It is so interesting how literally everything in math is connected and intertwined. This is really cool because if you don’t quite understand a certain topic or problem you can look at some things you do understand and connect it to what you are having trouble with.
That is the essence of what is known as the Langlands Program, named for Robert Langlands, who essentially created the whole schema...it relates to what are two entirely separate fields in mathematics, harmonic analysis and number theory, and the bridge that links them together.
Everything about this video was great! The visuals were tuned perfectly. The explanation was thorough but succinct. And the enthusiasm of the presenter really brings it all together. Great work!
7:20 Sometimes called the "naive sum" as well. It's also how you construct the Stern-Brocot tree, which enumerates all the positive rational numbers without repeating any.
Yeah. I wish it would've just kept doing numbers and faded out, to create the impression it could go on forever. Stopping makes it look like it fails at that number.
Every time I’m feeling particularly sharp or intelligent, I click on one of these videos and it instantly puts me back in my place 😅 Still, for my limited understanding in advanced math, it was quite interesting.
+jawad mansoor Riemann has done much more besides his hypothesis eg: introduced the term manifolds, riemann integrals, was one of the pioneers of non euclidian geometry (with gauss and some other russian guy), also physics and probably tons of things that im not aware of, he was one of the best mathematicians to ever live
I thought I was the only one who feels this way! I completely agree! There is just so much order and beauty in all the world I don’t know how to take it all in emotionally.
From what I can tell, the world is defined by mathematics and patterns naturally. Math is the translation for the patterns that took the chaos or the earliest known parts of the universe up till as far as we can see. When Mathematics fails is the day I'm lost lol. @@microbuilder
Despite being quite familiar with both the Fibonacci sequence and the Mandelbrot set, my mind was indeed blown. It's even more amazing how "number games" like this can relate to the physical world (at least the one we can perceive).
Test question: In the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, what would be the next number? Answer: So you take a point called c on the complex plane...
@@philpayton8965 It is valid for a joke though. The joke was that he's explaining a very easy concept in the most complex way imaginable using the most casual language possible.
@@nodezsh sorry man it was a bit pedantic of me it just used to be a pet hate of mine, probably fuelled by the fact I had a horrible micro-managing supervisor who started every sentence with "So...". it was a me problem, not a you problem, just ignore me. was a long time ago now anyway.
@@NwoDispatcher the exact opposite is true. Racial purity leads to an amplification of genetic defects over time. The largest gene pool is the healthiest.
@@NwoDispatcher If you truly believe that, don't ever have a DNA testing. You'll find out that you're anything but. Most of your ancestors had more IQ than you and had this idea that screwing around is more fun than raging about a concept that doesn't exist.
Amazing.... please do more videos about the Mandelbrot set. It is the most interesiting mathematical object I know of, in my opinion... Loving your videos!
I wrote a program to generate the Mandelbrot set many years ago and the interesting part was outside the iconic shape - the colours are formed as visual representations of the number of iterations (like a contour map) with the iconic shape merely the set of values that kept on iterating. They were the boring bit! Thank you for showing me what I was missing. I'll have to revisit that code with these extra features to explore!
I used to hate Mathematics. Long story short I developed Arithmophobia since an early age. Until tonight I watched a video about Fibonacci Sequence that introduces me a total new prospective of Math into my life. And for the first time in a long time 33 years more or less (I'm actually 37) I understood Mathematics 😱🤯😍 And after that I found this video is like a double 🤯🤯 sorry I had to is literally mindblowing. I think I can start saying I HAD Arithmophobia. Thank you!
I would 'guess'? it usually happens because of how cumbersome it is to get used to it from such a young age and to basically drill math into your skull by brute force. Maybe, for whatever reason you had a knack for math but never developed the skill to use it because of some bad experience learning it growing up, at a very critical time. But this here, this makes no sense. It's like finding a glitch in the matrix. That's why it's so fun.
When you really uncover it, it is for the same reasons, it is a way to describe or show the nature of the universe and consciousness. Just mathematicians see it in numbers and other people see it more spiritual, but it dissolves into the same sensations one has.
@@pizeblu well.. except that the way mathematicians see it actually makes sense, the way you see it doesn't.. it really have nothing to do with consciousness, the nature of the universe... It's just math As a non matematician myself I love it because it shows how something so complex and weird can come up from such a simple rule.. also because fractals are just weird, counterintuitive and fascinating.. but nobody who understand this even a tiny bit would say that it's connected with things like consciousness or the nature of the universe.. get your feet on the ground mate
@@raffaelepiccini3405 I just don't understand how so many people who had never communicated before are able to "figure out" fractals and how they relate to consciousness on their own.
Great explanation, thanks. By this construction the numerators are also the Fibonacci sequence, two terms behind the denominators. Since the ratio of subsequent terms in the Fibonacci sequences approaches the Golden Ratio as n --> infinity, this means that the ratios that you are considering approach the Reciprocal of the Golden Ratio, Squared. [I think this is right - and surely pretty well known. I just realized it from your presentation.]
Fractal sets and the Fibonacci sequence seem to be a base geography of our world. In this video you seem to show that the Fibonacci sequence auto-magically flows out of the Mandelbrot set. Extremely fascinating, thanks.
Soumil Sahu They don't. They explore a weird shape and say "Wow! Fibonacci sequence relates to it!" How do they find the weird shape to being with? Well, mathematicians make random problems up and hope they lead to something interesting. The Mandelbrot set was a lucky discovery!
Soumil Sahu sometimes it's a Mathematician, sometimes a "non- Mathematician" notices a pattern and wants to know: "does this 'thing' ever stop or does it go on forever?" They may get bored of it, or keep studying it, or even become obsessed with it (especially if their pattern appears to present itself everywhere; it's a constant reminder.)
Mind blown! I think it's so incredibly cool how sites like Numberphile, 3 Blue 1 Brown, and Brilliant are making mathematics fun and inspirational. If you haven't checked out Brilliant's site, I highly recommend it for any curious minds.
We also have the start of the Fibonacci numbers 0,1,1... in the complex plane. The zero in the centre can represent t=0 the moment of now in an individual reference frame. We also have negative 1 and positive 1 with a rotation 2π that is a constant represented by ħ=h/2π. Therefore we even have the start of the Fibonacci numbers 0,1,1,2,3,5,8,13,21... forming spiral on all levels of creation!
at 6:17, the components labeled "1/5" and "4/5" should actually be labeled "1/4" and "3/4". the "1/5" and "4/5" components are the next larger components down elephant valley.
Love these videos. But. Is it just me, every time I watch Dr Holly Krieger, I cannot help thinking about Nicole Kidman. The resemblance, the attitude, the mysterious charm. It is as mesmerizing for me as the Mandelbrot set. Am I alone? Anyone else?
[04:55] Riemann's analytic continuation does something like that curve-around to get its special answers... [07:13] the ratio of Fibonacci numbers→Golden Ratio... so ask what's the sequence of numbers of each, 1 '1', 2 '3's, 4 '5's, but 7 '8's is unsymmetric, Or is it....
Elegant, beautiful illustration of how math describes our universe. And, how most everything is connected. Thanks for the deep sense of awe I'm feeling right no.
*Brady always asks some great questions.* Correct me if im wrong but his qualifications are in engineering and not math(s)? He obviously has some math skills or at the very least a good math instinct, but how good are his actual math skills? Has he done any papers and if he has has he been cited much?
Bengineer8 He is but im pretty sure ive heard before that he has a qualification in engineering. And most journalists dont know anything about maths. It got me wonderin
my mind is blown off right now. I am amazed and mesmerised almost ecstatic to find out the relation between Julia, Mendelbrot and Fibonacci Thanks a lot
seriously- you guys and this channel have had an actual, noticeable effect on my life. i am filled with awe more often than i was before folowing you. i have begub studying math in my spare time and i f*ing love it! i cannot thank everyone associated with this enough.
But why should the Mandelbrot set have tendrils that coincide with their Fibonacci position?! I feel like I was told I’d get an answer and all I got was an amazing new mystery
Just noticed that at 6:07, the hyperbolic component labeled as 1/5 is actually the 1/4 component and the next largest one the right is actually the 1/5 component.
You could draw a straight line from 1/4 to the waist. Since the map is 1/2-sqrt(1/4-z), the straight line from 1/4 is still straight in the circle. And an arc subtends half the angle from a point on the circumference that it does from the center. So the bearing of the point on the circle from 0 is the same as the bearing of the point on the cardioid from 1/4.
I love mathematics because there’s so much hidden beauty and unexpected patters recur in seemingly unrelated systems. One can keep digging deeper and deeper and still find unexpected patterns that’ll keep you busy for a lifetime... if you let it! :)
2:10, they found us Interest in fractals from those sources did cause me to pursue the higher maths and actually learn a bunch of cooler things too in college. I don’t doubt a math focused documentary on visuals would contribute to greater interest in pure math.
So mandelbrot set which is supposed to be the equation that eliminates the electronic interference that is heard when transmitting by wire has nothing to do with the way electricity behaves or anything to do with atomic numbers or weight.
I have said it before and I will say it again. Dr Holly might as well be Amy Adam's more academically inclined sister. If Dr Holly ever makes a discovery worthy of a Hollywood movie, we know who to cast in it.
By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two. Some sources omit the initial 0, instead beginning the sequence with two 1s
In fact, there is an often-forgotten version of the Fibonacci sequence made up entirely of 0's. You start with 0 + 0 = 0, then you add the last two numbers together to get 0 + 0 = 0, then again, 0 + 0 = 0, and so on. You end up with a series (0, 0, 0, 0, 0, 0, 0, 0, 0...) that looks boring but is actually found all the time in nature. For example, once somebody ate all my cookies, so I had 0 cookies, but the weird thing is, the next day I still had 0 cookies, and then the next day 0, and then 0... cool, right? Who says maths has no application to real life?
This is amazing. I'm sure that somebody can show that this connection is absolutely natural. But it definitely is not obvious and that makes it so beautiful and funny. Thumbs up!
Holy $^@=!!! I'm very much a humanities individual.. waited until my senior year to take college algebra, etc. I was watching this really cool show on HGTV where this treehouse expert built a treehouse for these Montessori students, and he included the Fibonacci sequence in this awesome bench he made near the reading nook up in this treehouse..I discovered that the Fibonacci sequence is ALL OVER nature etc. in the shape of leaves, etc. I discovered the Mandelbrot Set quite by accident, as, for some strange reason, I've grown really attracted to math... so that I can understand it. If the Fibonacci Sequence is all over nature... where else is it??? The exact idea of the Mandelbrot Set did NOT occur to me, but my small, feeble noodle is TOTALLY in overdrive as I watch this..Love your videos, Dr. Krieger!!
Wow, my mind is blown!!!!!! I had no idea where mandlebrots even came from and cant believe my favourite subject of complex numbers are hidden in them!
The Mandelbrot set looks like it's rich with features when you zoom in on it this way 8:34 I've never seen it that way before. I just thought it looked the same way all the way down.
Final Spartan I meant what I said and I said what I meant. Trace back the rotations to 0% and you'll find your Fib value still one in the norm. So I suggest, in jest, indeterminant form. :D
'B.' in Benoit B. Mandelbrot's name stands for Benoit B. Mandelbrot
raspi1983 Old joke.
Wait, so what does the second 'B.' stand for? :-)
the second "B" stands for Benoit B. Mandelbrot
observerms
ua-cam.com/video/laHl-aFZUJI/v-deo.html The EDM in EDM Detection Mode stands for EDM Detection Mode.
I saw what you did there :)
It is so interesting how literally everything in math is connected and intertwined. This is really cool because if you don’t quite understand a certain topic or problem you can look at some things you do understand and connect it to what you are having trouble with.
That is the essence of what is known as the Langlands Program, named for Robert Langlands, who essentially created the whole schema...it relates to what are two entirely separate fields in mathematics, harmonic analysis and number theory, and the bridge that links them together.
EXACTLY! I also find fascinating how this figure is encoded in math and anywhere you go in the universe, the figure is still the same!
This video about Fibonacci numbers was as good as the last two combined!
not going to like because likes are at a fibonacci number
Underrated comment
Everything about this video was great! The visuals were tuned perfectly. The explanation was thorough but succinct. And the enthusiasm of the presenter really brings it all together. Great work!
7:20 Sometimes called the "naive sum" as well. It's also how you construct the Stern-Brocot tree, which enumerates all the positive rational numbers without repeating any.
Kudos to the animator. The scuttling mandelbug was a delight.
David Wiley The sound and the animation cracked me up.
No it was in fact the very opposite of a delight .
Yusss. I came down here to find the comments about it. That made me so happy. 4:24
It's a Miyazaki Mandelbug!
It's a Scuttlebug jamboree.
Two of my favorite concepts in one video. Today is looking like a good day.
Women and Paper?
Audio and Visual Stimulation
fibonacci and grills
markers and brown paper?
Fibonacci Numbers make it 3!
I lost her at 1+1 is 2.
Nathan Thames
That's kind of Numberphile's comment section in a nutshell
"PewDiePie's personal account" kek
Muhammad Mamoon 2+2 is 4, -1 is 3, quick maths
Well, you have the basics down.
Who thinks that’s funny?!!
Wow mind *BLOWN,* this is amazing
Who else just wanted it to keep on zooming in until infinity? [8:41]
You mean an infinitely long UA-cam video? No thanks.
Yeah. I wish it would've just kept doing numbers and faded out, to create the impression it could go on forever. Stopping makes it look like it fails at that number.
Nobody with half a brain thought it "failed" at that number
Here's one of the deepest zooms fellow Mandelbrot enthusiast ua-cam.com/video/0jGaio87u3A/v-deo.html
+
I love the little slot machine illustrating the iteration and the ping sound it makes. That's the way Mandelbrot sets should be computed.
Holly's laugh touches my cardioid :P
oof you better motice (this is not a typo)
Simp
@@dxrpz1669 incel
Incel
Every time I’m feeling particularly sharp or intelligent, I click on one of these videos and it instantly puts me back in my place 😅
Still, for my limited understanding in advanced math, it was quite interesting.
Riemann: My zeta function hides primes
Mandelbrot: My set hides Fibonacci
Ramanujan: -1/12 __
PlayTheMind riemann is way above mandlebort and ramanujan
Sharklops Haha.. nice one
What do you mean wrong, the limit of the nonconvergent sum of 1+2+3+4+5...+n where n=Alephnull-1 Does end up as -1*(1/12)
jawad mansoor YOU CANT JUST MAKE THAT CLAIM AND LEAVE
+jawad mansoor Riemann has done much more besides his hypothesis eg: introduced the term manifolds, riemann integrals, was one of the pioneers of non euclidian geometry (with gauss and some other russian guy), also physics and probably tons of things that im not aware of, he was one of the best mathematicians to ever live
It's pretty cool, that these two things have such a connection
But not terribly surprising, Fibonacci numbers pop up just about anywhere.
Nukestarmaster
I
do
not
think
so_about
these_numbers!
Fibonacci_numbers_are
definitely_not_anywhere,_you_idiot
it leads me to speculate that *everything* is, in fact, encoded in the Mandelbrot Set.
fukin druggos
@@albertb8999 I see what you did there, incorporating the sequence into your sentences.
Well played, Albert B, well played.
She's so cool!
And cute!
@@fantasick8880 😍
Angelic.
and preeeeeety!!
This is one of the very best layouts of this fractal relationship with the Fibonacci sequence
The beauty of this math overwhelms me with emotion. Perhaps that seems strange, but the beauty of how all this works out makes me want to cry.
I thought I was the only one who feels this way! I completely agree! There is just so much order and beauty in all the world I don’t know how to take it all in emotionally.
*The reason I love mathematics*
"Is the universe a fractal that can be calculated in equation?
Is it Fibonaccis perfect golden spiral or is it just my imagination?"
From what I can tell, the world is defined by mathematics and patterns naturally. Math is the translation for the patterns that took the chaos or the earliest known parts of the universe up till as far as we can see. When Mathematics fails is the day I'm lost lol. @@microbuilder
Beautiful Ladies teaching us?🤫
Peng broads?
Despite being quite familiar with both the Fibonacci sequence and the Mandelbrot set, my mind was indeed blown. It's even more amazing how "number games" like this can relate to the physical world (at least the one we can perceive).
I would tell a joke about Fibonacci.
But it's as bad as the two previous jokes you heard combined.
Cyberspine #groan
You shouldn't start with two zeros... :D
0 + 0 = 0
Cyberspine and where does your joke end? If you are going to be funny, at least have an educated punch line to go with it. Those are hilarious
@@bradleylomas7525 HAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHA AHBAHSBHABSH HAHAHAHAHAHAH
Thanks for the incredibly fascinating video. The more I learn about the Mandelbrot set, the more I like it. Dr. Krieger is excellent as always.
Test question: In the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, what would be the next number?
Answer: So you take a point called c on the complex plane...
So is not a valid word with which to start a sentence except in very rare circumstances, for example explaining the purpose of doing something.
@@philpayton8965 It is valid for a joke though. The joke was that he's explaining a very easy concept in the most complex way imaginable using the most casual language possible.
@@nodezsh sorry man it was a bit pedantic of me it just used to be a pet hate of mine, probably fuelled by the fact I had a horrible micro-managing supervisor who started every sentence with "So...".
it was a me problem, not a you problem, just ignore me. was a long time ago now anyway.
A new video of Dr. Holly, aka she who commands my heart, mind and soul. This is a great week indeed.
i was obsessed with the fibonacci sequence when i was little and i'm obsessed with the mandelbrot set now, seems like a perfect video for me lol
These inserted animations make all the difference - great thinking mr Haran!
Glad you liked them - they were done by Pete McPartlan
What I've learnt is no matter how many Mandelbrot videos I watch, I still have no idea how it's made. Only that it looks amazing on a projector!
Intelligence makes people more beautiful
Racial purity makes humanity beautiful
@AccuracyIsGone I agree... come go after the heretic of the g4y empire
@@NwoDispatcher the exact opposite is true. Racial purity leads to an amplification of genetic defects over time. The largest gene pool is the healthiest.
@@NwoDispatcher If you truly believe that, don't ever have a DNA testing. You'll find out that you're anything but.
Most of your ancestors had more IQ than you and had this idea that screwing around is more fun than raging about a concept that doesn't exist.
@@NwoDispatcher come on, evolution needs tension. How about you leave it be when it's so minor
Numberphile really nails it by explaining math in an entertaining and lighthearted way.
Next: how to cut a cake via prime numbers, Graham's number created by Conway's game of life, and the fractal dimensions inside Parker squares.
Do you want existential crisises? Anyway, cool subjects!
…while doing a dice trick represented by playing cards printed on the surface of a Klein bottle.
Everytime Holly laughs a furry baby kitten is born.
Amazing.... please do more videos about the Mandelbrot set. It is the most interesiting mathematical object I know of, in my opinion...
Loving your videos!
I wrote a program to generate the Mandelbrot set many years ago and the interesting part was outside the iconic shape - the colours are formed as visual representations of the number of iterations (like a contour map) with the iconic shape merely the set of values that kept on iterating. They were the boring bit! Thank you for showing me what I was missing. I'll have to revisit that code with these extra features to explore!
I used to hate Mathematics. Long story short I developed Arithmophobia since an early age. Until tonight I watched a video about Fibonacci Sequence that introduces me a total new prospective of Math into my life. And for the first time in a long time 33 years more or less (I'm actually 37) I understood Mathematics 😱🤯😍 And after that I found this video is like a double 🤯🤯 sorry I had to is literally mindblowing. I think I can start saying I HAD Arithmophobia. Thank you!
I would 'guess'? it usually happens because of how cumbersome it is to get used to it from such a young age and to basically drill math into your skull by brute force.
Maybe, for whatever reason you had a knack for math but never developed the skill to use it because of some bad experience learning it growing up, at a very critical time. But this here, this makes no sense. It's like finding a glitch in the matrix. That's why it's so fun.
oh yes, Holly Krieger
IBMicroapple There needs to be more Dr. Krieger videos.
I think I have a new crush.
@TheronQRamacharaka I'm guessing it's a perfect match. But something tells me the carpet is gone.
IBMicroapple simp
@@takotaw8453 still a virgin
Glad to see her again!
2:12 even non-mathematicians love this for different reasons xD
Shubham Shinde
Yes it is fun. They kind of look down on us as children.
When you really uncover it, it is for the same reasons, it is a way to describe or show the nature of the universe and consciousness. Just mathematicians see it in numbers and other people see it more spiritual, but it dissolves into the same sensations one has.
@@pizeblu well.. except that the way mathematicians see it actually makes sense, the way you see it doesn't.. it really have nothing to do with consciousness, the nature of the universe... It's just math
As a non matematician myself I love it because it shows how something so complex and weird can come up from such a simple rule.. also because fractals are just weird, counterintuitive and fascinating.. but nobody who understand this even a tiny bit would say that it's connected with things like consciousness or the nature of the universe.. get your feet on the ground mate
@@raffaelepiccini3405 I just don't understand how so many people who had never communicated before are able to "figure out" fractals and how they relate to consciousness on their own.
2:13 made me smile
The Mandelbrot Set will never be as beautiful as Dr. Holly.
I disagree :Ü™
Mandelbrot set is amazing. It's incredible how quite simple definition leads to infinitively complex structure.
Great explanation, thanks. By this construction the numerators are also the Fibonacci sequence, two terms behind the denominators. Since the ratio of subsequent terms in the Fibonacci sequences approaches the Golden Ratio as n --> infinity, this means that the ratios that you are considering approach the Reciprocal of the Golden Ratio, Squared. [I think this is right - and surely pretty well known. I just realized it from your presentation.]
The picture of the freshman sum they showed was wrong. Is it a Parker freshman sum? 🤔
I was searching for the comment pointing that out, wonder who misunderstood the freshman sum joke
For some reason they showed the multiplicative
*NEW RECORD* - Congratulations Numberphille. Only 12 seconds to completely confuse every atom in my head.
I await your next video.
I can see that nail and gear flag in the background :)
and a Reunion swamp hen!
This channel never ceases to amaze me.
So I guess it's time to fall in love again...
Mobin92 simp
Simp
Simp
Hi
Ha ha ha - he may be a math geek and be on about that !
Not only is the maths in this really cool, but I also loved the cheeky Nail and Gear hiding in the background :)
4:30 theory of T H I C C N E S S
Fractal sets and the Fibonacci sequence seem to be a base geography of our world. In this video you seem to show that the Fibonacci sequence auto-magically flows out of the Mandelbrot set. Extremely fascinating, thanks.
Math is amazing. Who even discovers this stuff?!
Soumil Sahu mathematicians
+Cellkist obviously, but who goes out of their way to say, "today im gonna pull out the Fibonacci sequence out of a weird shape"
Soumil Sahu They don't. They explore a weird shape and say "Wow! Fibonacci sequence relates to it!"
How do they find the weird shape to being with? Well, mathematicians make random problems up and hope they lead to something interesting. The Mandelbrot set was a lucky discovery!
Soumil Sahu sometimes it's a Mathematician, sometimes a "non- Mathematician" notices a pattern and wants to know: "does this 'thing' ever stop or does it go on forever?" They may get bored of it, or keep studying it, or even become obsessed with it (especially if their pattern appears to present itself everywhere; it's a constant reminder.)
People who think it's amazing
Mind blown! I think it's so incredibly cool how sites like Numberphile, 3 Blue 1 Brown, and Brilliant are making mathematics fun and inspirational. If you haven't checked out Brilliant's site, I highly recommend it for any curious minds.
she is BACK
Can you imagine how blown away Fibonacci would be if he could see the Mandelbrot set...
0:45 What's up with the up-arrow-paper appearing in all the videos lately? Oh, and 7:32 should be 1/2 + 1/2 = 2/4.
MasterHigure, That's funny, do more arithmetic.
Freshman Sum Freshman Sum!
Baaahahahahahahahahajahahahahahahajajaja
I mean, you messed up a Freshman sum. That's basically a Parker freshman sum right there.
Yeah, you said that Freshman Sum was in a certain way and showed it differently.
We also have the start of the Fibonacci numbers 0,1,1... in the complex plane. The zero in the centre can represent t=0 the moment of now in an individual reference frame. We also have negative 1 and positive 1 with a rotation 2π that is a constant represented by ħ=h/2π. Therefore we even have the start of the Fibonacci numbers 0,1,1,2,3,5,8,13,21... forming spiral on all levels of creation!
Person: "what the heck happened to your mind?!"
Me: "oh dont worry it was just blown"
Fabulous presentation, thank you for the intellectual depth charge -> factual recognition time bomb of realization.
SHE BLINDED ME WITH SCIENCE!!
This is math, you’re even blinded by vocabulary.
Thomas Dolby......luv science
at 6:17, the components labeled "1/5" and "4/5" should actually be labeled "1/4" and "3/4". the "1/5" and "4/5" components are the next larger components down elephant valley.
Love you Dr Holly!
Love these videos. But. Is it just me, every time I watch Dr Holly Krieger, I cannot help thinking about Nicole Kidman. The resemblance, the attitude, the mysterious charm. It is as mesmerizing for me as the Mandelbrot set. Am I alone? Anyone else?
Because we keep going between two fractions, does the fraction approach something?
trekky0623 I believe it approaches 1 - 1/φ, where φ is the golden ratio (1 + sqrt(5))/2.
So when do we get a zoom in at the golden ratio?
Approaches 1
zoom in infinitely and you will get the golden ratio.
[04:55] Riemann's analytic continuation does something like that curve-around to get its special answers... [07:13] the ratio of Fibonacci numbers→Golden Ratio... so ask what's the sequence of numbers of each, 1 '1', 2 '3's, 4 '5's, but 7 '8's is unsymmetric, Or is it....
ik i dont understand what they are saying on numberphile but i still like to watch the videos
The best Mandelbrot tour guide EVER!
Dr. Haran really makes great questions
He is not a doctor.
Wise Guy he is indeed
I love how Brady has the Nail & Gear in the background.
when shits stormy outside but a new numberphile video is up
Elegant, beautiful illustration of how math describes our universe. And, how most everything is connected. Thanks for the deep sense of awe I'm feeling right no.
*Brady always asks some great questions.* Correct me if im wrong but his qualifications are in engineering and not math(s)? He obviously has some math skills or at the very least a good math instinct, but how good are his actual math skills? Has he done any papers and if he has has he been cited much?
he is a journalist
Bengineer8 He is but im pretty sure ive heard before that he has a qualification in engineering. And most journalists dont know anything about maths. It got me wonderin
my mind is blown off right now.
I am amazed and mesmerised
almost ecstatic to find out the relation between Julia, Mendelbrot and Fibonacci
Thanks a lot
She has one of the cutest laughs
Your a creepy dude
Michael Eaves what? Why?
@@dmytronadtochyi9116 haha incel
seriously- you guys and this channel have had an actual, noticeable effect on my life. i am filled with awe more often than i was before folowing you. i have begub studying math in my spare time and i f*ing love it!
i cannot thank everyone associated with this enough.
But why should the Mandelbrot set have tendrils that coincide with their Fibonacci position?! I feel like I was told I’d get an answer and all I got was an amazing new mystery
Rick Weber Isn't that all what answers are?
That explanation just made me more confused. The explanation seems like an even crazier way for numbers to function.
I enjoy Dr Holly's videos. Brillance is when you can solve known math, Genius is when you discover/invent NEW math,
You had me at Fibona..wow those eyes...
Just noticed that at 6:07, the hyperbolic component labeled as 1/5 is actually the 1/4 component and the next largest one the right is actually the 1/5 component.
Gotta love that 9:59
Dr Holly Krieger and the Mandelbrot Set, name a more iconic duo... I'll wait.
Ah, Dr. Krieger! Must be my lucky day!
@TheronQRamacharaka jeez chill haha
We should all be so lucky.
You could draw a straight line from 1/4 to the waist. Since the map is 1/2-sqrt(1/4-z), the straight line from 1/4 is still straight in the circle. And an arc subtends half the angle from a point on the circumference that it does from the center. So the bearing of the point on the circle from 0 is the same as the bearing of the point on the cardioid from 1/4.
Math never ceases to amaze me.
I love mathematics because there’s so much hidden beauty and unexpected patters recur in seemingly unrelated systems. One can keep digging deeper and deeper and still find unexpected patterns that’ll keep you busy for a lifetime... if you let it! :)
I'm watching this on high, sounds awesome
2:10, they found us
Interest in fractals from those sources did cause me to pursue the higher maths and actually learn a bunch of cooler things too in college. I don’t doubt a math focused documentary on visuals would contribute to greater interest in pure math.
Exactly 10 minutes...
😍 it's beautiful
Jan Sanono It's actually 9:59
You are probably a physicist
If you take the frame count of 14975 @ 25 fps it's exactly 9:59, no .something, so John Ox is correct.
10minutes is the threshhold for more money/view
And the video isn't bad either.
So mandelbrot set which is supposed to be the equation that eliminates the electronic interference that is heard when transmitting by wire has nothing to do with the way electricity behaves or anything to do with atomic numbers or weight.
I could listen/watch Dr Holly Krieger all day.
listen? yeah right
Hey, thanks as always
I have said it before and I will say it again. Dr Holly might as well be Amy Adam's more academically inclined sister. If Dr Holly ever makes a discovery worthy of a Hollywood movie, we know who to cast in it.
But does 0 count as a fibonacci number?
By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two. Some sources omit the initial 0, instead beginning the sequence with two 1s
there are 2 definitions,one says that F1=1 F2=1,the other says that F0=0 F1=1 F2=1.But i don't think that F0 makes any impact,so it's usually omitted
In fact, there is an often-forgotten version of the Fibonacci sequence made up entirely of 0's. You start with 0 + 0 = 0, then you add the last two numbers together to get 0 + 0 = 0, then again, 0 + 0 = 0, and so on. You end up with a series (0, 0, 0, 0, 0, 0, 0, 0, 0...) that looks boring but is actually found all the time in nature. For example, once somebody ate all my cookies, so I had 0 cookies, but the weird thing is, the next day I still had 0 cookies, and then the next day 0, and then 0... cool, right? Who says maths has no application to real life?
Madder Sky; F0 = the inertial plane, before perturbation.
This is amazing. I'm sure that somebody can show that this connection is absolutely natural. But it definitely is not obvious and that makes it so beautiful and funny. Thumbs up!
Holy $^@=!!! I'm very much a humanities individual.. waited until my senior year to take college algebra, etc. I was watching this really cool show on HGTV where this treehouse expert built a treehouse for these Montessori students, and he included the Fibonacci sequence in this awesome bench he made near the reading nook up in this treehouse..I discovered that the Fibonacci sequence is ALL OVER nature etc. in the shape of leaves, etc. I discovered the Mandelbrot Set quite by accident, as, for some strange reason, I've grown really attracted to math... so that I can understand it. If the Fibonacci Sequence is all over nature... where else is it??? The exact idea of the Mandelbrot Set did NOT occur to me, but my small, feeble noodle is TOTALLY in overdrive as I watch this..Love your videos, Dr. Krieger!!
Judy Carter Holy Krieger
Wow, my mind is blown!!!!!! I had no idea where mandlebrots even came from and cant believe my favourite subject of complex numbers are hidden in them!
Nail and Gear!
Wow, this was the best video from you for a while
This was very interesting and well presented 👍🏻
I like how all these videos are done in sharpie on cardboard. It's a nice touch. Very satisfying, but I wonder how often they mess up?
2:40 what? i thought this was "Numberphile" and not "lets-not-get-into-that-phile"
s0mar
That's Numberwang!
Because numberphile has other videos on that topic, as do other UA-cam creators. And also because it's not the topic of this video.
Yeah, this video should've totally been a 4 hour lecture.
It's still a channel for casual viewers. It can't replace a degree in mathematics.
The Mandelbrot set looks like it's rich with features when you zoom in on it this way 8:34 I've never seen it that way before. I just thought it looked the same way all the way down.
So, where is zero component?
Krowwweee presumably 0/0ths the way 'round the circle. :)
NWRIBronco6 0/0ths is indeterminate form. I doesn't exists as any number or exists as all numbers. I think you mean 0th way around
Final Spartan I meant what I said and I said what I meant. Trace back the rotations to 0% and you'll find your Fib value still one in the norm. So I suggest, in jest, indeterminant form. :D
You see where things aren't, in the Mandelbrot set? It's right there.
0 is not included in the fibonacci sequence