Pi and the Mandelbrot Set - Numberphile

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Numberphile

Numberphile

8 жыл бұрын

This video features Dr Holly Krieger. More videos with Holly Krieger: bit.ly/HollyKrieger
More links & stuff in full description below ↓↓↓
Extra footage from this interview: • Pi and Mandelbrot (ext...
Thanks to Audible --- www.audible.com/numberphile
Since this was filmed, Holly has become a mathematics Lecturer at the University of Cambridge and the Corfield Fellow at Murray Edwards College.
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Пікірлер: 1 000
@jacoboking36
@jacoboking36 3 жыл бұрын
Pi is like that one uncle who just shows up out of nowhere in every scenario
@DirtBikes_MathGarden
@DirtBikes_MathGarden 2 жыл бұрын
nah that's e
@robertakerman3570
@robertakerman3570 2 жыл бұрын
I like Pie-must B someone's Unc.
@kasturylbs5905
@kasturylbs5905 2 жыл бұрын
Lur minta 4d buat malam ini. Hkong
@leeyenherngcalebpeircess6121
@leeyenherngcalebpeircess6121 Жыл бұрын
No it's more like he's nnever invite becaise he always turns up anyways
@brad1ey50
@brad1ey50 Жыл бұрын
e is the other uncle
@HansenSWE
@HansenSWE 8 жыл бұрын
"This video features Dr Holly Krieger." Viral.
@HansenSWE
@HansenSWE 8 жыл бұрын
So wait. Math geniuses, gather around, gather around. So if the number is within the mandelbrot set... if we do that calculation she was doing, will we never get a number larger than two? Regardless of how many times to do it? We just roll around inside that weird picture? Is that the whole point of the mandelbrot set? That we can do an infinite number of calculations without going higher than two? That sounds incredibly useful, but I just can't see how right now. It's like a safety mechanism for something. If I'm somewhat correct, how it this applied? It's very interesting
@bodhifyer
@bodhifyer 8 жыл бұрын
+Herr Hansen im no math genius at all, quite the opposite really. If I had to guess at the usefulness of the mandelbrot set, it would be to get a better understanding of the fundamental math of the shape of an abstract object. If it can be mathed then such an object could be a physical object somewhere in the universe which we could study from here on earth
@HansenSWE
@HansenSWE 8 жыл бұрын
Terrence Zimmermann Wow... I feel like less of a man than I did 5 minutes ago. Please tell me this was university physics and it's ok to not understand it perfectly.
@HansenSWE
@HansenSWE 8 жыл бұрын
***** Your comment was marked as spam and I had to restore it, brother.
@HansenSWE
@HansenSWE 8 жыл бұрын
Terrence Zimmermann Wait, you're talking about when magnetic fields change? Like from ferro to para? I've seen some stuff about that. Wish I paid more attention.
@panda4247
@panda4247 5 жыл бұрын
Holly: "...maybe the least efficient way possible to approximate pi" Matt Parker: "challenge accepted"
@aaronleperspicace1704
@aaronleperspicace1704 4 жыл бұрын
😂😂😂😂😂
@Thomas_Bergel
@Thomas_Bergel 4 жыл бұрын
panda4247 Matt would probably get a method that is almost as complex... a classic parker square
@gormster
@gormster 4 жыл бұрын
3blue1brown: hold my sliding square
@Triantalex
@Triantalex 9 ай бұрын
??
@KonJamo
@KonJamo 8 жыл бұрын
You english speakers might not realize this: Mandelbrot actually means Almond bread...to use Almond bread to approximate Pi is a very funny approach to baking :D a fan from Berlin, GErmany
@PoweDiePie
@PoweDiePie 7 жыл бұрын
Wow.
@thesentientneuron6550
@thesentientneuron6550 6 жыл бұрын
I do know a bit of german, but it did not occur to me
@Pterry23real
@Pterry23real 5 жыл бұрын
But Mandelbrot is just a surname. But another relative unusally name for the mandelbrot set is Apfelmännchen (little apple man), so you could bake pi with little apples ;)
@earomc
@earomc 5 жыл бұрын
sockington1 what do you mean
@mackan2277
@mackan2277 4 жыл бұрын
maybe make some pie out of almond bread :D
@Nilguiri
@Nilguiri 8 жыл бұрын
It's amazing how pi can just pop out when you are least expecting it, innit?
@aaaab384
@aaaab384 6 жыл бұрын
It would be if it did. But since it has a simple definition, of course it pops up everywhere. I always expect it to pop up, and I am not amazed when it happens.
@Gray-beard
@Gray-beard 6 жыл бұрын
Lol. Try 'cross training your brain' with Gematria, Pi is everywhere...
@IVAN-wj4td
@IVAN-wj4td 6 жыл бұрын
It's like the Spanish Inquisition!
@soso3792
@soso3792 6 жыл бұрын
Are you surPised? ...sorry my puns are horrible *leaves*
@N3bu14Gr4y
@N3bu14Gr4y 5 жыл бұрын
Just like Garfield on a Monday!
@rivaldobox
@rivaldobox 8 жыл бұрын
I really like how energetic she is when explaining things, it makes the video even better.
@yttrv8430
@yttrv8430 4 жыл бұрын
Dr Krieger: Well, I've already used "c", whatever, I'm gonna call this point "c", too. Gottsta love people like this.
@kevnar
@kevnar 5 жыл бұрын
I created a game using vectors when I was young. I made a point in the center of a sheet of graph paper and called that "The Sun". It was basically just a source of gravity. Then I chose some other random point on the page and called that a "meteor". Then I assigned some arbitrary motion vector to the meteor. -2x,1y or whatever. Then I'd move the meteor by that much. But every round, you have to adjust the motion vector, + 1 if you're x is negative, or -1 if your x is positive, and likewise with Y. The point was to simulate gravitation toward the sun and get the meteor into an orbit. I tried all day to figure out numbers that would make the meteor go into a perfect circle, or at least an ellipse, but all I ever got were these strange, repeating wiggling patterns. Years later, I saw a video on Lissajou curves. Here I thought those curves in my oribits were a failure to create a circle, but all along they were something people were trying to find in and of themselves. It's amazing what curiosity and boredom produces.
@qwertyTRiG
@qwertyTRiG 4 жыл бұрын
That's impressive!
@ColHogan-bu2xq
@ColHogan-bu2xq 3 жыл бұрын
Problem is : do we really know what the very "nature" of gravitation is ?
@SOCAKRKA
@SOCAKRKA 8 жыл бұрын
but what is the connection? i would really love this to be expalined in depth. othervise very nice video
@numberphile
@numberphile 8 жыл бұрын
+SOCAKRKA there's a link to more on Numberphile2 - see the video description
@SOCAKRKA
@SOCAKRKA 8 жыл бұрын
+Numberphile thanks, i guess i have to pay more attention before posting comments :)
@axiezimmah
@axiezimmah 8 жыл бұрын
+Numberphile that link isn't working though
@axiezimmah
@axiezimmah 8 жыл бұрын
***** virus?
@ccosborn2000
@ccosborn2000 8 жыл бұрын
I don't think anyone knows why the iteration counter will stop (ounce the function produces an answer greater than 2), and then recording that counter, why those digits are PI. Incredible. When you find out why let me know.
@Christian-Rankin
@Christian-Rankin 8 жыл бұрын
*insert filthy comment about obvious pretty women*
@Peteminator
@Peteminator 8 жыл бұрын
+Christian Rankin The maths is not the only beautiful thing in the video.
@Holexification
@Holexification 8 жыл бұрын
+Christian Rankin I though pretty smart women were imaginary, turns out they are real! Gosh this is complex...
@asdmla8777
@asdmla8777 8 жыл бұрын
+Christian Rankin 3:20
@gumenski
@gumenski 8 жыл бұрын
+Christian Rankin Annnd you were the only one to be that guy. Nice one
@TheLuxma
@TheLuxma 8 жыл бұрын
+Aelianus Lucius Decimus +1
@uritibon17
@uritibon17 5 жыл бұрын
"This is something that's like, totally natural to be interested in" - Dr Krieger
@totallyunmotivated
@totallyunmotivated 8 жыл бұрын
That woma- I mean that handwriting is perfect. Very legible.
@zh84
@zh84 8 жыл бұрын
Well, that is extraordinary. I never would have guessed. Will you post a link to an explanation of why this works?
@numberphile
@numberphile 8 жыл бұрын
+zh84 see link to extra footage in the video description
@Epoch11
@Epoch11 8 жыл бұрын
+zh84 I totally agree with you. This seems like witchcraft to me and I would love to see a detailed explanation about why this happens as it does.
@strangelyjamesly4078
@strangelyjamesly4078 8 жыл бұрын
+zh84 It happens because it does. The lower the value of epsilon the closer to the value of Pi the number of steps required to "bust". Coincidence.
@NotaWalrus1
@NotaWalrus1 8 жыл бұрын
+Strangely Jamesly Do you seriously believe that's a coincidence?
@moonanddarkness
@moonanddarkness 8 жыл бұрын
+Strangely Jamesly Damn dude, your teachers must have been really bad. "It happens because it does." It's the most mediocre answer one can get." And I'm surprised you actually believe this is a coincidence, specially when there is a link in the description to a video that explains that this number is actually Pi, not just a coincidence, that if you keep iterating to infinity you will get Pi and it also explains why.
@pokestep
@pokestep 8 жыл бұрын
Wow these videos about the Mandelbrot set were great, I finally know what it actually is! Holly Krieger is also great, I loved to see her explain it all, thanks for that. I sure hope to see more in the future!
@theulair
@theulair 8 жыл бұрын
This is the first simple explanation of the Mandelbrot Set and how it is drawn that i have seen in my life. Thank you!
@tilmohnen6521
@tilmohnen6521 5 жыл бұрын
Watch 3Blue1Brown's Video of aproximating pi with block collisions. There are also powers of 100 involved... I wonder whether its actually the same method in disguise...
@BigBoatDeluxe
@BigBoatDeluxe 8 жыл бұрын
Amy Adams discussing mathematics. I could get used to this.
@ESL1984
@ESL1984 5 жыл бұрын
*getting arrival flashbacks*
@carlos77121
@carlos77121 4 жыл бұрын
Underrated comment here.
@Triantalex
@Triantalex 9 ай бұрын
??
@BigBoatDeluxe
@BigBoatDeluxe 9 ай бұрын
@@Triantalex Dr. Krieger kinda favors actress Amy Adams. Kinda sorta.
@Quantiad
@Quantiad 8 жыл бұрын
Holly Krieger + Hannah Fry = Heaven
@littlemikey46
@littlemikey46 8 жыл бұрын
+iSquared My two favourite female mathematicians :D
@Quantiad
@Quantiad 8 жыл бұрын
+Jeremy Watts Haha! Mate, that's harsh but hilarious. Both geniuses and both very cute in my opinion.
@adymode
@adymode 8 жыл бұрын
+iSquared So special women, suz Dancso ahhhh
@Quantiad
@Quantiad 8 жыл бұрын
+Andrew Input Great shout. Another beautiful genius.
@whiterottenrabbit
@whiterottenrabbit 8 жыл бұрын
+iSquared Doctor, Doctor, gimme the news, I got a bad case of lovin' you!
@sandeepsreehari9188
@sandeepsreehari9188 4 жыл бұрын
How very interesting to see the link between Pi and the Mandelbrot set. It's really about taking particular values for C and Z. Thanks for the informative video.
@anraiduine1483
@anraiduine1483 8 жыл бұрын
Waaaa!! So cool!! What I find especially cool too is the fact that all functions (theoretically) eventually burst out, but the smaller the values, the longer they can be iterated and still remain within 2... It's an asymptote! With infinitely small values being infinitely iterable within the mandelbrot set! And to bring it back to the video, the greater the number of iterations, the closer they come to approximating pi! Insane!!!!
@eddotron1224
@eddotron1224 8 жыл бұрын
Numberphile's 314th video is about Pi, coincidence? I think not...
@hey8174
@hey8174 8 жыл бұрын
Dr Holly Krieger is increasing my intelligence.
@pacinpm2
@pacinpm2 8 жыл бұрын
I see what you did here.
@Epoch11
@Epoch11 8 жыл бұрын
+Tucense I'm sure it is expanding.
@hey8174
@hey8174 8 жыл бұрын
+Mark G ᕦ( ͡° ͜ʖ ͡°)ᕤ
@iDEaXANA
@iDEaXANA 8 жыл бұрын
+Tucense i don't see it. mind explaining?
@iDEaXANA
@iDEaXANA 8 жыл бұрын
+Tucense there must be something wrong with me.
@virondata
@virondata 3 жыл бұрын
This actually blew my mind. WOW thank you for this video.
@BobStein
@BobStein 8 жыл бұрын
Brady makes a good talk great with his graphics and just the right touch of comments and questions.
@SunriseFireberry
@SunriseFireberry 8 жыл бұрын
Can you use the Mandelbrot Set to approximate e? Or other transcendental numbers?
@hyperbole5726
@hyperbole5726 8 жыл бұрын
+TimeAndChance nah man, but try series and sequences
@hearueszueke6206
@hearueszueke6206 8 жыл бұрын
+TimeAndChance maybe...
@simoncarlile5190
@simoncarlile5190 8 жыл бұрын
+TimeAndChance Try to do it.
@allanfloyd8103
@allanfloyd8103 8 жыл бұрын
+TimeAndChance Doubtful... If you watch the extended explanation, it boils down to the fact that this function approximates the Tangent function, and that is basically made of PI. ;)
@canerkorkmaz9428
@canerkorkmaz9428 8 жыл бұрын
You can approximate ( and find ) using its Maclaurin series ( which is Taylor series at 0). e^x = 1+X/1!+x^2/2!+x^3/3!+... e = 1 + 1/1! + 1/2! + 1/3! ...
@weirdshamanwizzard3156
@weirdshamanwizzard3156 7 жыл бұрын
"This is a totally natural thing to be interested in" this statement just... i don't have any words for it (but i don't disagree)
@margarett.newman7574
@margarett.newman7574 3 жыл бұрын
Glad to have been shown that. Thank you!
@nintender6333
@nintender6333 6 жыл бұрын
Thats absolutly awesome! Im 17 and I write about the mandelbrot Set for school (I have about 18 pages which is more than enough), but I think about getting this into my seminar work
@ComicBookGuy82
@ComicBookGuy82 8 жыл бұрын
0:43 and that's why you should pronounce Z as Zed
@geuwglesuxballz6074
@geuwglesuxballz6074 8 жыл бұрын
+LaVelle I am open to zed being the preferable pronunciation. How was that demonstrated here?
@ZPSBestProfileName
@ZPSBestProfileName 8 жыл бұрын
+GeuwgleSuxBallz It sounded a lot like the c, which, wasn't too confusing, but I could see it irking some students at the back of a lecture hall.
@unvergebeneid
@unvergebeneid 8 жыл бұрын
+LaVelle As a German, I prefer zee British pronunciation as vell.
@ZPSBestProfileName
@ZPSBestProfileName 8 жыл бұрын
Penny Lane Nice.
@ZPSBestProfileName
@ZPSBestProfileName 8 жыл бұрын
Penny Lane Yeah I presumed you were joking about being German.I thought going with French would be better as they literally say "ze", but appreciated the wordplay all the same.
@michaelbauers8800
@michaelbauers8800 8 жыл бұрын
A friend and I were delaying going back to programming, so during lunch break, we did a bit of python to show this works in base 2. I will paste the program here. Note that you might see a discrepency in digits due to rounding. Also note I used an alternate starting value.
@michaelbauers8800
@michaelbauers8800 8 жыл бұрын
import cmath import math def f( c, z): return z*z + c def doit(c, e): i = 0 temp=f(c,0) while abs(temp)
@michaelbauers8800
@michaelbauers8800 8 жыл бұрын
You can modify the value of 20 used in range, and see more digits. For those not familiar with Python, bin gives the binary representation of the number.
@alihijazi4451
@alihijazi4451 7 жыл бұрын
I giggled a lot at the end of the video, from pure joy. That's AWESOME. I love math.
@jameswilson6352
@jameswilson6352 8 жыл бұрын
This is an absolutely amazing discovery!
@TheRocketMaster2013
@TheRocketMaster2013 8 жыл бұрын
Numberphile! Congratulations on 314 videos!
@megamillionfreak
@megamillionfreak 4 жыл бұрын
She is so intelligent. And a great voice and presentation. I could listen to her for hours, days.
@Quadflash
@Quadflash 6 жыл бұрын
Fun! Fascinating! And, completely surprising. Thanks!
@brazenzebra
@brazenzebra 3 жыл бұрын
A beautiful video gift from a math angel of heaven.
@SeanForeman
@SeanForeman 3 жыл бұрын
Even after watching the additional video this is still baffling amazing to me. I am a software engineer and I find it fascinating that the number of permutations in a particular calculation could result in a known value... but you have to move the decimal place! It feels like there is something else amazing hiding in that idea that could be used to speed up certain calculation by skipping permutations and knowing the overarching value representing iterations.
@adheesh2secondsago630
@adheesh2secondsago630 2 жыл бұрын
No, this is very inefficient, u can't skip anything since output of previous is used as input to second iteration
@jonathanford9354
@jonathanford9354 Жыл бұрын
I think the exact formula is pi = lim e--> 0 of N(e)*sqrt(e). Hence if we divide e by 100, the output "shifts" by one decimal place (My N(e) is defined such that it's equal to N(0.25+e) in the video).
@MijinLaw
@MijinLaw Жыл бұрын
On 3 blue 1 brown they have several videos of pi showing up in weird places, and he manages most times to show how there is some analogy to a circle in the system. e.g. There's one where a heavy object collides with a much lighter one and a wall, with perfectly elastic collisions. As you make the heavy object increasing powers of 10, the total number of collisions tends towards pi times a power of ten. It's mind-blowing, but he manages to explain how it actually can be mapped to movement around a circle. In the case of the mandelbrot set, multiplication of complex numbers directly involves movement in a circle, the connection is probably simpler.
@Dazbog373
@Dazbog373 8 жыл бұрын
Least efficient but one of the most interesting ways of approximating pi
@andersonantunes4257
@andersonantunes4257 8 жыл бұрын
This is actually really cool!
@KC9MDO
@KC9MDO 8 жыл бұрын
The number of steps (N) to get over became closer to representing PI the larger N became. I love this kind of number theory, thanks.
@williamlavie8532
@williamlavie8532 8 жыл бұрын
Great video. I would have been interested to know why this method allows us to approximate pi though...
@numberphile
@numberphile 8 жыл бұрын
+William Lavie extra video on Numberphile2 channel
@wii3willRule
@wii3willRule 8 жыл бұрын
Blew my mind... why is it like this?
@hearueszueke6206
@hearueszueke6206 8 жыл бұрын
+wii3willRule we dont know
@daedra40
@daedra40 8 жыл бұрын
+Haris Ziko (PiMathCLanguage) The universe refuses to be all so direct with us!
@allanfloyd8103
@allanfloyd8103 8 жыл бұрын
+wii3willRule Follow up explanation in the description and at the end.
@stevoofd
@stevoofd 2 жыл бұрын
The mandelbrot set is like the gift that keeps on giving
@meredithhargrave1178
@meredithhargrave1178 8 жыл бұрын
I'm in algebra 1. This is all way over my head, but I still love watching these videos.
@PhysicsPolice
@PhysicsPolice 8 жыл бұрын
Wow! Why/how does this trick work?!
@numberphile
@numberphile 8 жыл бұрын
+PhysicsPolice seen the extra footage on Numberphile2?
@DrDress
@DrDress 8 жыл бұрын
+Numberphile Y U NO put link at end of video?
@colouredmirrorball
@colouredmirrorball 8 жыл бұрын
+DrDress Y U skip commercial?
@whiterunguard7408
@whiterunguard7408 8 жыл бұрын
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 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@gckbowers411
@gckbowers411 8 жыл бұрын
+Whiterun Guard The first decimal place is wrong.
@jestemqiqi7647
@jestemqiqi7647 8 жыл бұрын
"Mandelbrot" is german and means "Almond bread"
@jestemqiqi7647
@jestemqiqi7647 8 жыл бұрын
gabriel schilhan No.
@shorterneilisbored7078
@shorterneilisbored7078 7 жыл бұрын
Dammit, i'm allergic to numbers.
@theleftuprightatsoldierfield
@theleftuprightatsoldierfield 7 жыл бұрын
Knewity Mandelbrot is also close to an anagram to almond bread. Mandelbrot can be rearranged to almond bre. It is missing an a and a d
@shiva_hardly_sarcastic
@shiva_hardly_sarcastic 6 жыл бұрын
First of all its a name and doesn't has to be translated
@amawalpe
@amawalpe 6 жыл бұрын
It’s almost an anagram because words have the same root : mandel -> almond ; brot -> bread :)
@josejrtuti
@josejrtuti 8 жыл бұрын
I love this channel!
8 жыл бұрын
Omg, a video about my two favorite topics in mathematics!
@nousefor1
@nousefor1 8 жыл бұрын
3:19 That's what I always tell the ladies about my Mandelbrot Set :\
@BigNickontheDrum
@BigNickontheDrum 4 жыл бұрын
Dr. Holly Krieger: Mandelbae
@stv3qbhxjnmmqbw835
@stv3qbhxjnmmqbw835 3 жыл бұрын
Man of culture
@Tertious89
@Tertious89 8 жыл бұрын
I love complex numbers. There are just do many interesting and thought provoking applications when they are involved.
@Peter-pp6kj
@Peter-pp6kj 8 жыл бұрын
Please more videos with Holly! :-)
@DimitrisAndreou
@DimitrisAndreou 8 жыл бұрын
They forgot to explain why it is so!
@kemkyrk8029
@kemkyrk8029 8 жыл бұрын
I'm disturbed with that... I mean, the number of required steps to get bigger than 2 is some kind of "continuous" (if it takes n steps to a number to blow out, then you can get another number very close for which it will take exactly n+1 steps to blow out). Therefore, for every integer n, there is a real number which blows out of 2 in exactly n steps. Since you can do that for every integer 3, 31, 314, 3141, 31415, you can find a sequence of real number whose number of steps converge to π*10^smth. I think it's interesting that this sequence is just some kind of .25 + 10^-2n but, it's not that magical that it converges to π, since you know that such a sequence exists. You can do that with every real number...
@kemkyrk8029
@kemkyrk8029 8 жыл бұрын
Oh ok, so then, I can call that wonderful :))))))
@TheArunster
@TheArunster 5 жыл бұрын
6:14 "That's Cool!" Love the enthusiasm!
@ryanedwards5545
@ryanedwards5545 6 жыл бұрын
subscribed. this was great.
@rorycollier7521
@rorycollier7521 7 жыл бұрын
Never been so heartbroken to see a ring on someone's finger. :( On topic though, super interesting video. I love this channel! :)
@DrNPCabd
@DrNPCabd 8 жыл бұрын
Only Mathematics are more beautiful than Holly...
@iaalias4013
@iaalias4013 2 жыл бұрын
That is absolutely amazing
@karlmahlmann
@karlmahlmann 8 жыл бұрын
A very fun to watch video.
@aakksshhaayy
@aakksshhaayy 7 жыл бұрын
Damn it someone put a ring on that lol
@misterhat5823
@misterhat5823 7 жыл бұрын
And here I thought I was the only one who looked.
@jairochang9505
@jairochang9505 5 жыл бұрын
already has one 💍 02:01
@Harlequin314159
@Harlequin314159 8 жыл бұрын
Hang on..... but why!?
@nosuchthing8
@nosuchthing8 8 жыл бұрын
Amazing video
@Axterrix
@Axterrix 8 жыл бұрын
It is very interesting. Thank you!!!
@WahranRai
@WahranRai 5 жыл бұрын
The sexiest teacher in youtube !
@alainischileno
@alainischileno 8 жыл бұрын
I wrote a simple program and it only works up to 0.2500000001, only by adding two zeros, and only when it's followed by a 1 each time. For instance: 0.2501 gives us 312, and 0.250001 gives us 3140, but 0.25001 is 991. And putting 0.250002 instead of 0.250001 gives us 2219. Can someone prove me wrong?
@RaidChampion
@RaidChampion 8 жыл бұрын
+Alain Rochette It does work. Formally, it is (epsilon^(1/2))*N(c) which converges to pi. If you use 0.25001 for example, epsilon = 0.00001 and N(c) = 991, then epsilon^(1/2)*N(c) = 3.1338 ...
@MichaelS-vy1ku
@MichaelS-vy1ku 8 жыл бұрын
+Alain Rochette Harmonic oscillation?
@alainischileno
@alainischileno 8 жыл бұрын
RaidChampion Thanks! they didn't explain that in the video, which is why i was confused.
@alainischileno
@alainischileno 8 жыл бұрын
RaidChampion tried it again and this time it works pretty much up to 0.2500000000001, anything smaller than that and the approximation actually gets further away, do you know why this is?
@linuslee6314
@linuslee6314 8 жыл бұрын
+Alain Rochette my guess would be that that's the limit of precision of whatever programming language you're using. If you want to get more accurate, you might try using eg MATLAB or octave for mathematical computation.
@TheOutZZ
@TheOutZZ 8 жыл бұрын
WOHO :D! A Mandelbrot set video on my B-DAY!
@yoniziv
@yoniziv 3 жыл бұрын
This is amazing!!!
@random554468
@random554468 8 жыл бұрын
I understand that the mandelbrot set uses c and z as variables, but it is extremely confusing when talking about it and you are pronouncing both varables as "see" instead of "see" and "zed". And then using another c as the outside variable.
@geuwglesuxballz6074
@geuwglesuxballz6074 8 жыл бұрын
+random554468 That would be confusing, but I have yet to encounter anyone that pronounces z as see. Since this speech impediment is apparently quite rare, this is a non-issue as demonstrated in this video by a person who pronounces them quite distinctly, as is nearly always encountered.
@unvergebeneid
@unvergebeneid 8 жыл бұрын
+random554468 c is see and z is zee. I didn't have any trouble telling the difference and English is not my native language.
@omp199
@omp199 8 жыл бұрын
+Penny Lane But /s/ and /z/ are distinct phonemes in your native language, aren't they? (My understanding is that "reisen" and "reißen" make a minimal pair which establishes the existence of distinct phonemes /s/ and /z/ in German. However, I have seen this disputed, so feel free to disagree.) It might be that they are not distinct phonemes in +random554468's native language. In any case, it is neither polite nor helpful, when someone has difficulty with something, to reply, "Oh, really? Well, _I_ have no difficulty with it whatsoever!
@Sixsince-dd2eu
@Sixsince-dd2eu 7 жыл бұрын
c is see and z is zee. I didn't have any trouble telling the difference and English is my native language.
@niteexplorer9934
@niteexplorer9934 8 жыл бұрын
i'm depressed now
@ashr2526
@ashr2526 8 жыл бұрын
You really are doing the lords work, thanks dude!!
@dozer1642
@dozer1642 3 жыл бұрын
Dr Holly you are amazing.
@michaelbauers8800
@michaelbauers8800 8 жыл бұрын
I read that a student ( at the time of discovery) discovered this. Dave Boll
@djkafab4boll500
@djkafab4boll500 8 жыл бұрын
You are correct, Michael. My husband, Dave Boll, discovered this in 1991 as a grad student in Fort Collins. Aaron Klebanoff did the proof in 2001.
@michaelbauers8800
@michaelbauers8800 8 жыл бұрын
The proof is worth looking at, found it online some time ago. I don't pretend to fully understand it, but I always like trying to understand what I can :)
@ccosborn2000
@ccosborn2000 8 жыл бұрын
I believe that this wasn't found until a computer was used to do boo-coo calculations and color all those little dots depending on how fast the iteration goes to infinity.
@mana24
@mana24 8 жыл бұрын
i am here for the beautiful person in the vid
@LRibeiro97
@LRibeiro97 8 жыл бұрын
I had to comment: THIS IS AWESOME!!!
@samueldevulder
@samueldevulder 8 жыл бұрын
Ah Holly... I could spend hours iterating her videos again an again :) I wish there could be more of them on youtube.
@681726
@681726 8 жыл бұрын
The question is "why?"
@saparchitekt
@saparchitekt 8 жыл бұрын
JFK
@bytefu
@bytefu 8 жыл бұрын
+benheideveld Jelly Fish Kebab?
@suave319
@suave319 8 жыл бұрын
I need an explanation for this sorcery!
@manudelmarche
@manudelmarche 6 жыл бұрын
You just opened the door for conspiracist to tell us that the illuminati have taken off from Planet Nibiru and are headed towards planet earth in an attempt to ensure that 911 was actually a fractal simulation based on alien lasers fired from their bases located on the dark side of the moon and reflected by a giant dyson sphere operated by monsters who escaped the CERN evil portals after scientists have run within the LHC a PI approximation algorithm based on the mandelbrot set drawn by protons shot at each other :-D
@wernerruch6218
@wernerruch6218 8 жыл бұрын
This was fascinating.
@lockythindromen3974
@lockythindromen3974 8 жыл бұрын
+1 for recommending Sage!
@escraftTH
@escraftTH 8 жыл бұрын
I HATE THE SOUND OF SHARPIES ON PAPER!!! SOMEONE PLEASE HELP ME. AHHHH!!!!
@erelde_
@erelde_ 8 жыл бұрын
+3.141S92653S29793238462643383279502884I97I69E99 You're on the wrong channel then ^^ (truth is, I dislike it as well)
@Cr42yguy
@Cr42yguy 8 жыл бұрын
+3.141S92653S29793238462643383279502884I97I69E99 you should really think about that "S2" in your name and maybe change it to "S8" ;)
@hearueszueke6206
@hearueszueke6206 8 жыл бұрын
+3.141S92653S29793238462643383279502884I97I69E99 yes PI, the sound is annoying, but it is a great video, or not?
@dlwatib
@dlwatib 8 жыл бұрын
+3.141S92653S29793238462643383279502884I97I69E99 Mute!
@KCSutherland
@KCSutherland 8 жыл бұрын
I agree with Cr42yguy. 3.141 S! 92653 S2!! 979... Try 3.141592653589793238462643383279502884197169399375105820974944 or so.
@dentalhams
@dentalhams 8 жыл бұрын
Are those lightsaber earrings?
@TheZenbudda
@TheZenbudda 8 жыл бұрын
Love pi. Love the Mandelbrot set. Thanks for the marriage in concepts!
@stevenhernandez8966
@stevenhernandez8966 5 жыл бұрын
Great videos...
@Tobbzn
@Tobbzn 8 жыл бұрын
But... why?
@guilemaigre14
@guilemaigre14 8 жыл бұрын
+Tobbzn because we can :)
@troll00712
@troll00712 8 жыл бұрын
Guess i have to wait fro the English translation to come out.
@dushyanthabandarapalipana5492
@dushyanthabandarapalipana5492 3 жыл бұрын
Thanks a lot!
@muthukumaranl
@muthukumaranl 2 жыл бұрын
Holy crap that was awesome!!!
@OpenMind3000
@OpenMind3000 8 жыл бұрын
nice sache, aber sie sollte aufjedenfall mal Mandelbrot ein bisschen besser aussprechen. :D
@TheSammy2310
@TheSammy2310 8 жыл бұрын
+OPEN MIND Simon, du hier? :D
@PurzelPadauZ
@PurzelPadauZ 8 жыл бұрын
+OPEN MIND Ausserdem könnte sie mal aufhören, Pi wie Kuchen auszusprechen.
@Serfuzz
@Serfuzz 8 жыл бұрын
+OPEN MIND Weisst du denn auch, wie er seinen Namen ausgesprochen hat? Er war immerhin Franzose.
@okaydokey7852
@okaydokey7852 8 жыл бұрын
+Serfuzz ja danke ich nehm einen Hamburger ohne Gürkchen, ne große Pommes und zwei Eimer Popcorn.
@expertizzlist
@expertizzlist 8 жыл бұрын
+OPEN MIND Oh Gott und wieder ein deutsches Dummbrot, das unbedingt auf deutsch kommentieren muss - und sich natürlich noch über die Aussprache eines "deutschen" Namens aufregen muss. Komm, geh Pillen flitschen und Traumtagebuch schreiben, aka deine Kernkompetenzen. Dumme Sau.
@ewouthonig371
@ewouthonig371 3 жыл бұрын
What would be someone's motivation to figure out and study something that is of absolutely no value in the real world?
@inside91
@inside91 5 жыл бұрын
Hi! Thank you for the video! I have a question: Could you recommend an entertaining math book for someone with a bachelor's degree in maths? Or perhaps even better a nice webpage that links to interesting journal articles? Thanks!
@laurapelayo7250
@laurapelayo7250 5 жыл бұрын
I wish you guys had a podcast 😭
@marcotizzano77
@marcotizzano77 6 жыл бұрын
Dr Holly Krieger, I'm in love with you 😍😁
@Fresse
@Fresse 8 жыл бұрын
How do I conquer this fair maiden?
@shameekbaranwal
@shameekbaranwal 8 жыл бұрын
+idkagoodusernameyet just find the last digit of pi
@quoabell
@quoabell 8 жыл бұрын
+SKBytes it's 4.
@shameekbaranwal
@shameekbaranwal 8 жыл бұрын
Are you sure? I mean, i need to know how
@shirankao69
@shirankao69 8 жыл бұрын
+SKBytes Alright, here you go. The last digit of pi is 0. Yes, I can prove it.
@shameekbaranwal
@shameekbaranwal 8 жыл бұрын
Prove
@stefanamg63
@stefanamg63 8 жыл бұрын
This blows my mind!
@sator666666
@sator666666 6 жыл бұрын
Amazing!
@idriscarney5299
@idriscarney5299 3 жыл бұрын
Too high for this
@chapinward
@chapinward 8 жыл бұрын
by god, she is beautiful..
@SimonLaudati
@SimonLaudati 5 жыл бұрын
So fascinating
@endeuinable
@endeuinable 8 жыл бұрын
That was really cool. It would have been interesting to get a hint about the reason behind this relationship
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