyoumadfan
10 сағат бұрын
I'm a simple man. I see a Sierpinski triangle, I get traumatic Signalis flashbacks. :)
@catmacopter8545
9 сағат бұрын
normals can't triforce
@Little-pluto-behind-neptune
9 сағат бұрын
relatable
@citypavement
8 сағат бұрын
Where is the reference? I only see a coincidence. If anything, it's the other way around.
@polyrhythmia
8 сағат бұрын
So there's only a handful of Fermat primes?
@lyrimetacurl0
8 сағат бұрын
I wonder if there's a connection between Fermat Primes and Triperfect Numbers.
@stefansynths
5 сағат бұрын
How do we know a certain polygon isn't constructable? The method we use for all the others doesn't work, sure, but could there be another approach that no one has thought of yet?
@jatsko3113
3 сағат бұрын
Because that specific method - compass and straightedge - is what defines the concept of constructibility.
@bengoodwin2141
10 сағат бұрын
I think it wasn't super clear, is that list the only odd constructable polygons? So there's a finite number of them?
@Milan_Openfeint
9 сағат бұрын
Depends on the number of Fermat primes. They get big fast, so we didn't check many, and I guess there's no proof either way. Statistically, the chance of Fermat number being prime is 1:2^n while size is 2^2^n, so I'd guess maybe there's one more somewhere and that's it.
@bengoodwin2141
9 сағат бұрын
@@Milan_Openfeint the statistical argument doesn't seem very sound. Nothing involved is truly random, but we'd need some kind of breakthrough on prime numbers to understand better. If the series is finite, it would be surprising if there are any more. If it is infinite, then they must just get more and more spaced apart, like the primes.
@Milan_Openfeint
9 сағат бұрын
@@bengoodwin2141 I was thinking like 1/2+1/4+1/8... is finite, you'd only get 2 primes ever if these were the chances, and the chances are actually lower.
@nilesspindrift1934
4 сағат бұрын
And nice inkwork!
@Waffle_6
4 сағат бұрын
not really
@youtou252
6 сағат бұрын
she's the Galadriel of math, convince me otherwise
@MrBmarcika
5 сағат бұрын
what we get is the mod 2 pascal triangle right?
@vapormermaid
Сағат бұрын
As soon as I saw the number in the thumbnail I knew it had something to do with powers of 2.
@keir92
9 сағат бұрын
immediately my brain is wondering why that's exactly one more than 2^16
@corcorandm
9 сағат бұрын
My favorite is pascals triangle color in the odd values
@joannehorn637
6 сағат бұрын
Ahh it's like last week's maths circle! 😉
@bengoodwin2141
10 сағат бұрын
Hey, that's a power of two Edit: one more than
@asheep7797
10 сағат бұрын
Nah, it's one more than a power of two.
@bengoodwin2141
10 сағат бұрын
Right, sorry, meant to say that @@asheep7797
@gummibando
10 сағат бұрын
@@asheep7797 "It's one louder."
@aalhard
3 сағат бұрын
That was neat
@darkhorse1236
8 сағат бұрын
It almost looks like this binary sierpinksy construction is related to Pascal's (binary) triangle
@boskayer
7 сағат бұрын
How do you prove that line is one fifth of the great circle?
@stanimir5F
3 сағат бұрын
13:11 "I am sure you can all see it" Pffff that was the most obvious thing. My first thought was 4294967297 = 641 x 6700417 I mean... if you don't know that, do you even math?
@davidalearmonth
9 сағат бұрын
I guess that Mersenne primes are better. :)
@Mizar88
10 сағат бұрын
my mind is blown
@definitelynotadj
2 сағат бұрын
Can anyone explain how she constructed the midpoint of the line at around 4:50? I feel like i understood how to make the perpendicular line but i couldn't follow the midpoint.
@WK-5775
6 минут бұрын
To construct the midpoint of a line segment, draw (segments of) circles with identical (and sufficiently large) radii around both end points of that line segment. The line through the two intersection points of these circles is the perpendicular bisector of the given line segment, and its intersection with it is the midpoint.
@idrisbalavakos
2 сағат бұрын
I could smell that Sharpie from here
@0dWHOHWb0
7 сағат бұрын
10:07 Patterns fool ya how they fool ya... how they fool ya...
@fiftyyearoldjosephhileman4543
8 сағат бұрын
Another place to find it is in pascals triangle mod 2
@algoboi
2 сағат бұрын
What about the Rule 90 of the Elementary Cellular Automata?
@barutjeh
Сағат бұрын
You won't be surprised who discovered that that Fermat number isn't prime: Euler.
@phyarth8082
4 сағат бұрын
Why Gauss wanted a heptadecagon on his tombstone?
@paaaaaaaaq
6 сағат бұрын
Who draws seven like that? It becomes one so easily.
@Axacqk
8 сағат бұрын
Is that just Pascal's triangle mod 2?
@mathphysicsnerd
7 сағат бұрын
There's a very noticeable audio desynch where the audio is more than a second ahead of the visuals. Is this a KZitem bug or is anyone else experiencing it?
@threepointonefour607
5 сағат бұрын
Works on my machine
@AnimusInvidious
2 сағат бұрын
Shoutout to triforce from Zelda!
@abc123evoturbobonker
4 сағат бұрын
Praise be to the Sphere
@masterimbecile
9 сағат бұрын
Those nails tho…❤❤
@robm1283
9 сағат бұрын
One more than the max number of rows you used to be allowed to use on Excel.
@grLoLaras
6 сағат бұрын
Rule 33 reminder of the parker square
@sk8pkl
4 сағат бұрын
If we can construct a 81 side polygon... How come cant we make a 9 one out of those 81 points!?
@sk8pkl
4 сағат бұрын
Oohh 51. Im sorry. Nevermind.
@DeadJDona
9 сағат бұрын
6:00 but you can build 10 sided polygon now
@hans_bier
9 сағат бұрын
What about a twelve sided polygon?
@Milan_Openfeint
9 сағат бұрын
2*5 and 2^2*3 are both constructible, but also not odd
@pulsefel9210
4 сағат бұрын
that is kinda odd how that triangle refuses to not pop up
@abhijiths5237
4 сағат бұрын
why does the of those numbers binary make the triangle?
@mattwillis3219
9 сағат бұрын
Siripinsji coming out of the tabular render from a freakin binary plot it syper weird
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