The Magical Fraction 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999

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The Magical Fraction 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999

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The number 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 has the Fibonacci numbers in order for every group of 24 decimals. This video explains why the pattern emerges. (sources, proofs, and links below)
Via Futility Closet: www.futilityclo...
WolframAlpha verification: www.wolframalph...
Pingala described the Fibonacci sequence 1,000 before: • The "Fibonacci" Sequen...
Blog post: mindyourdecisio...
"A Magic Trick from Fibonacci" by James Smoak and Thomas J. Osler. This academic paper explains why the fraction and related fractions have the Fibonacci numbers. www.rowan.edu/o...
The polynomial x/(1-x-x^2) is a generating function for the Fibonacci sequence. Here are some proofs.
math.stackexcha...
austinrochford....
www.cut-the-kno...
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Пікірлер: 412

@shadowkiller0071 8 жыл бұрын

You sound so angry at the start lmfao

@prohacker5086 6 жыл бұрын

WHY IS THIS FRACTION GENERATING THE FIBONACCI NUMBERS *WHATS GOING ONN?*

@AMa-us8de 4 жыл бұрын

So it's not just my imagination of him being mad lmao

@NoNTr1v1aL 4 жыл бұрын

The numbers...WHAT DO THEY MEAN?!!

@wanderer3362 4 жыл бұрын

*IN ORDER*

@shekharthingore9477 4 жыл бұрын

Hes gone mad at the fraction lol

@OFFONE 4 жыл бұрын

When you’re going through a divorce but your students need to learn math.

@escapistsmusicstuff 4 жыл бұрын

I N O R D E R

@mjzudba5268 2 жыл бұрын

@Sadia Subah it's a joke, that's what's going on

@TrimutiusToo 8 жыл бұрын

it is not 24 bit, it is 24 digit strings...

@lapidations 4 жыл бұрын

Which would be a LOT more than 24bits. I mean, at the very least 24 bytes, right?

@qwertyqwerty-jp8pr 4 жыл бұрын

@@lapidations well, it is exactly 24 bytes, both in ASCII and utf8 format

@herohamp2 4 жыл бұрын

@@qwertyqwerty-jp8pr some say the only reason UTF-8 was adopted was because Americans didnt have to change thier systems to read English character

@qwertyqwerty-jp8pr 4 жыл бұрын

@@herohamp2 hmm, it still save some storing space (although it is totally not important these days since text files is so small compared to other file types)

@RoyBrush 4 жыл бұрын

It depends on the encoding. :) If you're encoding your strings as ASCII characters, where each character is 7 bits (although usually we use a full byte for a character in practice) then yeah, it'd be 24 bytes. However, we're only using the characters 0-9, which means we have a lot of waste. What if we just used 9 symbols instead? How many bits would we need per character? Well, 9 in binary is 1001, so 4 bits. Great! We've cut this in half! Now we're down to 12 bytes, which is great! But we still have some wasted space we're not using in each half-byte, since we never use the values 1010, 1011, 1101, or 1111! Okay, we can do better. Well, what if you had a packed binary encoding, where each segment in the string (each "character") was a binary number that could accommodate a 24 digit decimal number. So that is, what if instead of a decimal string, I had a binary string, how many bits would I need to store a 24 digit decimal number in binary directly? Well, the number of bits is only 80 bits, or 10 bytes, so better again. Now I can fit my 24 digit number into just 1 of my 10 byte "characters". Even the 10 byte encoding has a lot of redundancy, since most numbers will be packed with leading zeros, so we could possibly even use some kind of binary terminator to reduce this, but then you have characters where their length depends on their value (this actually happens with unicode characters in real life), but yeah, worth thinking about maybe. Anyway, for a packed representation with uniform character representation similar to ascii, I think the 10 bit example is pretty much as good as you'll do. Here's some Javascript code that I wrote which allows us to encode numbers or ascii into this format, and then allows us to convert out of this format into numbers of ascii. I've put it on multiple pastebins, if you run it on jsfiddle or repl.it you can see it actually run. Otherwise, you can read the code on pastebin (of course, you can take the code from pastebin and throw it in your browser's console if you want to run it too): pastebin.com/6AtWPUeB jsfiddle.net/hs3x1ne9/ repl.it/repls/JoyfulWarpedServices

@alavi9494 8 жыл бұрын

I wonder who invents these problems

@ATXpert 8 жыл бұрын

people who are alone and bored :)

@vinbia8615 8 жыл бұрын

It's a pretty neat (and also obvious) implication of generating functions if you're a math nerd learning combinatorics.

@PyroclasticFlow 7 жыл бұрын

or people who are doing their jobs...

@Reivivus 7 жыл бұрын

Mathematics professors who are using their cleverness to increase the probability that you will fail to exponentially likely.

@ryanye8441 5 жыл бұрын

people who spend too much time on math than his girlfriend :D

@carlosgeonzon7499 4 жыл бұрын

I'll just edit this so you'll wonder why I got 600 likes.

@Jack-zd3vr 4 жыл бұрын

Then there’s always that pathetic turd who says “It’s only highschool level math you plebeian”

@niveditachowdhury9499 4 жыл бұрын

And then someone with zero sense of humour: "That is actually pretty easy to understand 😒"

@mhd8499 4 жыл бұрын

JoyCon Boyz Forever It’s pretty simple tho, I took this in high school

@Jack-zd3vr 4 жыл бұрын

Rimmita Chowdhury ^ found them

@carlosgeonzon7499 4 жыл бұрын

@@Jack-zd3vr Your prophecy has come true

@NXeta 7 жыл бұрын

hooly shit, first 12 sec of this video and I can tell by tone of your voice you aren't fucking around for this one 👍

@2394098234509 7 жыл бұрын

Holy shit that's funny

@Purple101 4 жыл бұрын

Why is this even in my recommendations, I just want to watch minecraft

@mokutomedia1253 4 жыл бұрын

Its here to teach you how to use redstone

@vierspartan117 4 жыл бұрын

KZfaq Is trying to save your brain

@blue_the_duke 4 жыл бұрын

@@vierspartan117 lmao

@warioseggs 4 жыл бұрын

@@vierspartan117 nah i think its trying to make it mush

@lvbboi9 4 жыл бұрын

Yall should watch sumthing better

@ffggddss 8 жыл бұрын

This works because 1/(1 - x - x²) is what is known as the "generating function" for the Fibonacci sequence. And the reason it is THIS polynomial in the denominator, is the recursion formula that the Fibonacci sequence obeys Fᵢ = Fᵢ₋₁ + Fᵢ₋₂ when it's written as: Fᵢ - Fᵢ₋₁ - Fᵢ₋₂ = 0 so that if you write the operator that diminishes the index by one, as ∆, this can be written: (1 - ∆ - ∆²)Fᵢ = 0

@ffggddss 7 жыл бұрын

Some of them I can make from my keyboard; others I've copy-pasted over time, collecting them in a txt file for later use. I am in MacOSX, where: ∆ = option-J ∑ = option-W π = option-P, etc. I'm told that Windows users can get most any crazy characters with other keyboard tricks that call up Unicode characters. the subscripts & exponents are ones I've copy-pasted, e.g., ⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁻ ⁺ ⁼ ⁽ ⁾ ᴰ ª ͩ ᵉ ͪ ᵏ ᵐ ⁿ ᵖ ͬ ᵗ ͭ ˣ ʸ ʹ ʺ ‴ ° ˅ ˆ ˜ ˙ ᵀ ₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₐ ₐ ₔ ᵢ ₒ ᵣ ᵤ ᵥ ᵥ ₓ ᵦ ᵨ ₊ ₋ ₌ ₍ ₎ Good luck!

@seersam 7 жыл бұрын

Ah, I was asking for the subscripts and exponents. I thought it's something else other than a simple character - really didn't figure this out

@ffggddss 7 жыл бұрын

Well if you can't find the ways to get them, you can copy-paste them from my previous comment ;-)

@enejidjsi5939 3 жыл бұрын

@@ffggddss thx, where can i learn more about these "operators"? I am not very experienced but i'd love to learn. Thank you,

@ffggddss 3 жыл бұрын

@@enejidjsi5939 I don't know any place you could find all of them; they just come up in certain contexts around other mathematical topics. In the case of this one, it and a few others like it, come up under difference equations/numerical integration techniques. The former relates to the method of finite differences; the latter, to numerical solution of differential equations. Fred

@oggo6783 7 жыл бұрын

why am i telling myself i understand this?

@GrandMoffTarkinsTeaDispenser 7 жыл бұрын

What did you not understand?

@stuntman3614 4 жыл бұрын

Maybe because u do?

@maniebrahimi7952 4 жыл бұрын

It’s really easy tbh, it’s just a random function that generates fibonacci numbers, nothing hard to understand

@99gypsies 3 жыл бұрын

@@maniebrahimi7952 It has nothing to do with intelligence, per se. Of course, some intelligence is required, but there are MANY kinds of intelligence. I can understand some things much better than most people and I can do some things that most people cannot do. I excelled at English, History, Art, etc., but I don't have a clue about math! I LOVE it, but I don't get it. I can't play the violin either or fix a washing machine, though I CAN change a lightbulb. It's rather ignorant to say, "tbh this is really easy." I DO believe it is easy enough for someone with a grasp of math, but when I look at it, it is like looking at Japanese writing. It is just a string of numbers and symbols. ;-) I am an artist and I LOVE fractals! That is, I love the way they look when they are visually represented on computer streams -- they are one of the most interesting and beautiful things I've ever seen. This makes me interested in Fibonacci sequences. I have a vague idea how math can be translated into images because I suspect that there are mathematical formulas or code written into every material thing -- I don't know if they determine the thing or just define the thing -- but it is harder for me to understand how math becomes colors, for some reason . . . do you just enter a Fibonacci sequence into computer software code and then these endless, unique, and diverse patterns and colors just appear? I've tried to look it up to understand how it works, in the past, but I did not find anything that explained it to a math illiterate. ;-)

@-roxas-6608 4 жыл бұрын

Me at 2AM clicking this video thinking im smart enough to watch it

@pugpugsly2829 4 жыл бұрын

You sound like 40 different emotions are inflicting you

@AutoBusee 4 жыл бұрын

Math in class: 2 + 10 Math in test:

@whatifwaterwaschunky7199 4 жыл бұрын

Mumbo: The redstone is simple The redstone: 2:01

@avinashrao4791 4 жыл бұрын

Bruh that was worst joke I've ever heard...

@whatifwaterwaschunky7199 4 жыл бұрын

@@avinashrao4791 Im gonna guess you haven't heard many jokes

@thenewguy7527 4 жыл бұрын

that's exactly why it's so unfunny. simple problem being showcased + overused "meme"

@833Rowan 4 жыл бұрын

a man of culture i see. and to that phoenix guy. Everybody gangsta til the house starts walking

@lvbboi9 4 жыл бұрын

@@whatifwaterwaschunky7199 no It was just a terrible joke Not everything needs a Minecraft joke I watch Mumbo And I am truly dissapointed

@timharrod 8 жыл бұрын

Wow, that's cooler than 1/998,001.

@RandomHandle-fun2rhymes 4 жыл бұрын

1/998001 is 1 or 998001

@godnmaste Жыл бұрын

@@RandomHandle-fun2rhymes lol

@alan2here 8 жыл бұрын

Various interesting 1/x that I've heard of or found. I'll give short versions but to expand pad out with 9s on the left and as appropriate on the right part of the number as well. --- "x" can be: 998 - Doubling 998001 - Increment 998999 - Fibonarchi 998998 - Sum of all previous, also increment alternate values. From some old notes I'm not sure about now, where N is the group of digits and G is the length of each group. Sequence | Approximately 10^G-x | x^N (10^G)^y | N^y (10^G-x)^y | (x^N)^y (10^G/z-x)^y | ((x*z)^N)^y x, y | sequence, sequence name, simpler approximate sequence 1, 1 | 1 1, 2 | N 1, 3 | (1/2)N(N+1), Triangle Numbers, N^2 1, 4 | (1/6)N(N+1)(N+2), P + Triangle Numbers, N^3 2, 1 | 2^N, Powers of 2 2, 2 | 2^N(N-1), Powers of 2 squared, (2^N)^2 3, 1 | 3^N

@chrisg3030 8 жыл бұрын

+Alan Tennant I found a 1/x that gives successive powers of 5: 1/1.9999... goes 0.5...25...125...625.... Also 1/1089 = 0.000918273645546372819100... which, as I'm sure you notice, contains a palindromic segment consisting of digit pairs summing to 10. As I said in another comment, I'm looking for a 1/x that gives the Narayana's Cows sequence, OEIS A000930.

@alan2here 8 жыл бұрын

I'm not sure I can follow that, or other attempts to look it up.

@alan2here 8 жыл бұрын

Thanks :)

@Languste 8 жыл бұрын

+Alan Tennant One question: Are you all math-students or professors or so? ^^ Because I am a German pupil (16 years old), and even though I understood the video I have no clue what comments like yours shall mean :p Just interested in your ages and job :3

@Languste 8 жыл бұрын

Eric Zhang ok thx :3

@Corpulous 8 жыл бұрын

Is the pattern also related to the fact that if x^2-x-1=0, x is equal to the golden ratio?

@leonardo21101996 8 жыл бұрын

+Doraemon ドラえもん Golden ratio and Fibonacci sequence are related. One way to see this is calculating P^n, where P is the golden ratio and n is a whole number, and writing it as a*P+b, with integers a and b. You will see the fibonacci sequence apearing on the coeficients a and b. P^1=1*P+0 P^2=1*P+1 P^3=2*P+1 P^4=3*P+2 P^5=5*P+3 In general: P^n=F_n*P+F_(n-1)

@Sashafomin95 8 жыл бұрын

+Doraman yes, indeed. it's due to the fact that characteristic polynomial of Fibonacci sequence (P(x) = x^2-x-1) is skew-symmetrical in a sense that x^2*P(1/x) has the same roots as P(x) only with different signs. In your words, minus-golden ratios: -a_1 = -(1-5^0.5)/2 and -a_2 = -(1+5^0.5)/2. And the fact that any Fibonacci number can be explicitly expressed in the terms of the roots a_1 and a_2 as following: F_n = C_1*(a_1)^n + C_2*(a_2)^2. Or considering F_1 = F_2 = 1 F_n = ((a_2)^n - (a_1)^n)/5^0.5 (also known as Binet's formula) In general, one should look for the next pattern in denominator: 1 - (b_1 + b_2)*x + (b_1*b_2)*x^2, where b_1, b_2 are roots of characteristic polynomial (of the second degree) of sequence. Being more general x^n*R(1/x) where R - is any polynomial (of the n_th degree) of sequence. It's just so happen that Fibonacci sequence has yet another nice, pleasing (for humans) structure.

@chrisg3030 8 жыл бұрын

+Doraman You may have noticed my comment asking for help in finding a fraction whose decimal expansion exactly matches not the Fibonacci sequence but a companion sequence known as Narayana's Cows (OEIS A000930) which goes 1 1 1 2 3 4 6 9 13 19 28 41 60 88 129 . . . based on the recurrence formula a(n) = a(n-1) + a(n-3), which basically means you add a number not to the next but to the one after. Its ratio constant is not the Golden Ratio, but approx. 1.4656, so not equalled by the formula you quote, but x^4 - x^3 - x = 0. From there could we go to 1/x - x^3 - x^4 and onwards using the method in the video get the fraction I seek? I've already found an approximate fraction by trial and error, 1/989999, but the correspondence breaks down at the 14th term. Putting lots of 9's on each side like in the video doesn't seem to help.

@Sashafomin95 8 жыл бұрын

Chris G considering the recurrence formula: a(n) = a(n-1) + a(n-3), you've got the characteristic polynomial almost right. Because we're not particularly interested in any zero-roots, the final formula for it will be: P(x) = x^3 - x^2 - 1 (btw, the degree of polynomial is the number of initial conditions for sequence to be uniquely determined). Now, one can easily get the denominator using the formula I provided: x^3*P(1/x). If you did that carefully you would get x^3*P(1/x) = x^3*(x^(-3) - x^(-2) - 1) = 1 - x - x^3. So that's what the denominator will look like. However, you probably should ask a question about the numerator. And there is no simple answer to that. And the reason for this is that you must solve cubic polynomial i.e. find the roots of characteristic polynomial P to get the numerator brutally (luckily, Cardano did it for us a long time ago and there are explicit formulas for the roots of up to 4th degree polynomials). Though maybe there is some workaround way, I cannot provide you with the formula right now. Maybe it's 1 and maybe not, I don't know. But I can assure you that the denominator is exactly 1 - x - x^3 and you will get a valid result by putting there 10's.

@Languste 8 жыл бұрын

+Олександр Фомін What are your jobs and how old are you guys? Because even though I understood the video, I have no idea of what these comments are actually about :p I am 16 (German pupil), just wondering about how old you are and what you are working as :)

@darjfag4539 4 жыл бұрын

Why is this in my recommendation

@alexzzander_2823 4 жыл бұрын

Because you are a math master

@thephysicistcuber175 4 жыл бұрын

The real question is why is KZfaq 4 years late again?

@nziom 4 жыл бұрын

Same

@chigzii8314 4 жыл бұрын

Me at 2:30AM

@weselycat1386 4 жыл бұрын

Because it's epicccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

@MrOligi3003 8 жыл бұрын

My favorite is 1/89 = 0.0123595... . 89 is the 11th Fibonacci number.

@romekhanna 4 жыл бұрын

Why the fraction is good pls explain sir/mam

@romekhanna 4 жыл бұрын

@@peytonsawyer562 thank you so much allison!!!! It was a great proof!!!!

@sonicrider321 4 жыл бұрын

People with OCD - GET RID OF THAT 8, ITS KILLING ME INSIDE

@RussellTheOgre 7 жыл бұрын

I watched this in the hopes of understanding what was being talked about- I leave here now with an upset stomach and pressure in my head.

@erik19borgnia 4 жыл бұрын

I'm so glad youtube recomended me this old video. I love all your videos! Thanks for all of them!!

@EllipticGeometry 8 жыл бұрын

Hmm, seems I missed out on all the fun. I created this class of fractions myself less than a month before this video was posted. When I came across 1/998001 for the umpteenth time I looked into other things you can encode in a fraction. You can do all sorts of things like polynomials and exponentials, and some operations to combine them. The Fibonacci sequence was among the ones I highlighted at the time. I doubt I got this ball rolling with my tiny reach, but it's a fun possibility to entertain. Note that the pattern doesn't break down too badly when numbers get too large. They're just carrying over to adjacent digits, nothing else. Say, the base 1000 version gets in trouble at 610 987 1597. The extra digit in 1597 carries over to 987. When you perform all the carrying including 2584 following it, you get 610 988 599. That's much like 1/998001 once it reaches what's supposed to be 998. The important thing to realize is that if you cancel the carrying using a proper parallel calculation, your digits are still congruent to the actual numbers!

@JMCamps 4 жыл бұрын

If 1/(1-x-x²)= F1+xF2+x²F3+x³F4+... It means that if x=1 , F1+F2+F3+...=(-1) √-1=i=√(F1+F2+F3+...), "i" (a complex number) is equal to the square root of the sum of all Fibonacci numbers (and they are Natural numbers) 🤯😱

@Nikioko 3 жыл бұрын

This also works with 1/9899, 1/99989999 or any number (10^(2n-1) - 10^n - 1)^(-1).

@filipsochor8277 4 жыл бұрын

1:58 X squared, not cubed. Only read wrong, text is fine. I love Your vids. Keep it up please.

@99gypsies 3 жыл бұрын

You mean shaken, not stirred.

@filipsochor8277 3 жыл бұрын

@@99gypsies as far as science goes, no, I don't. But if we are talking jokes... Yeah. Also I would have probably laughed more, if I knew the refference in english, not having to translate it😂

@99gypsies 3 жыл бұрын

@@filipsochor8277 Well, my sense of humor may be a bit abstruse even for native English speakers. ;-) -- since Sean Connery just died, I have the famous line, "shaken not stirred" in my mind. And when I read your comment -- that famous James Bond line came to mind. Perhaps Bond could have ordered a martini and said, "squared, not cubed" and it might have been a nice double entendre for math geeks, even if it made no sense at all to the rest of us. ;-)

@go4ryan 9 жыл бұрын

Great video; really well explained. Thank you!

@Amr-Ibrahim-AI 7 жыл бұрын

Thanks for the great simplification. I love your videos

@Soldier-Cat 4 жыл бұрын

Looking at all those numbers give me a mini anxiety attack in my head 😞

@jeremykates7276 4 жыл бұрын

Anybody else notice that 1/7, 2/7, etc are all the same 6 digits repeating in the same order just starting at a different value

@abcabc-uv6ce 4 жыл бұрын

Jeremy Kates thx i never notice that. 1/7 can be easily remember by doubling 7 three time and the last one add one 7 14 28 57 1/7 = 0,142857......

@TheHuesSciTech 4 жыл бұрын

If you go through the exercise of doing division by hand, you'll realise that the only thing determining the next digit you find is the carry digit from the previous digit. But that carry digit is determined solely by the previous digit. So, 1 must always be followed by 4, 4 must always be followed by 2, etc etc. It's thus unavoidable/inevitable that the same pattern emerges.

@lordx4641 4 жыл бұрын

@@abcabc-uv6ce sir is it Fibonacci no or hemchandra no??

@RicardoSilva-zd9nm 4 жыл бұрын

Maybe this could explain en.m.wikipedia.org/wiki/Cyclic_number

@H-G0 4 жыл бұрын

Teather:The test isn't hard The test:

@joes7263 8 жыл бұрын

i have one question: you say the generating function for the fibonacci sequence is $\frac{1}{1-x-x^2}$, but in the description and on various other internet pages i found $\frac{x}{1-x-x^2}$ instead. which function is the right to use?

@Shockwave33333333333 4 жыл бұрын

Why am I here and why did I think I'd understand anything he said?

@davidspencer3726 9 жыл бұрын

Interesting, so if x=1 then the sum of the Fibonacci sequence is equal to -1.

@naimsantos2430 6 жыл бұрын

NOpe

@thenewguy7527 5 жыл бұрын

Yes.

@sb-hf7tw 5 жыл бұрын

Wow, cool!👍👍👍

@ItIsMeTime123 4 жыл бұрын

The heck is a Fibonacci?! Why am I even... _...KZfaq..._

@Jack-zd3vr 4 жыл бұрын

Code

@99gypsies 3 жыл бұрын

All I know is his codes produce the most amazing things called fractals -- check them out. But I am not sure how his math differs from Benoit Mandelbrot's sequences. I THINK Mandelbrot invented or discovered fractals and Fibonacci added it to it somehow?

@nitinsharma9793 4 жыл бұрын

Why is the equation [1/(1-x-x²) = Fibonacci Series] (1:59) not valid for a value of X greater than or equal to 1?

@nakoamechi 4 жыл бұрын

Great! Watching this at full volume for an excuse that I did study.

@lazyjones6266 4 жыл бұрын

HELP ME: at 0.40 starts a "long division" but i don't understand the method. PLEASE: Can someone give me a step by step explanation? IT'S IMPORTANT. Thanks!!!

@paulosullivan3472 3 жыл бұрын

Okay but given there are an infinite number of integers I can guarantee that for any given list of numbers there is a fraction which will produce that exact series of numbers as a binary.

@samantharuiz8522 4 жыл бұрын

yt reccomends this to me while i study for my algebra II exam. totally gonna ace this test guys😎😎

@user-wf7uf2jp8x 8 жыл бұрын

when you found this out by yourself before anybody else knew about it and then someone else came and make it popular-

@fountainovaphilosopher8112 6 жыл бұрын

Rawriors Cat Nice pfp lol

@nataflet 8 жыл бұрын

For = X=10^(-1) or 10^ (-6) or 10^ (-9) or 10^ (-154) or 10^ (-253) or 10^ (-1114) or 10^ (-1390) (and more), the big number is a prime (89, 999998999999 etc)

@sohamagarwal5809 2 жыл бұрын

That was truly mind boggling!!!

@Crokuran 4 жыл бұрын

I think KZfaq is recommending us these math videos to make us the secret generation of mathematics who learned more than like 5 years of education ever could

@domiswan254 4 жыл бұрын

And the number 1/999,999,999,999,999,999,999,999,999,999,999,998 gives...the powers of 2!

@kcg6016 4 жыл бұрын

idk why i clicked on this video but now i have no option but to look at comments...

@Naarden4ever 8 жыл бұрын

Soo the decimals will start to repeat. Obviously the first obstruction you're going to hit is the fact that the integers that make up the fibonacci-sequence are going to be larger than the 24 spots that this number is giving you. But if the Fibonacci-sequence is getting displayed correctly, and the number displaying it is a rational number... It sounds counterintuïtive.

@giannisr.7733 5 жыл бұрын

congrats on 1 million, you have made me love maths, thank you😂

@Salah.alkhalifa 4 жыл бұрын

I don’t see a problem in this problem!

@brytonduropan6741 4 жыл бұрын

oh yes big words that i remember from math class yesterday.

@PepperStockings 4 жыл бұрын

Yeah, youtube thought it was a great idea to send me this in 2019.

@yourenekst 4 жыл бұрын

shut up you pepega

@thegoldenapple5314 4 жыл бұрын

How did i end up from minecraft redstone to this?

@mindslayer6810 4 жыл бұрын

At 3:03 the numerator was multiplied by 10^-48 But how can we multiply just the numerator not denominator and not disrupt the equation

@833Rowan 4 жыл бұрын

all it does is move the decimal to the right place doesnt do anything to the numbers but if it bothers u just imagine its x/1-x-x^2

@kimmovillacorta7677 5 жыл бұрын

Solving for the zero of the denominator will give you the reciprocal of the golden ratio

@rohannuckchady2900 8 жыл бұрын

i like the fact that you seem to h8 fibbonacci :3

@pattyrick5479 6 жыл бұрын

isnt that big number with all those nines a glitch prime?

@Czeckie 7 жыл бұрын

I'm quite late to the party, but you actually don't get all of the fibonaci numbers up to 24 digits - it will get distorted after a while. You can see this phenomenon by computing the same thing for only two digits, that's x=10^-2, the magical fraction is then 1/9899. You will get 1, 2, 3, 5, 8, 13, 21, 34, 55 AND 90, error! Try to figure out why is it like that

@harshsinghal4342 7 жыл бұрын

its because numbers are overlapping because the denominator is quite small.

@MrPlaiedes 4 жыл бұрын

Why cant it ever be aliens?

@anassalman9464 4 жыл бұрын

Can this make humans more humans than they are,is this useful for making us better?

@pendragon3350 4 жыл бұрын

Is this question make humans more humans than they are? Or is it just another useless KZfaq comment?

@anassalman9464 4 жыл бұрын

@@pendragon3350 no, it's a question of me, I mean what I'm asking, if you don't have an answer, don't put your self inside, you don't have to.

@lapidations 4 жыл бұрын

It made me happier to know this, I think it's awesome.

@sanskrutisharma6790 4 жыл бұрын

liked it the moment you said pingala sequence :)

@cxpKSip 7 жыл бұрын

why does 1/99999...9998 print all powers of 2?

@alexhells2367 3 жыл бұрын

If we put x=1 then sum of the Fibonacci numbers is -1. How is this possible !

@mosab643 4 жыл бұрын

He should've mentioned that the relation only works for very small values of x.

@gamingmusicandjokesandabit1240 2 жыл бұрын

Plot twist: KZfaq moderated the title because it thinks you're spamming 9's in the title.

@avinashrao4791 4 жыл бұрын

What... What are we talking about?

@NormanicusDiabolicus 8 жыл бұрын

A very interesting video indeed but how is it proven that the division 1/(1-x-x^2) continually generates the fibonacci coefficients for all increasing powers of x ?

@NormanicusDiabolicus 8 жыл бұрын

+NormanicusDiabolicus Just worked out proof:- Multiplying (1-x-x^2) and F1+xF2+x^2F3 ...... and then collecting coefficients of same powers of x gives 1 as x^n(F(n)-F(n-1)-F(n-2))=0

@shahriyarhussain3931 4 жыл бұрын

Did anyone’s KZfaq app freeze and stuttered after opening it!??!?!?

@karanchowdhary5969 4 жыл бұрын

As it is money not mentioned in Indian currency

@purusotamasahoo9687 3 жыл бұрын

Anyone got any idea how a person might have ended with this fraction?

@aaroncutting 4 жыл бұрын

By the engineering approximation; the answer is 0

@MikhaelAhava 4 жыл бұрын

Who made this? Or discovered, pretty neat.

@SKO_PL 6 жыл бұрын

You didn't prove the series is convergent... WRONG! If you don't see a problem, just check what plugging in x=1 gives...

@SuperMtheory 9 жыл бұрын

Fantastic video!

@randomuser5443 4 жыл бұрын

After so long, this always happens

@sb-hf7tw 5 жыл бұрын

I love Fibonacci but hats off to PINGALA who discovered it a thousand years ago!👍👍👍 Great mindyourdecision!!! 👌

@d1o2c3t4o5r 4 жыл бұрын

There is one too many 9s in the expression. The number is too large by a factor of 10.

@geetaagarwal4622 5 жыл бұрын

Someone please solve my doubt:1/1-x-x^2 :gives fibonacci numbers just substitute x=1,1/-1=-1 and that is sum of fibonacci numbers

@joes7263 8 жыл бұрын

another youtube-guy left a comment with: $\frac{1}{89}=0,01123595...$ so for the fibonacci number 89 there a the first six fibonacci numbers in order in the decimal representation. is there a correlation between a fibonacci number as divisor and fibonacci numbers in order? : Thx in advance for your help :)

@chrisg3030 8 жыл бұрын

I'm very interested in a family of companion sequences to the Fibonacci, including one known as Narayana's Cows (OEIS A000930) which has the recurrence An = An-1 + An-3, and goes 0 0 1 1 1 2 3 4 6 9 13 19 28 ... How to construct the fraction and its decimal expansion featuring this sequence?

@chrisg3030 8 жыл бұрын

+Chris G I'm getting somewhere with this question. 1/989999 has a decimal expansion matching this sequence for the first 13 terms before it comes to 89 instead of 88.

@RubyPiec 4 жыл бұрын

1/998,001 is still my favorite fraction

@bobeatyourbrains 7 жыл бұрын

that long division thoooooooooooooooooo

@koji2107 4 жыл бұрын

Him intestine 2.0 Me: *1+1=7*

@warsnitin4473 4 жыл бұрын

I think you mean *Einstein*

@ikchess 7 жыл бұрын

Is this a generating function for the Fibonacci numbers then?

@rielitty 4 жыл бұрын

_i dont get it but i feel like my iq got raised by 1/99999999999_

@karanchowdhary5969 4 жыл бұрын

For completion please give your book free no money to your book

@sumyiuli7803 8 жыл бұрын

I wondered to myself, what happens if I substitute other numbers?

@binomialchaos9520 7 жыл бұрын

so does this work for all base numbers or just base 10 (decimal)?

@OmSingh-ge1uy 4 жыл бұрын

And KZfaq is recommending me now Its been freaking!!!! 4yrs!!!!!!

@icebear326 4 жыл бұрын

My head hurts. I'm only in algebra 1

@InvitingShores 9 жыл бұрын

As always very interesting subject.

@Carl_Hoff 4 жыл бұрын

Interesting... however 1/999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 is a rational number so doesn't its decimal representation have to terminate or start repeating itself at some point. How many digits must one go before this starts to repeat? How many digits are in the segment that repeats?

@neo1410 4 жыл бұрын

...It seems it is finite? My calculator shows it ends with ......17711?(or at least this is what my calculator gives me)

@animefangamer277ominous_ab7 5 жыл бұрын

0.000000000000000000000000000000000000000000000001000000000000000000000001000000000000000000000002000000000000000000000003000000000000000000000005000000000000000000000008000000000000000000000013000000000000000000000021000000000000000000000034000000000000000000000055000000000000000000000089000000000000000000000144000000000000000000000233000000000000000000000377000000000000000000000610000000000000000000000987000000000000000000001597000000000000000000002584000000000000000000004181000000000000000000006765000000000000000000010946000000000000000000017711000000000000000000028657000000000000000000046368000000000000000000075025000000000000000000121393000000000000000000196418000000000000000000317811000000000000000000514229000000000000000000832040... = 1 / 999,999,999,999,999,999,999,998,999,999,999,999,999,999,999,999 (1 Quindecillion - 1 Septillion - 1)

@animefangamer277ominous_ab7 4 жыл бұрын

The Other Way To Read The Denominator Is... “1 Quindecillion - (1 Septillion + 1)”! As... 1 / (1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 - 1,000,000,000,000,000,000,000,001) No Wonders Why It Uses The Fibonacci Sequence! (Some Of The Numbers Are Actually Prime...) The Terms (Without 0, And Repeating “1”) Goes... 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811... (You Get The Point...)