Whoa.

@ObjectsInMotion

3 жыл бұрын

Wau.

@unspeakableanomony5340

3 жыл бұрын

Wow.

@cemgecgel4284

3 жыл бұрын

Wow.

@ayushdeep7900

3 жыл бұрын

Wow

@dipi71

3 жыл бұрын

You mathematicians with your ultra-technical terminology, haha!

I like the Fibonacci series where you start with 0, 0. Its easy to remember

@jetison333

3 жыл бұрын

I can even calculate any item in that sequence in my head ;)

@NStripleseven

3 жыл бұрын

The formula for a term in the sequence is the simplest I’ve ever seen

@darthgeeek

3 жыл бұрын

Math truly is amazing

@cmyk8964

3 жыл бұрын

Ah yes, the sequence that correctly predicts the exciting things that happens in my life

@minerforstone4136

2 жыл бұрын

I love how you choose the simplest possible sequence and it's "golden ratio" is undefined

The moments when his amazed face perfectly merges with himself are really trippy. Nice touch =P

@niccy266

3 жыл бұрын

It's called the buttercup challenge, he links it at the bottom of the description

@ryla22

3 жыл бұрын

It made me look up the song Really good song

@tomppeli0

3 жыл бұрын

@@niccy266 1

@mrss649

3 жыл бұрын

Lol yes

@flisboac

3 жыл бұрын

Kinda freaks me out, tho

Well, I mean... the Fibonacci sequence was discovered thinking about the ideal procreation of rabbits, and it's pretty hard to have a negative rabbit mate with a positive rabbit

@themathaces8370

2 жыл бұрын

That's what mathematicians do... Extending simple ideas to random dimensions...

@jayfredrickson8632

2 жыл бұрын

You can but then they mutually annihilate and you get a huge explosion

@reubenmanzo2054

2 жыл бұрын

They say opposites attract, don't they?

@fders938

2 жыл бұрын

Don't even get started with imaginary and 4D rabbits

@mr_waffles_the_dog

2 жыл бұрын

All you have to do is swing the rabbits around your head at a moderate fraction of the speed of light, and you get a handy anti-rabbit

Fun fact: Phi (1.618) is really close to the ratio between miles and kilometers (1.609) which means you can use adjacent Fibonacci numbers to quickly mentally convert back and forth between them. For instance: 89 miles is nearly 144 km (it's actually 143.2), or 21 kilometers is roughly 13 miles (13.05). You can even shift orders of magnitude to do longer distances! e.g., 210 miles is around 340 km (multiplying 21 and 34 by 10) which is close to the actual answer of 337.96 km.

@witerabid

3 жыл бұрын

🤯

@nuklearboysymbiote

3 жыл бұрын

OH MY GOD

@Kebabrulle4869

3 жыл бұрын

I use this trick all the time, it’s so useful

@jonathanfeller

3 жыл бұрын

I find it easier to just do x+(x/2)+(x/10)

@XMarkxyz

3 жыл бұрын

Finally a good way to do it quickly, but I still think the imperial units are hideous, just a little less than what I thought before

φ : Let's see what's at the end of this infinite sum... φ : π!? π : Hey. φ : What are you doing in complex space? π : I work here. It's my job to be here at all times.

@weckar

3 жыл бұрын

π : I was here long before you got here, and will be here long after you leave.

@mr.champion7304

3 жыл бұрын

*rational numbers in geometric sequences intensifies*

@FourthDerivative

3 жыл бұрын

"Wait, it's all pi?" "Always has been"

@sharpfang

3 жыл бұрын

C'mon. You've messed with complex numbers. How are you *not* expecting a π there? Also, mandatory e, this time wearing the disguise of 'ln'

@lucyf6516

3 жыл бұрын

sharpfang dude most people don’t intuitively know that pi has something to do with the complex plane lol. I’m sure you’re very smart. Here’s a gold star ⭐️.

Missed opportunity: you could have had your amazed face trace the path of the graph shown on the screen at the time.

@jamesthomas3871

3 жыл бұрын

I think he tried. It was awfully close, wasn't it?!

@arranmcgown2386

3 жыл бұрын

I thought he was going to

@pronounjow

3 жыл бұрын

He sure Parker Squared that one!

I have to say, I'm a tiny bit disappointed that his amazed face didn't follow the graph. It even pointed at his face! 6:45

@trickytreyperfected1482

2 жыл бұрын

Love the name

this aint no sit down maths. we standin up now

@Vaaaaadim

3 жыл бұрын

Rise up gamers

@volodyadykun6490

3 жыл бұрын

I think Matt isn't stand-up comedian, he's sitting all the video, he's more of sit-down comedian

@thecuriousgorilla6005

3 жыл бұрын

Calm down Nolan

@standupmaths

3 жыл бұрын

Ha. I’m filming in a small room at home during the lock-down.

@demonking86420

3 жыл бұрын

He's doing the Parker Square equivalent for standing up (dead meme I know)

I was waiting for the line, "And so I contacted Ben yet again and for some reason he blocked me and stopped responding to my e-mails."

I've always preferred the 0, 1 start. With these numbers often found in nature, adding a moment of creation feels profound.

@rarebeeph1783

2 жыл бұрын

it also feels even simpler than a 1, 1 start, like if you had to enumerate all the possible starts, you'd start something like "(0, 0); (0, 1)"

@KarstenJohansson

Жыл бұрын

I think both are found in nature. In some spiraled plants, there is a gap in the center which is effectively 0. Others have something in the center which is effectively 1. Until your comment, I'd never considered that. I'm pretty sure that the vast majority of fib-nth() functions consider the 1st nth to be 0.

The line looks like my Doctors Signiature

@georgplaz

3 жыл бұрын

underappreciated comment!

@AlanTheBeast100

3 жыл бұрын

Looks like my doc's prescription for ... well anything and everything.

@Darqice

3 жыл бұрын

I'm actually thinking of trying to align my signature to this plot just for my internal giggles :D Would also make a nice company logo.

The synchronized "Matt Parker's Maths Puzzles" cards were... _chef kiss_

@standupmaths

3 жыл бұрын

thankyouverymuch

@caster-

3 жыл бұрын

I hadn't even noticed! Very nicely done!

@Danilego

3 жыл бұрын

6:49 this is so oddly satisfying

@Nate9273

3 жыл бұрын

MammamiaDasAhSpicyMeatball

@hecko-yes

3 жыл бұрын

a channel after my own heart

The Fibonacci convention was huge this year -- it was as large as the previous two put together. ThankyouladiesandgermsI'llbehereallweektrythechicken

@zaraak323i

3 жыл бұрын

Tipyourwaiters!

@quesoestbonne

3 жыл бұрын

@Idiot Online Wondering Aloud 👏, 👏, 👏👏,👏👏👏,👏👏👏👏👏,👏👏👏👏👏👏👏👏,👏👏👏👏👏👏👏👏👏👏👏👏👏.....

@stevemattero1471

3 жыл бұрын

Wait there's a fibonacci CONVENTION??? When and where!?

@demonking86420

3 жыл бұрын

Oh get the heck out, I just got that

@Lawrencelot89

3 жыл бұрын

@@stevemattero1471 Location: just add the coordinates of the locations of the last two conventions. Time: just add the dates of the previous two conventions to get the new date.

This reminds me of an experiment I did with Conway's life. I started wondering what would happen using the standard life rules with a bounded game, but set a cutoff for how many steps the game would iterate. I then took the union of each iteration of the previous game to create a seed for a new game, and continued to repeat the process. I mainly was doing this to see if you could use GOL to generate interesting height maps when I found an interesting property. For some reason if my iteration value was 2 meaning 2 distinct steps after the initial state to create a new input, the mean value of my bounded inputs approached pi. When they surpassed pi they would eventually trend back down to pi. I have no idea why pi arose because I am not that skilled at math, but I still wonder why that generation of inputs for a board state would trend towards it. The most I discovered was that method of generation retained symmetry if it existed in the initial board state meaning a blob in the very center would create symmetry along the diagonal, horizontal, and vertical axes.

@av3stube480

3 жыл бұрын

Okay I lack the mental capacity to imagine what you did but I'm really interested in why would Pi appear there...

@adityaekbote8498

2 жыл бұрын

Yo idk what you are saying but that looks exciting let us know if you find anything

@creativenametxt2960

2 жыл бұрын

Interesting. Would you provide more details?

@pranavkondapalli9306

2 жыл бұрын

you did an experiment with 'Conway's life' lmao what PS: ik what GoL is

@trickytreyperfected1482

2 жыл бұрын

@@pranavkondapalli9306 wow, I didn't even notice that first read through. That's an unfortunate typo for OP to make.

The Binet formula for the Lucas sequence is actually simpler than the Fibonacci sequence: (ϕ)^n + (-1/ϕ)^n = nth Lucas number

@yogi30051972

Жыл бұрын

That's amazing.

Now I want to see a 3b1b style animation of the 2d inputs moving around to their 2d outputs

@fibbooo1123

3 жыл бұрын

One of the “results” of the 3b1b videos is exponentiation moves complex numbers around in circles- so presumably like that? But maybe not since there are 2 exponentiations being added

@volodyadykun6490

3 жыл бұрын

Also just all the colours ordered as inputs mapping to their outputs

@violetsteele350

2 жыл бұрын

He commented on this vid. You could comment on his commeng

Can we just take a moment to appreciate the editing involved for the amaze face

@Woe_YT

3 жыл бұрын

Its actually pretty simple, you just cut a still from a frame of the video and then move it to the time and place in the video in reverse. It is a cool effect though.

Gosh darn it, now I want to look at Fibonacci quarternions!

5:34 this excites me uncontrollably it's impossible not to smile

@tony_yt5967

2 жыл бұрын

“Ofc you’re dividing it by the sq root of 5, big fan!”😂😂made me happy made me smile nice 👍🏽

Heh, that random pi at the end. That's something I love about maths, if you're ever hungry you never have to go far to find a delicious pi.

@vblaas246

3 жыл бұрын

I want to know why though. Is it because every periodic system has a (circumpherence/2r)*dt relation? What about an 'oval', it can always be projected back to a circle right? Giving you a pi in every periodic system somewhere?

@TheBasikShow

3 жыл бұрын

V Blaas I’m not sure exactly why this particular pi shows up, but complex analysis is absolutely riddled with pi so it isn’t that surprising. In particular, this function is made of exponentials, and complex exponentials are inextricably linked with pi.

@ottolehikoinen6193

3 жыл бұрын

2/5ths make it sound he could've used τau and get rid of the pesky 2.

@wilddogspam

3 жыл бұрын

@@ottolehikoinen6193 2/5 * 1/π =4/5 * 2/τ though.

@criskity

3 жыл бұрын

@@TheBasikShow I remember when I took Complex Analysis in college, the answer to the exercises we did was almost always pi. If not, it was zero, 2pi, or pi/2.

I've always been a fan of the 0, 1 start, glad to see it got some recognition

@andymcl92

3 жыл бұрын

I too like that start, although the 1,1 makes most sense with the origin story (breeding rabbits).

@OscarCunningham

3 жыл бұрын

@@andymcl92 In the 1st generation you have one pair of young rabbits and no mature rabbits. So in the 0th generation you must have one pair of mature rabbits and one pair of young antirabbits. Then the mature rabbits give birth to the young pair we see in the 1st generation, but there are no mature rabbits left in the 1st generation because the antirabbits grow up and annihilate them.

@Chris_Cross

3 жыл бұрын

But to me, it doesn't seem like it should work. The reason there is the two "1"s is because there's nothing before it. So if you start at 0, there's nothing before it, so you put another 0. "0, 0". But then, if you try to make the sequence by adding the two previous numbers to get the next, it just becomes and infinite string of "0"s.

@peglor

3 жыл бұрын

I like to start with two zeros - makes the maths much simpler...

@crustyoldfart

3 жыл бұрын

Why not make it completely general and start with the integers A,B ? So the series progresses A,B,A+B,A+2*B,2*A+3*B,3*A+5*B.... And we see that adjacent Fibonacci numbers occur in the coefficients. We can legitimately make A,B anything we chose including +ve and -ve values chosen at random.

The positive only values look like a growing spiral from the side, while the negatives create a spiral we serve head-on. If you used them as different POV, you could maybe plot out the tips of leaves or the sharp bits of a pinecone. It's really neat..

I love that you've made a living of messing around with interesting numbers and sharing it with us. I used to do things like this on my TI-86 graphing calculator, but never got far enough to make these kinds of incredible graphs (it was far beyond my mathematical understanding). Thanks for sharing your passion!

To explore this further would clearly require a large investment of time and effort. I suggest you apply for a Grant. Sanderson, ideally.

@pamdemonia

3 жыл бұрын

I see what you did there and I approve!

@anirudhranjan7002

3 жыл бұрын

For those who don't know, Grant Sanderson is the host of 3Blue1Brown

@anuwamy969

3 жыл бұрын

@@anirudhranjan7002 he already comment

19:44 Here comes Matt’s π day calculation 2021.

@twojuiceman

3 жыл бұрын

I thought the same thing. Use that absurd formula for area under the curve to calculate pi

Very interesting, that plot of the Binet sequence appears to spell out 'Jeremy Bearimy'...

@pedrosso0

2 жыл бұрын

Jeremy Bearimy you say?

Matt just looks so happy, and it makes me happy. This is actually a really cool find! Well done!

The ‘face’ bits were great. Nice effect.

Find someone who looks at you with the same excitement that Matt gets around numbers.

@georgplaz

3 жыл бұрын

with detached heads floating in space? no thanks!

This is just such a cool maths revelation, with an amazing payoff and one of the absolute best editing jokes I've ever seen. That's pi outta pi from me, even if I apparently can't read 3d plots very well.

6:44 actually looks like an inwards spiral beeing (exponentially) accelerated to the right

@PiercingSight

3 жыл бұрын

That was my thought too. Could help explain why pi shows up a few times. The Fibonacci numbers may just be a 1d slice of a 2d projection of a 3d spiral.

@mryellow4633

2 жыл бұрын

Wow interesting observation. Meanwhile the negative numbers in the Binet formula formed an actual spiral 7:09. If the positive inputs can be described as an "inward spiral" then the negative numbers would be an outward spiral.

@kylecow1930

2 жыл бұрын

Yeah it is!!, the (-phi)^-n term acts as a spiral exponentially decresing in radius and the phi^n acts to push the centre of the spiral to the right exponentially

"What a stupid idea! Who wants a video about Fibonacci numbers at 3 in the morning!?" Matt Parker: "Oh boy, 3 AM!"

@soupisfornoobs4081

3 жыл бұрын

Now me at GMT+2, knowing sleep is a social construct

@alexandermcclure6185

Ай бұрын

Literally anyone awake at 0300 just wants something to do.

3Blue1Brown has a nice way to represent 4D graphs. What he does is draw the transformed gridlines of the input space. It's like what you did with the graph with the real number line as input.

@olmostgudinaf8100

3 жыл бұрын

Did no one think of using colour for the 4th dimension?

@MPSpecial

3 жыл бұрын

He also used colour gradients in another video (about finding the zeros of a complex function I believe)

@f.p.5410

3 жыл бұрын

Those graphs don't always look good, and they can even be more confusing for non-injective functions. Watch 3b1b video on Riemann's zeta, the map looks cool but it doesn't tell you anything about the function. You can't really recognize slopes and shapes, it's a mess. Unfortunately, this function looks like the kind of function which would be too messy to represent as a grid mapping.

@f.p.5410

3 жыл бұрын

@@olmostgudinaf8100 Yes, and it's really useful from a topological perspective. For example, a Klein bottle is quite intuitive if you colour the overlapping part because you can see the neck part moving in the "colour dimension". It's less useful for complex functions because you can't really see slopes. It's hard to tell if a colour is shifting at a parabolic/exponential rate. It's still used a lot through a plotting technique called domain colouring, but it's still not a perfect way to plot complex functions. There isn't a perfect way unfortunately, you'll always have some drawbacks.

@teamupleft7097

3 жыл бұрын

What about two overlapping 3d surfaces attached to the 2D complex plane? Like the thumbnail for this video but with one real surface and one imaginary surface.

That was really sweet. I saw the title and started trying to imagine an equation describing a curve like that, with zeroes where the Fibonacci numbers are. Didn't realize that such an elegant parameterized version already existed.

I love your enthusiasm, my dude. Keep learning, growing and challenging yourself and others! :)

You could utilize time representing one variable. An animated 3D graphic may be used to visualize a 4D equation.

@himanbam

3 жыл бұрын

You can kinda already do that with his program by sliding the complex input value.

@sherlock_norris

3 жыл бұрын

Or you can colorcode the complex plane and then color it according to the complex output.

@elvis_mello

3 жыл бұрын

That seems like something a physicist would do

@buddyclem7328

3 жыл бұрын

Yes! I want to see this!

@davidpalomino9138

Жыл бұрын

While this does work in theory, it's not going to be like what most may imagine. Since the full plot is a 2D manifold embedded in 4 spacial dimensions, a 3D cross section would just be a 1D manifold embedded in 3 spacial dimensions.

playing buttercup while he does the amazed face... LMAO

@zozzy4630

3 жыл бұрын

Started reading through the comments hoping someone had already ID'd the song for me. Thank you

@ALZlper

3 жыл бұрын

@@zozzy4630 You mean Darude Sandstorm?

@Rabbit-the-One

3 жыл бұрын

@@ALZlper I think he does indeed mean Sandstorm by Darude.

@colinsanders3124

3 жыл бұрын

@@ALZlper The song is Buttercup by Jack Stauber

@colinsanders3124

3 жыл бұрын

@@zozzy4630 kzread.info/dash/bejne/l2alqZeup6eph5c.html

1:34 I just love Matt's humor, where he randomly does stuff, never addresses it, etc. Plz never change

Love the various faces. Nice video editing! The goodbye face kept me watching all the way through the Jane St. promotional-a first for me. Nice audience hook, Matt!

i just realised that the curve that goes through 1 twice is actually a spiral/cone looked at from the side :D

@Microtherion

3 жыл бұрын

I think it could even be described as an 'epicycle'. (Oy, Ptolemy: no! I respect your attempt to maintain the geometric integrity of our planet's immediate locality, but if you was to come round here, and start arranging *my furniture* into a highly idiosyncratic theological exegesis, I would say - 'Ptolemy, nooo! Outside now! You are not in the bustling multicultural milieu of ancient Alexandria. This is Lambeth. Now get your pharaonic physog out of my impromptu courtyard knees-up, you stripy antediluvian muppet!' Etc). :)

The way Matt's goodbye face's hand was animated was wigging me out for some reason. Does not tarnish the good maths though.

@MCAndyT

3 жыл бұрын

Really kept my attention while he did the sponsored portion. Very clever, that one...

@fennecfoxfanatic

3 жыл бұрын

That animation kept me on my toes! More intense than the bouncing dvd logo

@gordonrichardson2972

3 жыл бұрын

Gordon Wiley Tom Scott did a video on green-screen perspective errors being creepy.

@kuromurasakizero9515

3 жыл бұрын

it seemed like it was both timed to the beat of the music and slightly off at the same time. Methinks he learned a new editing trick and enjoyed it a lot :)

@partywumpus5267

3 жыл бұрын

@@kuromurasakizero9515 definitely looks like he's having a fun time with it

When I learned Fibonacci sequence in 99 (i was 15), I tried to extended backwards, but I lacked the math to understand this whole "bi infinite" sequence. Watching this video was a real time travel to the past. Nice work!

Very informative, lots of effort put in. Some of the best math content I've seen.

The "other" thing I loved about this was the "how we got there" story. A great example of the mindset to approach problems scientifically and what to look for :)

@OH-pc5jx

3 жыл бұрын

Yeah I really liked this video start to finish - but I *really* wish he’d done a domain colouring/colour wheel plot!! I find them so much more intuitive

I “enjoy” math and this is WAY out of my understanding of math ,but I just love the content. Thank you!

@Ragnarok540

3 жыл бұрын

I was going to say this is not complex at all but yeah, is a bit complex. Get it? Is easy, thought, except for the 4D visualization part.

@sebastianjost

3 жыл бұрын

@@Ragnarok540 4d visualization can be done a lot better when using colors. I've explained that in this comment section before so I won't do it here again. But if you search, you will find how it's done.

@carrotfacts

3 жыл бұрын

@@Ragnarok540 For someone who watches math youtube videos for fun, it's quite difficult. Glad you get it so easily, though

@tirocska

3 жыл бұрын

@@carrotfacts Could you explain which part(s) you find difficult? Just curious.

@andrewosborne1447

3 жыл бұрын

I mean, all he did was say “here’s a solution to a recursion. It’s continuous on C”.

I love your videos! I don't really understand the complex maths involved, and I don't think I ever will get to. But maths really spark an interest and curiosity in me, I love to learn more and take a peek into this otherworldly stuff!

Was able to graph the 2D slice with real inputs, working on the complex input/complex output graphs excellent project thank you Matt!!

90% of the budget for that amazed face effect at 6:47 Edit: I stand corrected 7:28 btw for plotting complex functions, I've been trying for a while to make a program the plots the path of f(x + ti) in 3D where t is just the time. This could be a 4D plot

@louismichaud9379

3 жыл бұрын

What is the song called

@leomadero562

3 жыл бұрын

Buttercup

The amazed face absolutely cracked me up!!!

This is so awesome. Love the energy and passion. ❤️

Beautiful! I never thought about using anything other than positive real numbers in the Fibonnaci sequence until today.

Matt! You are already in python. Take a look at the library "matplotlib" it can do zoomable/movable 3D plots directly from python.

@vibacourtney-battista6918

3 жыл бұрын

What software could I code an interactable fractal zoom using python?

@RubenMoor

3 жыл бұрын

Seems crazy to me to rely on excel when you have matplotlib - or at least I wouldn't admit it 😬

@andrewosborne1447

3 жыл бұрын

Matplotlib, pandas, numpy.

@ThaiNguyen-bl1pi

3 жыл бұрын

Ruben Moor you underestimate the obsession of Matt with Excel

It hit me near the end how good of a job you've done of editing this. The virtual plot that you're actually pointing to points on like a weatherman. Also I suspect you just learned how to do the face thing and it's really cool.

It's insane how often pi shows up in any level of math. Funnily enough it's the first example I given when helping students to better understand infinite series and what they're useful for (alongside Euler's identity). Very cool video that I wish I wouldn't have waited so long to watch.

@nutronstar45

Жыл бұрын

always with a 2.

Hell yes! Been thinking about this for two years but couldn’t visualize it without the tools!

What I would do is the way 3blue1brown did the display of the Zetta function: start with a grid in the complex plane, and animate distorting it

"A third" incorrectly stated as 0.333, yet time stamped at 03:33 is some fine trolling... 🧐

@i_booba

3 жыл бұрын

That's some fine detective work also, dang.

I really enjoyed the graphics/effects this video, along with the content 👍

6:50 - next level videoediting - I love it

Matt: Uses Python for computing the values Also Matt: Uses Excel to plot the values computed using Python We need to talk about Matplotlib. Or should I call it Mattplotlib?

@silverzero9524

3 жыл бұрын

Mattdoesntplotlib

@MaxDiscere

3 жыл бұрын

Matplotlib sucks, excel is far better if you want to be fast

@trueriver1950

3 жыл бұрын

@@MaxDiscere Agreed Excel is great for a fast and dirty first look. But it's no good at all if you want to be able to zoom, change point of view, etc

@iabervon

3 жыл бұрын

Mattplotlib will give you graphs that are interesting and look good, but if you happen to look at them diagonally one of the ways, they don't quite add up. Also, some of your numbers appear in two places for some reason.

@pascalschetelat7198

3 жыл бұрын

Wow, lots of people here need to learn to use matplotlib which is arguably both faster and and more powerful than excel. Plus it is interactive and give nice looking graphs

I love how excited Matt is about everything.

This is one of the awesome channel in you tube and I love it and learn from it. Thank you so much sir.

That first graph made me the most excited I've been about math, *ever!* :D

6:29 this is the shadow of a spiral (3D onto 2D plane). Then the next part of the video shows a spiral, which is still a shadow of the spiral, but seen from a fairly easily guessed angle in 3d space.

@timh.6872

3 жыл бұрын

That's a good catch! It does look like a projection of a decaying helix.

@atomictraveller

3 жыл бұрын

i saw nonlinear damped mass spring (have a vid on using quadrature osc to appx sine and cosine) s0 = 1.f; s1 = 0.f; // init s0 -= w * s1; s1 += w * s0; // loop .. where w = angular frequency 2 * pi * hz / samplerate

This was one of the coolest Fibonacci maths I've ever seen!!!

This is so cool. Thank you for making this video

LOVED this video my dude! Thank you!

If the surface have not a name yet It could be named "the Parker's Blanket"

This guy went insane. Really maths “y”. Imaginative. I love how he opens he mouth to show his excitement.

Loved the 3D representation of a 4D concept, super cool Would love to see a follow-up video with bigger graphs!!!

6:45 Liked and subscribed just for that meme. Good job, Matt :D

Can't wait to see the quaternionic version of this video!

@angeldude101

2 жыл бұрын

Quaternions don't really add much beyond more complex planes (which is very useful when doing 3D rotations). The dual and split-complex numbers on the other hand do have some interesting behavior, but neither can act as a square root of -1.

I’m wondering what are the properties of the loop that the two 1’s form... I don't know why, but it was the part that I found the coolest

@theot1692

3 жыл бұрын

I wonder what the area of the loop is

@richardpike8748

3 жыл бұрын

@@theot1692 I was about to say this lol. I also wonder the area of the loop. And if you wanted to go deeper I guess you could also do analysis of curvature, length, etc... never know what you might find.

@gajbooks

3 жыл бұрын

The real question is does the loop shrink in the complex plane, and if so where does it reach zero size?

@richardpike8748

3 жыл бұрын

@@gajbooks volume of the loop? o_o

@hwliebenberg5487

3 жыл бұрын

I dont think the line crosses the x axis at all, I believe that from the point of perspective where you looking from the X/Y axis vantage point it looks like it crosses the x-axis, but it doesn't, it loops around it, just like a inverse spiral if looking from the vantage point of Z/Y axis. (I dont know, it just looks like it)

Wow! That's amazing and cool! Those are neat looking graphs! 👍🏼😀

I loved this video!! THANK YOU!

Nice new point of view, thank you :). Also, by the way, in the log abs plot, you can see the two binet terms as two planes, which I find constructive. Remark: Personally I like to plot the abs and use colors for the output phase, to keep it 3d. It distracts a little bit from the phase, but often you don't really need it, and e.g. with the log abs you can see the zeros and poles quite well.

@MajikkanBeingsUnite

2 жыл бұрын

That sounds awesome! 😸 It will both show the angle and make it 🌈rainbow, which automatically boosts the awesomeness of a mathematical plot by about omega! Sadly, no version of Geogebra I've ever tried can make multicoloured outputs 😿 so it's gonna have to be a new file, not an updated version of this particular interactive.

I never expected that the graph of the negative positions of the fibonacci seqeuence would give a fibonacci spiral, amazing!

This is one of my favorite channels specifically because I think this is the only person I've ever seen excited as I get for math

This should have been in my complex analysis module. Also, the limit of the integral of the Binet function - mind blown 🤯

Hey Matt, looks great. However, you should try taking the logarithm of the absolute value, when plotting, since the fibonacci series is an exponential series and thus diverges quite fast. That would also help showing the zeroes and the "waves" you can see in the function.

@joshcork2201

3 жыл бұрын

This works when the output is large, but for small values, log is a very large negative number. Furthermore log is undefined at 0.

You’ve likely already heard of it, but you could also look at the 5-adic interpolation of the Fibonacci numbers; this yields a 5-adic continuous function in fact! Really cool stuff. Unfortunately, I think you‘d run into the same difficulty (or more) getting a visualization of the result.

ok i really like the buttercup challenge thing you had going on, I've been listening to a lot of jack stauber recently and I thought it was really cool to see one of his songs appear in one of your videos!

That loop in the graph is mind-blowing!

In regards to where Fibonacci starts, I’d always been taught it starts 0 1.

@ComradeTiki

3 жыл бұрын

Zero indexing... nice.

Trippy. You kinda lost me when you started plotting 4D, but I stayed an it was cool. Way over my head, but cool. I loved the limits at the end. Gorgeous. No wonder some folks believe there is something magical about these number. It is pretty.

Great video, as always!

Amazing! Good work!!

9:00 you could use a 3d plot with the input complex n being the 2d surface of the x-y plane, and the z axis being one output, and then either use some color gradient for the other output instead of a 4th dimension, or animate the 3d plot over time as the 4th dimension so that we could get some idea of how it changes as you slide along that 4d axis. I've done a bit of this sort of sliding through the 4th axis by animating with 3d slices to show simple 4d objects like hyperspheres in wolfram mathematica, but my trial has expired for that and I haven't gotten around to learning python yet to do it myself. Loved this video!!! Edit: you (and Ben) did some stuff like this, I just commented too early lol.

@revenevan11

2 жыл бұрын

Re-watching this video, I'm realizing how close I was to pushing back into the negative numbers when I was learning about the fibonacci sequence! (Basically, as a kid, I realized that 0, 1, 1.... was more of the fundamental starting point, so when I wrote my fibonacci generator on my TI-84, I started with 0 and 1 😁)

I can't believe you did all of this teasing and then didn't show the plot across the line containing the zeroes

This deserves a double like... Nice job Steve

I like how at 1:35 it is perfectly synced between the text in the previous video and the current video

Very cool. You could probably use time as the fourth dimension of the graph by animating it. It wouldn't be exactly the same thing, but it would bwe about as close as you could get.

First time I’ve seen e, pi, and phi all together like that

I was taking a course regarding the Laplace Transform , lo, about 40+ years ago, and, as a part of it, the prof introduced the notion of "difference equations" (cf. "differential equations") and the difference equation analog of the LT called the "Z Transform". As he went into the idea, I realized that you could use the Z transform to redefine a Fibonacci sequence as a function of the two initial values (this was a variable Fib sequence, not just the uniform standard one) and the "n-th" value you wanted -- that is, rather than have to calculate all the intermediate numbers, you could get the n-th term by simply plugging in N, F-sub-0 and F-sub-1. And, in fact, this was the subject for the next day's class/lesson. I always love it when I see where the class is going ahead of time. Not sure if that can be turned into a segment, but you might enjoy looking over it either way. Transforms are pretty cool things. And the LT is actually pretty primitive, being one of the first tools invented to manipulate, analyze, and understand the concepts of differentials.

The best I have seen in this series

You give "domain coloring" a try next time you want to visualize functions of complex numbers.

I was surprised at how easy it is to graph in Desmos: \frac{\left(\phi^{t},0 ight)-\frac{1}{\phi^{t}}\left(\cos\left(t\pi ight),\sin\left(t\pi ight) ight)}{\sqrt{5}} Set your preferred boundaries for _t_ Or, if you want animation, restrict _t_ to [0,1] and replace every instance of _t_ with _at_ for some variable _a_

Still my favorite stand up maths video. That loop de loop is insane!!

Tiene mirada de loco, pero sus vídeos son amenos y muy educativos. Well done, Matt. Thanks, wholeheartedly!