Part 2 is at: kzread.info/dash/bejne/rGWIqsN7pMabgqg.html Check out some Numberphile T-Shirts and other stuff: teespring.com/stores/numberphile

@jjason18795

5 жыл бұрын

Numberphile is this and old video? Matt has shaved his head on his channel

@SaborSalek

5 жыл бұрын

At 7:23 you made a small mistake because the very next line is not an exact statement, but an approximation, which is only true for n going to infinity.

@JorijnLamberink

5 жыл бұрын

@@SaborSalek watch the whole video before commenting please

@SaborSalek

5 жыл бұрын

+PlopKonijn I did. He mentions it but he doesn't acknowledge that this video is kind of pointless because he wants to prove his point by using the same trick (approximating) he did last time - which he was criticized for by the Reddit user.

@wierdalien1

5 жыл бұрын

@@SaborSalek no he does acknowledge it. He talks about the rounding error.

Matt has two expressions: pleased with himself, and displeased with someone else

@imagineaworld

3 жыл бұрын

@Dr. M. H. hahaha xD *laughing from US

@ryanmunn4134

3 жыл бұрын

666 likes ooooooh spooky

@monasimp87

2 жыл бұрын

@@ryanmunn4134 0 likes spooky

@SquirrelASMR

2 жыл бұрын

@@monasimp87 000000h spooky 👻

@YagerMaelStrom

Жыл бұрын

@@ryanmunn4134 1200 likes ooooooh spooky

The Lucas numbers should be classified as a Parker Sequence due to their almost correctness.

@gehrehmee

4 ай бұрын

THIS is the real burn. Well played.

The video is 11:23 long, what an ingenious "coincidence"!

@nero3700

5 жыл бұрын

You must be on mobile... It adds another second for no reason.. Sorry to tell the video is actually 11:22 long...

@maxhaibara8828

5 жыл бұрын

Or is it?

@fdnt7_

5 жыл бұрын

Vsauce music plays

@austingulotta9817

5 жыл бұрын

@@fdnt7_ Vsauce, Michael here. Is time theft a thing?!

@DominicMcCool

5 жыл бұрын

It rounds it up....

"...Let's do what we do to celebrate things in mathematics, let's try to generalize them" WOOOOO PARTY!!!

@dragoncurveenthusiast

5 жыл бұрын

When he said that I paused to check whether someone already commented about it :-D

@CarbonRollerCaco

3 жыл бұрын

Celebrating a job well done by taking it into overtime. Proof that you love your work.

"I should give him directions to the nearest... maths... department-what?" This is why I love Matt

@jamesthelemonademaker

9 ай бұрын

I am actually dying of laughter right now and in tears typing because of this edit

The Golden Trilogy: an epic saga on the war between the Lucasians and the Fibbonaccis.

@anononomous

5 жыл бұрын

Having a war over a slightly different reading of what is effectively the same thing... Nah, would never happen...

@mattf6900

5 жыл бұрын

REEEEE

@IceMetalPunk

5 жыл бұрын

+anononomous But hey, at least it would be a slightly different reading of maths as they exist in the real world, so that's a step up from *cough* some things *cough* .

@shruggzdastr8-facedclown

5 жыл бұрын

anononomous: ...kinda like the conflict between the Palestinian Liberation Front and the Liberation Front Of Palestine and the Front For The Liberation Of Palestine?

@underslash898

5 жыл бұрын

@@shruggzdastr8-facedclown you mean kinda like the conflict between the people's front of judea and the judean people's front?

That Parker Square at 6:05

@martinzijnkanaal

5 жыл бұрын

Sneaky bastards

@PhilBoswell

5 жыл бұрын

I think that's the same one from a different angle…

@bgezal

5 жыл бұрын

Soon after, the link to merch appeared.

@NicklasUlvnas

5 жыл бұрын

@2:40

@imaytag

5 жыл бұрын

The op was referring to the one that flashed onto the picture on the wall at 6:05, not the one on the desk.

”5 is the only Fibonacci number that’s equal to its position.” 1: ”Am I a joke to you?”

@teunvandiedenhoven1105

3 жыл бұрын

IMO, the fibo numbers start with 0, 1. So no fibo # is equal to its position

@PC_Simo

3 жыл бұрын

@@teunvandiedenhoven1105 That is true, if you consider 0 to be Fibonacci number #1; rather, than Fibonacci number #0. Matt was considering the fibo numbers to start from 1, 1,…, in which case, both 1 and 5 would meet the criteria; although, either way, 1 occupies 2 positions (#0 & #1, or #1 & #2).

@CarbonRollerCaco

3 жыл бұрын

1's the Schrödinger's Fibonacci number; literally in the right place and the wrong place at once.

@mauefw

2 жыл бұрын

Not to mention 0, the 0th Fibonacci number.

@Jivvi

2 жыл бұрын

@@teunvandiedenhoven1105 they do start with 0, but they start with the 0th number in the sequence, not the 1st.

As a math student named Lucas, I cannot describe how amazing it feels to have the great Matt Parker describe why Lucas numbers are better than Fibonacci numbers...

7:23 I am calling Matt out on this hidden and sneaky rounding.

@nametry3

2 жыл бұрын

YES I thought the same thing hahah

@goutamboppana961

2 жыл бұрын

explain plz i am curious

@nametry3

2 жыл бұрын

@@goutamboppana961 The golden ratio doesn't equal exactly the next Fib. number divided by the current. The division between consecutive Fibonacci numbers is an approximation of the golden ratio, and if you assume it's exactly the same, you get the result Mr. Parker is showing. There's the sneaky rounding!

@WooperSlim

2 жыл бұрын

Matt admits his hidden and sneaky rounding at 9:51

"Proxy Pylon" is actually the name of an opening gambit you can perform in the StarCraft/StarCraft 2 games. It's considered to be a 'cheap' tactic, so I'm glad you weren't beaten by it :D

@AkiSan0

5 жыл бұрын

and "ze" probably means "the".. and we need additional pylons!

@tahmidt

5 жыл бұрын

I am so glad someone caught that! My life for Aiur!

@maciejkszczepanski

5 жыл бұрын

Actually "proxy something" refers to basically any production facility (or a pylon) placed strategically outside your base to either conceal your plans or shorten the time needed for your units to reach the desired position. It can be used in a cheesy way to one-base someone into oblivion but these are also common during the middle and sometimes even late game. Proxy pylons especially.

@tomrivlin7278

5 жыл бұрын

I was waiting with bated breath for someone who knew more SCII stuff to give me the deep dive on the strats like this. Thanks :P

@yuribruxel6074

5 жыл бұрын

The meaning of his account was the only part of the video I could understand.

What an exciting time to be alive

@iski4317

4 жыл бұрын

How are you verified?

@samisiddiqi5411

2 жыл бұрын

Why are you verified?

I've never laughed so hard at a Numberphile video. As soon as I realized Matt was circling back to his favored Lucas sequence I lost it. That delivery was perfect Matt!

I feel like Lucas numbers versus Fibonacci numbers debate is kind of like pi versus tau...both of some advantages but they're closely related so it doesn't really matter which one

@harshsrivastava9570

5 жыл бұрын

*pi vs tau

@timothyalexander5388

5 жыл бұрын

@@harshsrivastava9570 oops typo thanks

@DeathBringer769

5 жыл бұрын

Yup, reminded me of that debate as well, minus the little difference how Parker was on the popular side of the argument with Pi vs Tau (picking Pi's side) whereas here he's in the less popular side, fighting against the very common/very popular Fibonacci sequence and the Golden Ratio, lol. We've seen him tackle this topic before though too so the opinions he expressed here weren't too surprising given that us long time viewers already knew what to expect ;)

@jbobsully11

5 жыл бұрын

“so it doesn’t really matter which one” ...except pi is superior.

@jfb-

5 жыл бұрын

I used to think π was better but then I did complex analysis and the amount of times you have to write 2π is annoying

Matt: 5 is the only fibonacci number equal to its position First fibonacci number: they ask you how you are, and you just have to say you're fine when you're not really fine, but you ...

@PC_Simo

Жыл бұрын

I guess that’s, what we call: a ”Parker Fun Fact” 😅.

Oh, Matt is admitting he is wrong... wait! He's turned it around! He is right again!! Hooray!!! (I'm a fan of Matt Parker, in case you didn't notice.)

@mementomori7160

5 жыл бұрын

That "plot twist" is so beautiful.

@2adamast

5 жыл бұрын

Just a abusing an equal sign here or there

@lukesomers2031

5 жыл бұрын

Yeah, irrational number equals integer. Hrmmmm.

@moormonkey

5 жыл бұрын

And then he was wrong again

@Icerecruit0

5 жыл бұрын

Parker square...

6:50 "5 is the only Fibonacci number which is equal to its position"... what about 1?

@Xnoob545

5 жыл бұрын

1,1 so 1's position is first AND second so it's position is 1.5 and it's approximately 2

@amxx

5 жыл бұрын

"so it's position is 1.5 and it's approximately 2" Wow, hold your horses! I was here to do maths, not physics :P

@Xnoob545

5 жыл бұрын

@@amxx if u watch favremysabre when u say horses the horse that talks is Lucas

@Xnoob545

5 жыл бұрын

So its like a joke

@Theo_Caro

5 жыл бұрын

That is a trivial case.

Did anybody else feel a little thrill of anticipation when Matt said “let’s generalize it and call it a day”? Like, oh boy, can’t wait to see how he burns the internet back :D

@PC_Simo

Жыл бұрын

I did 😅.

Matts hair grew back!

@DeserdiVerimas

5 жыл бұрын

The sequence of Matts head tending towards a sphere is not convergent, it turns out.

@kal9001

5 жыл бұрын

Only some of it :P

@wolframstahl1263

5 жыл бұрын

Some of it at least ;)

@fireflash6012

5 жыл бұрын

What happened to it in the first place? I seem yo be living under a rock

@kissassparty

5 жыл бұрын

This is probably an earlier recording before he shaved it.

No that was an unexpected turn of events. Always finding new ways to never admitting defeat. 👏😂 Matt, you are a true man's man! 👍

@dancrane3807

4 жыл бұрын

A true math's man.

I am quite happy that Matt did another Numberphile. He has a very nice presentation.

I don't know which is better, Matt's epic comeback or the fact that this video is exactly 11:23 minutes long...

We he said F_n*phi= F_n+1, he was rounding. That's only true as n tends to infinity.

@romygomezjr

5 жыл бұрын

Exactly!!!! It wasn't a good burn

@SaborSalek

5 жыл бұрын

Yeah, good that other people also caught it. We should upvote all the comments that mention this so that Matt and Brady realize it.

@OmaMansou

5 жыл бұрын

Theo_Caro YES ! Oh my god ! I was like WHAT IN THE WORLD IS HE DOING ??

@Killerkarpfm

5 жыл бұрын

He said that in the end ^^

@1996Pinocchio

5 жыл бұрын

He even said that himself. But at least, there's a comment for the system. gj

Why the Fibonacci numbers are better: if you stop the continued fraction of the golden ratio at finite points, you get ratios of Fibonacci numbers

How dare you admit that you were wrong without comparing your oponent to Hitler , this is not how internet arguments are supposed to work!

This is like a mathematical rap battle

There's a lot of reaching in both arguments methinks 😂

@unoriginalusernameno999

5 жыл бұрын

FutureNow Hey when are you going to start making more videos?

@FutureNow

5 жыл бұрын

notKARTHIK. Hey, so my upload schedule right now is roughly once per month so there will be a new video by this weekend.

@Reluxthelegend

5 жыл бұрын

welcome to arguments in the internet

@hps362

5 жыл бұрын

Well technically you reaching tending towards infinity and then it works perfectly yeah.

@AHBelt

5 жыл бұрын

Maybe he just wants to be Golden ratio'd.

9:24 classic parker joke

Golden Age of Meme

4:00 Well, surely 'not very precise' and 'rough and ready' are familiar terms for Matt 'Parker Square' Parker.

6:05 love the "That's a classic Parker Square move" in the upper right!

1. Matt thinks Lucas numbers are better than Fibonacci numbers 2. Lucas numbers are better because otherwise you need to split it into 2 sets of fibonacci numbers to accomplish the same thing 3. You need two sets of pi to get Tau 4. Tau must be better than Pi because otherwise you need to split it into 2pi to accomplish the same thing 5. Matt must think that Tau is better than Pi.

Backwards Fibonacci 5, 3, 2, 1, 1, 0, 1, -1, 2, -3, 5 Backwards Lucas 11, 7, 4, 3, 1, 2, -1, 3, -4, 7, -11 EDIT: Whoa, what's this? A second like bomb?

@butterflygroundhog

5 жыл бұрын

Palindrome sequence; I like that!

@3ckitani

5 жыл бұрын

Interesting

@dante224real1

5 жыл бұрын

backwards sequence 5x, 4x, 3x, 2x, x, 0, -x, -2x, -3x, -4x, -5x SPOOOOOKKKKKYYYYYY COIIINNCCCIIIDDDEENNNSSSCCCSSSCCSCSCCSCSCCSCSSCSSSSSSSSSSSSSSS

@slightlokii3191

5 жыл бұрын

Backwards Fibonacci is actually 5, 3, 2, 1, 1, 0, 0, 0...

@AhsimNreiziev

5 жыл бұрын

+[Slight Lokii] 1 - 0 = 1 though, and not 0.

I remember this back when it was posted on his subreddit over an year ago, it took you guys a long time to get around to it.

Damn I love this channel. Fascinating content as always.

Looks like he was more of an Artosis Pylon.

_Fun and informative video; _*_thanks_*_ for doing this_ 👍

Both approaches are awesome. Mind blown.

The Parker Square merch card at 6:00 when he admitted he was wrong was hysterical.

It's almost as if the Lucas Number are BASED on the Fibonacci Numbers!

@harshsrivastava9570

5 жыл бұрын

It's actually the other way around

@captapraelium1591

5 жыл бұрын

How so?

@rebeccamccreary8530

5 жыл бұрын

Harsh Srivastava Fibonacci published his number in Liber Abaci in 1202.

@HL-iw1du

5 жыл бұрын

beirirangu CAPITALIZING words doesn’t make your ARGUMENT any better

@LechuvPL

5 жыл бұрын

But if you do the same with Lucas numbers you get Fibbonacci numbers. Well, multiplied by 5, but still. So Fibbonacci numbers are based on Lucas numbers, wich are based on Fibbonacci numbers wich are ba... ~[1 infinity later]~ In fact, in similar way it's possbile to construct any Fibbonacci sequence from any other you (just need to multiply these numbers by some factors) for example to make the third sequence (3,1,4,5... (I forgot the name)) from Fibbonacci you need to take a Fibbonaci number, multiply by 5, then add the prevoius one multiplied by -2

Today getting video from 3Blue1Brown and Numberphile😍😍😍

@blue9139

5 жыл бұрын

That is nice

I was waiting for it, Matt did not disappoint.

200 years ago the title would be an enigma

They're good sequences, Brent.

"five is the only Fibonacci number that is equal to its position" Correct me if I'm wrong, but doesn't it start with one?

I love it that the moment Matt said he always admits when he's wrong, a link popped up for Parker Square merchandise :D Well played.

*AT TIMESTAMP [**03:18**]:* This means that the Golden Ratio can be defined as *0.5 + √1.25* as well!

L_n = phi^n + (1 - phi)^n the true "no rounding" version

Unless you can get the Lucas numbers out of Pascal's Triangle more simply than the Fibonacci sequence, Fibonacci wins hands down.

The generalized sequence also works in reverse, to find Fibonacci numbers with indexes zero or lower. Before seeing this, I never thought to go in the other direction. Pretty neat!

GOSH I LOVE THIS CHANNEL AND I LOVE MATH

I am not convinced I am on zeproxypylon's side on this one that rounding step is just too ugly for me. p.s.: this new argument is almost like a parker square.

7:30 Fn + φ = F(n+1)? That doesn't sound right.

Aw man I love this channel

"It turns into a bit of a philosophical discussion about the square root of five" is a phrase you just KNOW involves Matt Parker somehow.

If Lucas numbers are the Fn+1 and the Fn-1 together, then their origin is Fibbonnaci (himachandra). There is no debate.

@ffggddss

5 жыл бұрын

Circular reasoning. You've assumed that the Fibbonnaci numbers have been pre-defined in order to define the Lucas numbers. You can just as easily do the reverse, and define the Fibbonnaci numbers in terms of the Lucas numbers. But in my view, what makes the Fibbonnaci numbers more basic, is that they use the recursion that both sequences use, but with the simplest non-trivial starter pair: (0, 1). Every sequence a(n) that uses the Fibbonnaci recursion, can be written as a linear function of F(n) and F(n-1). And in particular, every integer sequence a(n) that uses that recursion, can be written as an integer linear function of F(n). Fred

I still think that hidden rounding effort counts as cheating. zeproxypylon gets my vote

@nonpopscience3291

5 жыл бұрын

100% agree

@cogmonocle2140

5 жыл бұрын

Yep! He does exactly the same rounding by saying F_n*phi = F_(n+1). Zeproxypylon is correct

@karoshi2

5 жыл бұрын

Right. Even worse when one tries to hide it: I don't have to round. Oh, look, a squirrel! *trick*

@recouer

5 жыл бұрын

i'd have to disagree on that because the earliest number aren't of much interest if you want a precise value of the golden number. We are talking about converging speed and we can see that in fact this series converge faster to the golden number than the fibonachi one. thus you'd need less calculus to approach the rounded value to the n-th decimal to get it hence its usefulness. edit: though a bit of mathematic rigor would be welcomed as his demonstrations reminds me of how i did maths in HS...

@karoshi2

5 жыл бұрын

recouer, actually it's about elegance I think. As how much less precise calculus than (1+sqrt(5))/2 (which is exactly phi) do you want?

« What do we do to celebrate things? » « We make them less special »

Omg Matt. I think you summoned the evil know :-) Very nice Video. I love that "Burned with your own arguments"-discussions :-) Thanks

So doesn't that mean the Fibonacci numbers generate the Lucas numbers which makes them (the Fibonacci numbers) more fundamental?

@DeathBringer769

5 жыл бұрын

Yes, but I don't think Parker likes highlighting that little aspect... ;)

@Tippel3

5 жыл бұрын

That depends on the point of view. You can also turn this statement around and say the opposite.

@insanitycrafter8553

11 ай бұрын

From my limited observations, adding the Lucas Numbers in the same way gives you the fibonacci sequence multiplied by 5.

I have used a spreadsheet to work out which fractions m/n best approximate to the golden ratio as n increases. For n=1, the closest approximation is 2/1. For n=2 it is 3/2. For n=3 it is 5/3. For n=4 there is no approximation better than 5/3. For n=5 the closest approximation is 8/5. The next n which produces a closer approximation is n=8, for which 13/8 becomes the best approximation to the golden ratio. After that better approximations are achieved by is 21/13 and then 34/21. I didn't continue the spreadsheet any further. It is the Fibonacci numbers which are clearly providing the best approximations. 34/21 is accurate to within 0.0010 whereas (for example) 47/29 is out by 0.0026

@Moinsdeuxcat

5 жыл бұрын

Yes, this fact is actually obvious because of the continued fraction of the golden ratio.

I can't imagine Numberphile without the markers and brown paper, but by God the sound it makes is like nails on a chalkboard for me!!

Responding to an exact argument by hiding your rounding errors? What a Parker rebuttal! :P

10:34 classic parker phrase

Fibonacci numbers are just Parker Lucas numbers

That was some nice math judo, Matt. Taking your opponent's argument and revealing that it is actually an argument in your favor.

I saw the rounding :P I didn't expect that conclusion, though. That was great.

No, you can't assume that Fn*phi = Fn+1. That would be rounding since the ratio between Fn and Fn+1 only aproaches phi. You can only get the lucas numbers by doing some kind of rounding. Edit: Wait, you talked about it

Kind of a null point since you can just generalise the Lucas numbers back into the Fibonacci numbers; personally, I'm with zeproxypylon on this since he was actually able to get Matt Parker to admit he was wrong (sort of).

@FirstnameLastName-gx6wk

3 жыл бұрын

You can take any of the sequences and add the surrounding digits to forma new one. For example, the Lucas numbers, using the same formula, generate 5,5,10,15,25,40 and so on, which then can generate 15,20,35,55,90

@FirstnameLastName-gx6wk

3 жыл бұрын

Also, if you work out the simple formula, you get: a,a+b,2a+b,3a+2b,5a+3b,8a+5b, and so on, giving you two more sets of Fibonacci numbers

I love that when Parker admits he is wrong @6:08 the card pops up saying: *want to buy some Parkersquare merchandise?* Love it!

Reflecting on ones own mistakes is a most beautiful thing.

So the biggest take away from this is closing your eyes and rounding in prayer will give you any set of numbers you like to fit any argument! See I can maths two!

You made a mistake! phi^n is not equal to F(n+1)+F(n-1), it's only approaching at +inf. So Fibonacci is still better.

@fulvius72

5 жыл бұрын

But that is also true about Fibonacci: 1, 1, 2 . . . 3rd term divided by the second is 2/1 = 2, not phi. They approach the actual golden ratio in the limit as the number of terms approaches infinity, because only then will the ratio between two (extremely large) integers begin to approach an irrational number.

“A bit fuzzy and almosty” - so it was the Parker Square basically.

those parker square popups are so much on point in all your videos

We did it reddit!

Johnny joestar knows the golden ratio

@Luffy-yz9gj

5 жыл бұрын

Sir Lagsalot Is this a fibonacci reference?

@Grimizu123

5 жыл бұрын

What a slow dancer

Brilliant video again!

"Someone on the internet had a different opinion." A portentous phrase.

Why did 10 die? He was in the middle of 9/11.

@wierdalien1

5 жыл бұрын

Out

@xenonram

5 жыл бұрын

That's a weird joke to say. And by weird I mean creepy and sick.

@sneakrrr

5 жыл бұрын

controversial and irrelevant joke

@SaborSalek

5 жыл бұрын

+Sneakr Nothing controversial at all, only people in the US find this unfunny.

@wierdalien1

5 жыл бұрын

@@SaborSalek no its pretty unfunny.

Watched the whole video and I have one question... Where's the beef?

@Rohit-ty6hn

5 жыл бұрын

Sebastian Elytron 😂😂

@BattousaiHBr

5 жыл бұрын

on the parker grill.

@IzzyIkigai

5 жыл бұрын

Someone just rounded it down

@chrisg3030

5 жыл бұрын

Sebastian Elytron That has to come with a sequence known as Narayana's Cows (OEIS A000930) with a recurrence Cn = Cn-1 + Cn-3. The ratio between successive terms is approx. 1.4656. We could call that the Beefy ratio designated by the Greek character Moo. Moo^2 - Moo = 1/Moo

@Jivvi

4 жыл бұрын

Watch part 2.

I love the Parker Square flashing up there for a split second. XD

Your points for the Lucas numbers was a real parker square of an argument

The Lucas numbers do NOT satisfy L_n = round(phi^n) for all n, since L_1 = 1 does not equal round(phi^1) = 2.

6:15, “Let’s do what we do to celebrate in mathematics, we try to generalise them”. You know Matt’s got something up his sleeve when he says this 😂😂

I saw that coming, but still, it was amazing!

You can represent the Fibonacci Numbers as F(x)=(φ^x-cos(πx)φ^-x)/√(5) And the Lucas Numbers as L(x)=φ^x+cos(πx)φ^-x And, in general, for any sequence with initial values S(1) and S(2), and with the same recurrence relation as Lucas and Fibonacci, we can write our sequence as S(x)=A*φ^(x-1)-Bcos(πx)*φ^(1-x) with A and B such that A=(S(1)(φ-1)+S(2))/√(5) B=(S(1)φ-S(2))/√(5) (Also, for some reason, the first two formulas for Lucas and Fibonacci share some sort of symmetry that reminds me of the relationship between cosines and sines, and I can see what he's saying about how they're sort of tied together)

Matt stop You’re making just a Parker square of yourself

It still involves rounding, so is complete rubbish. You haven't thrown a gauntlet, you've just waved gauntleted hands.

This was fantastic

"...the ratio of the golden ratio" a Parker sentence if I ever saw one.

But [phi^n/sqrt(5)] gives us the n-th fibonacci number. Also, I'm not either camp, recurrence is the lord of them all.

Wait....... Why does matt has a full set of hair... Hmm suspucious (?)

@maxchatterji5866

5 жыл бұрын

Tuvi Its not the real Matt Parker. He’s more of a Parker Matt Parker.

@Arycke

5 жыл бұрын

Pre recorded and released now o.o I thought about this Tuvi

"I should give him directions to, the nearest... maths department" I have not had such a strong or sustained laugh in quite a while sir. Bravo.

I love that when Matt talks about his failures, a card pops up advertising Parker Square merch. It's hilarious, but also great marketing!

Where is zeproxy??? Are you here???

7:23 - Parker Generalisation. I don't believe that F(n) * Phi = F(n+1), because as already explained in the video, the golden ratio is what the Fibonacci numbers tend to as a ratio between them, so does not yield perfect results prior to infinity, which is quite a lot of numbers, to say the least, so will not be a correct generalisation due to inaccuracy. Let's take the 5th number. The 5th Fibonacci number is 5. Phi ^ 5 = 11.0901699.... Using the Parker Generalisation: F(n+1) + F(n-1), we get 3 + 8 = 11. Of course, 11 ≠ 11.0901699... So we have proven this to be wrong. Edit: nevermind... Didn't watch till 10:00.

"Let's celebrate your victory like any other mathematician: generalising it-" *_Gets some popcorns_*

“Five is the only Fibonacci number which is equal to its position.” 0 and 1: Are we a joke to you?