One-bonacci, two-bonacci, three-bonacci, four. Five-bonacci, six-bonacci, seven-bonacci, more.
@assassin01620
6 жыл бұрын
One-bonacci, two-bonacci, three-bonacci, four. Four bonaccis make a metallic ratio and so do many more!
@jeremyheminger6882
6 жыл бұрын
"Metallic Ratio" is the name of my new Tool tribute band.
@MisterAppleEsq
6 жыл бұрын
Nice.
@fossilfighters101
6 жыл бұрын
Woah Mister Apple what're you doing in this comment section?
@Pfhorrest
6 жыл бұрын
Are you going to produce n-bonacci variants of Lateralus?
@clyde8759
6 жыл бұрын
Jeremy Heminger lol
@MisterAppleEsq
6 жыл бұрын
+fossilfighters101 I mean, right now I'm replying to your comment.
@Artifexian
6 жыл бұрын
Amazing! Had no idea these existed.
@cuzeverynameistaken1283
6 жыл бұрын
Had no idea you watched numberphile. Ive been following you since 4000 subs
@harry_page
6 жыл бұрын
Hey Edgar!
@Artifexian
6 жыл бұрын
Yup! Numberphile is one of my favourite channels.
@natheniel
6 жыл бұрын
It's one of everybody's favourite channels!
@unvergebeneid
6 жыл бұрын
PBS Infinite Series had a video on these. If you like Numberphile, you'll probably also like them!
@matin563
6 жыл бұрын
I also like the fact that the golden ratio is pronounced as *fi* (phi) and it can be found in the *fi* bonacci sequence
@damianzieba5133
2 жыл бұрын
That's why it is called fi
@EtienneBotek
2 жыл бұрын
@@damianzieba5133 phi is for Φειδίας
@PC_Simo
Жыл бұрын
So do I 😎. Φbonacci.
@alexandermcclure6185
Жыл бұрын
@@PC_Simo Shouldn't it be φbonacci instead of φibonacci? φ sounds like fi, not not f.
@PC_Simo
Жыл бұрын
@@alexandermcclure6185 True. I think my train of thought changed, mid-word. 🤔😅 *EDIT:* I made the correction ✅😌👍🏻.
@AdeptAscent
6 жыл бұрын
This video and the golden ratio (why so irrational) video were the most fascinating two videos I have ever seen on this channel. I hope you guys do more videos on these metallic ratios and how weird they are
@markiyanhapyak349
5 жыл бұрын
They aren't weird; They are constant.
@flymypg
6 жыл бұрын
I especially love Numberphile videos that provide generalizations, revealing the wider mathematical landscape extending from and encompassing a better known starting point.
@jamezer7revel471
6 жыл бұрын
The ratios are winning some medals here
@Advection357
6 жыл бұрын
Just the gold counts.. the rest are participation trophies
@thelastspartanS117
6 жыл бұрын
Hopefully no one MEDDLES in the award ceremony
@thelastspartanS117
6 жыл бұрын
Im sure the ratios have the Mettle to withstand such buffoonery
@anticorncob6
6 жыл бұрын
It’s Gold = 1 Silver = 2 Bronze = 3 Just like medals in the Olympics.
@debayanbanerjee
6 жыл бұрын
Jamezer7 Revel I think you meant 'metals'. Not medals. ;-)
@TheInselaffen
6 жыл бұрын
Britain; home of the Aluminium Falcon.
@halyoalex8942
3 жыл бұрын
Sounds like an odd crossover of Iron Man and Falcon from Marvel...
@WolfWalrus
6 жыл бұрын
Of course, the Golden Ratio has the special property of allowing [Infinite Spin] according to the ancient Zeppeli family technique
@zanly5039
4 жыл бұрын
and the silver ratio allows for the almost-infinite spin
@rubenbohorquez5673
4 жыл бұрын
@@zanly5039 ah yes, the TREE(3) spin, not infinite, but stupidly big!
@roskataka2574
4 жыл бұрын
I see what you did there, fellow JoJo fan :
@ramiroseltzer5278
4 жыл бұрын
the Golden Ratio also allows cripples on a horse and a wheelchair to walk... its amazing what math can do
@yazanabdalluh6251
2 жыл бұрын
@@zanly5039 no its for polnareffs silver chariot to spin
As a marine biologist, I love these. Forms like this pop up all over the undersea world, especially among invertebrates. Well done!
@WhiteChocolate74
2 жыл бұрын
Ocean studies are underrated 💙
@rhods23
6 жыл бұрын
surely then, the 49° one should become the peregrine ratio?
@fossilfighters101
6 жыл бұрын
Ooh yeah!
@TheOzumat
6 жыл бұрын
It needs to be named after a metal. Aluminium is actually really nice for this purpose, as it's associated with aviation, which in turn is associated with birds.
@theRealPlaidRabbit
6 жыл бұрын
Or "Pippin" for short.
@benjaminmiller3620
6 жыл бұрын
Compromise and call it the Aluminium Falcon ratio?
@rewrose2838
4 жыл бұрын
@@benjaminmiller3620 Peregrin-inium
@OlbaidFractalium
6 жыл бұрын
Wow! I did not know The Great Wave of Hokusai is geometric designs.
@WildAnimalChannel
6 жыл бұрын
yeah, if you fudge the results enough.
@donaldasayers
6 жыл бұрын
Looks more like a dragon curve to me.
@pleindespoir
6 жыл бұрын
Hokusai >>> Hokuspokus
@BainesMkII
6 жыл бұрын
Yeah, there was a *lot* of fudging required to make that painting fit the desired spirals. The best match was the middle spiral, and even there they had to cheat by jumping from the inside to the outside of the wave to get an overlap that ran for more than two and a half "squares". To fit the big spiral, they had to use two completely separate waves, half the length of the spiral matched nothing, and half of one of the waves didn't match. The small spiral didn't match at all; you could have claimed numerous random shapes matched as well as that small spiral.
@genghiskhan6688
6 жыл бұрын
Isn't it Kanagawa?
@SteamPunkLV
6 жыл бұрын
omg I hate when my nails looks like goddamn polygons xD
@ziquaftynny9285
6 жыл бұрын
Yeah, I didn't know people trimmed their nails like that. I usually cut them by the side then tear the rest off.
@munro22
6 жыл бұрын
Ziquafty Nny that’s not human
@ziquaftynny9285
6 жыл бұрын
No u
@EchoHeo
6 жыл бұрын
Ziquafty Nny yes me
@UnderscoreZeroLP
6 жыл бұрын
I bite my nails. So much easier
@angst_
6 жыл бұрын
So, I love the format of your videos! Someone who's passionate about something explaining it to the viewer/Brady as if just having a conversation. Brady seems to talk juuust enough and asks the perfect questions to make the conversation flow. Plus these recent animations are top shelf art!
@DeathlyTired
6 жыл бұрын
All of these ratios are very important, integral even, to design in modern artisitic origami; especially the most usual kind that develops from a single, uncut square, to the finished model. You could perhaps talk to luminaries of the field such as Dr. Robert Lang for the intersection betweeen mathematics, origami, and it's real world applications.
@markiyanhapyak349
5 жыл бұрын
Wow!
@brnsndwch
5 жыл бұрын
6:40 P=NP solved
@efulmer8675
3 жыл бұрын
Hah. That made me laugh.
@pakfu
6 жыл бұрын
I’ve been on YT for like 12 yrs and this ranks in one of my favourite videos ever. Thank you so much.
@leoangere5310
5 жыл бұрын
"Copper, nickel... aluminium?" That one cracked me up. Awesome content as always. I'll have to use these metallic ratios in my photo cropping (I've used the golden rectangle but then defaulted to boring ratios like 1:2, 1:3, etc.)
@benjaminolanderrasmussen3049
6 жыл бұрын
What would the ratio for the phi-bonacci sequence be called?
@ericluque6573
6 жыл бұрын
i was thinking the exact same thing
@benjaminolanderrasmussen3049
6 жыл бұрын
Eric Luque. When you remember the numberphile videos that you have recently watched :)
@heyandy889
6 жыл бұрын
the very golden ratio
@primarysecondaryxd
6 жыл бұрын
The golden-golden ratio. Plug it in to (N+sqrt(N^2+4))/2 - > The golden golden golden ratio, plug it in to (N+sqrt(N^2+4))/2 -> The golden golden golden golden ratio. Etc.
@BubbaJ18
5 жыл бұрын
Or π-bonacci?
@hayleys_comet276
2 жыл бұрын
It seems kind of interesting that that Silver Ratio has the square root of 2 in it, the Golden Ratio has the square root of 5 (I think that’s what it was) in it, and the Bronze Ratio has the square root of 13 in it. I think those are all Fibonacci numbers. It probably doesn’t mean anything though because I don’t know much about math yet.
@jerombastiaansen9495
5 жыл бұрын
7:20 That's the solution to x² - Nx - 1
@ultra6334
2 жыл бұрын
Wow, makes so much sense, as phi's value is x^2 - x - 1, you just multiply that degree 1 x with some number to get these ratios
@matthijshebly
6 жыл бұрын
The continued fractions are cool too and worth a mention: Golden ratio: 1 + 1 / (1 + 1 / (1 + 1 / (…))) Silver ration: 2 + 1 / (2 + 1 / (2 + 1 / (…))) Etc. Furthermore, you could expand into real numbers, with e.g. 3/2 giving an alloy of Gold and Silver, i.e. Electrum: 0, 1, 3/2, 13/4, 51/8, 205/16, 819/32, … which quickly converges to a ratio of 2. Let's call 2 the Electric Ratio. The numerators of the fractions follow an interesting pattern: 3 * 4 + 1 = 13 13 * 4 - 1 = 51 51 * 4 + 1 = 205 205 * 4 - 1 = 819 Etc.
@wanderingrandomer
6 жыл бұрын
Ahh, this makes more sense People would always overlay the golden ratio spiral over everything, even when it didn't fit, and it never made any visual sense to me. Now I know why... long story short, idiot conspiracy theories who know nothing about maths have been misleading me to the nature of logarithmic spirals.
@MarvinFalz
5 жыл бұрын
The golden ratio also appears in photography, which I wouldn't call idiotic nor conspiratory, but maybe in need of aditional information. But I would call New Age idiotic, since some New Agers use the fibonacci sequence as well as elements of quantum physics as proofs for their New Age teachings.
@mwu365
4 жыл бұрын
your short story was as long as your long story
@Homs86
4 жыл бұрын
same here. woodworking school is kinda obsessed with the golden ratio bcs"so pleasing" blabla finally there is light :)
@bruhmoment1835
4 жыл бұрын
Well, it IS a JoJo reference
@zyrota4295
2 жыл бұрын
I love watching this channel because it makes you feel as if you stopped by the maths nerd's office and they just started to explain to you this cool math thing.
@cbbuntz
6 жыл бұрын
I noticed some similar properties to the silver ratio to the golden ratio a while back. 1 / (2^0.5 + 1) = 2^0 .5 - 1 1 / ( 2^0.5 - 1) = 2^0.5 + 1 and a few others.
@3c3k
2 жыл бұрын
This is not related to the ratios
@cbbuntz
2 жыл бұрын
@@3c3k Actually it is. It's related to pell number generation
@3c3k
2 жыл бұрын
@@cbbuntz Have you not learned surds in school?
@zanti4132
4 жыл бұрын
Interestingly, the odd entries in the sequence for the Silver Ratio are the large numbers (i.e. the diagonals of the right triangles) for all the Pythagorean Triples where the two smaller numbers (the legs of the triangles) differ by one: 0^2 + 1^2 = 1^2 3^2 + 4^2 = 5^2 20^2 + 21^2 = 29^2 119^2 + 120^2 = 169^2 696^2 + 697^2 = 985^2 etc. Furthermore, you can generate all these Pythagorean Triples by selection the two consecutive entries in the Silver Ratio and applying that m^2 - n^2 / 2mn / m^2 + n^2 formula to generate Pythagorean Triples: m = 2, n = 1: Generates 3-4-5 m = 5, n = 2: Generates 20-21-29 m = 12, n = 5: Generates 119-120-169 m = 29, n = 12: Generates 696-697-985 etc.
@MasterHigure
6 жыл бұрын
They're not really logarithmic spirals, though, are they? A true logarithmic spiral isn't piecewice circles.
@Tumbolisu
6 жыл бұрын
The formula is correct, but the whole "circles inside squares" thing is just an approximation.
@stevethecatcouch6532
6 жыл бұрын
The spiral he drew was the golden rectangle spiral, not the golden spiral. Another spiral that approximates both of them is the Fibonacci spiral, in which successive Fibonacci rectangles are used in place of the golden rectangle.
@chrisg3030
6 жыл бұрын
Dr Gerbils But isn't each of those successive Fibonacci rectangles, created each time a square is added, itself a golden rectangle, that is one whose aspect ratio is golden?
@stevethecatcouch6532
6 жыл бұрын
Chris G, No, the aspect ratio of a Fibonacci rectangle is only approximately the golden ratio. For example, 13/8 = 1.625, not 1.618 ...
@chrisg3030
6 жыл бұрын
Dr Gerbils I think I get it. "A golden rectangle with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship (a+b)/a = a/b = Phi" (Wikipedia). Rectangles with Fibonacci number sides only approximate to this relationship. But if true golden rectangles were successively formed in this structure instead, what kind of spiral would result?
@fabianr253
2 жыл бұрын
16:10 How I hypnose myself to stay consistent at learning
@manueldelrio7147
6 жыл бұрын
Love Tony's videos!
@Banana_Split_Cream_Buns
Жыл бұрын
So the Pell sequence features 13^2=169, which is interesting as the Fibonacci sequence features 12^2=144.
@garrettkrawczyk9414
6 жыл бұрын
What about a super metallic ratio where the ratio is between the golden ratio & silver ratio, silver ratio & bronze ratio, etc.
@chrisg3030
6 жыл бұрын
Using the formula (n + sqrt(4 + n^2))/2, so that when n=1 we get the golden ratio, and when n=2 we get the silver, then when n=1.5 we get the ratio exactly 2. Now if we construct a regular figure with the number of sides equal to the number under the radical, then it would be interesting to look at a figure with 6.25 sides to compare diagonal lengths on and see if any of them are in an exact 2:1 ratio, just as you get a silver ratio for a similar operation in an octagon. How would you interpret that? I tried a hexagon with a side produced by a quarter beyond the join with the next.
@RaunienTheFirst
6 жыл бұрын
@@chrisg3030 when I did the calculation for what I'm calling the half-bonacci, i.e. where N=0.5, I get the ratio to be (1+sqrt17)/4 Not sure where you got 2 from
@chrisg3030
6 жыл бұрын
RaunienThe First I got the denominator 2 from the formula at 7:21. I plugged in 1.5 in place of N since this value is half way between 1 (plugging in which gives you the Golden ratio) and 2 (plugging in which gives the silver ratio), and seemed to be what Garret Krawczyk was asking for, rather than the half-bonacci of 0.5. So with mine we get (1.5 + sqrt(4 + 1.5^2))/2 which gives a sequence ratio constant of exactly 2. Moreover for the Golden ratio the number under the radical in the formula is 5, for the silver it's 8, but for this intermediate case it's 6.25, so I was (not quite seriously) imagining a figure with 6.25 sides. Your figure would have 17 sides which sounds interesting..
@geoffroi-le-Hook
3 жыл бұрын
so an 18-Karat ratio ...
@LMacNeill
6 жыл бұрын
It's just so fascinating how mathematics show up literally *everywhere* you look! Of course I've seen these spirals everywhere, but I've just never though about how you could describe them using mathematics. Fascinating!
@AnthonyYandow
6 жыл бұрын
I really enjoyed watching Brady with the camera in the window reflection! Neat little "behind the scenes included"
@Mezzo_Roo
6 жыл бұрын
I learned this ratio from persona 5... I should probably stop playing so many games
@ThePrimevalVoid
6 жыл бұрын
Man, the animations are getting trippier by the video.
@johnsnow5305
6 жыл бұрын
I've always loved geometry. It was my best math subject in school. When they started to introduce algebra and calculus and abstract trig (ie not showing how it actually plays out in physical space), it became less fun. I think it's important to combine the abstract facts we gain from geometry in an interesting way like you guys often do.
@G8tr1522
2 жыл бұрын
pretty much every great mathematician pre 1900 would agree with you I think.
@properbeatz
6 жыл бұрын
Im 27 years old and I just found out what the metal part of a ruler was for... Thanks Numberphile!
@nowonmetube
5 жыл бұрын
How did you not think about that yourself
@stan-bi3hl
3 ай бұрын
@nowonmetube how much do you think about rulers in your life
@xevira
4 жыл бұрын
The "Japanese" ratio could also be called the Electrum Ratio. You start off by removing a single square used to get a Golden Rectangle, and end up with a Silver Rectangle instead.
@rider2fois
4 жыл бұрын
An interesting thing about logarithmic spirals is that you can use them to define the analytic extansion of the zeta function.
@wrog7616
6 жыл бұрын
This seems like a great way to find new HUGE primes! I would run this on my computer if I didn't have 1 problem: 10^308 < INFINITY < 10^309 Steps: 1. start with a prime like 5 2. 5 --> 29 3. 29 --> some other prime 4. some other prime --> some other prime And so on till you get a new BIGGEST PRIME!
@josevillegas5243
4 жыл бұрын
Well, that depends in which is true: A. If the index is prime, then the number at that index is prime. vs. B. If the number is prime, then its index is prime. With B, you may have numbers at prime indices that are not themselves prime
@kinshukdua
6 жыл бұрын
OMG I just learned about the Silver ratio in Persona 5 and Numberphile uploaded a video about it, am I on something lol?
@meegz149
6 жыл бұрын
How has no one mentioned Persona 5 yet?!
@mioszchrzempiec4429
4 жыл бұрын
9:10 I never thought that watching a numberphile episode would be useful in persona 5
@testkiller6225
5 жыл бұрын
the reason why we like geometric spirals in nature is the growth it represents, that it is alive. When we see it in art, it shows the artist's realization to make his art be alive.
@dkamm65
6 жыл бұрын
Could you not use this Pell Sequence to find very large primes? Since the numbers in the sequence grow exponentially faster than the position, couldn't you calculate the number in the (very large prime)th position to find a gargantuan prime?
@user-ct1ns6zw4z
6 жыл бұрын
The 7th pell number is 169, which is 13^2. All pell primes have prime indexes, but not all prime indexes correspond to pell primes. You might call them "pell pseudoprimes".
@nowonmetube
5 жыл бұрын
I thought the same thing, and another person besides you in the comments section as well. If there isn't a sequence that could find prime numbers. But if there is, we surely still haven't found it yet.
@p23570
4 жыл бұрын
i learn so many new words watching these videos. hache, maths, etc...
@Funkotronimus
6 жыл бұрын
I’m gonna start a support group for Americans who pronounce “H” as “Haych,” and “Z” as “zed”
@RiamiAurum
6 жыл бұрын
Bob Trenwith that's the point, he's supporting those Americans tbat pronounce it that way
@izicial7469
6 жыл бұрын
I thought these guys were based in the UK. So wouldn't it make sense for them to say hache and zed???
@ratlinggull2223
6 жыл бұрын
As a foreigner, pronouncing h as 'eich' instead of 'heich' actually saves breath since your tongue isn't optimised for English. But Americans have no reason to because they're hecking native.
@UnderscoreZeroLP
6 жыл бұрын
Saying haytch isn't british
@PhilBoswell
6 жыл бұрын
+Underscore Zero it is when you want to read something over the phone and you don't want the recipient to think you're saying "eight". Yes, I know you can use the Phonetic Alphabet (which I learned almost before I could read ;-) but people are lazy :-P
@iAmTheSquidThing
6 жыл бұрын
Pete's animations often elevate Numberphile videos into something beautiful as well as informative.
@sebastianzaczek
6 жыл бұрын
Hey Numberphile! I recently was playing around with numbers and i came up with a rediculous fractal-like fraction (here is the first bit of it): ((((1/2)/(3/4))/((5/6)/(7/8)))/(((9/10)/(11/12))/((13/14)/(15/16)))) I hope you understand how it's built up. Then i wanted to see what this equals, and the larger i made the fraction, the closer it got to sqrt(2)/2: (1/2)=0.5 ((1/2)/(3/4))=0.666... (((1/2)/(3/4))/((5/6)/(7/8)))=0.7 ((((1/2)/(3/4)... (13/14)/(15/16)))) =0.7061728395... (((((1/2)/(3/4)... (29/30)/(31/32)))))=0.707023939... ((((((1/2)/(3/4)... (61/62)/(63/64))))))=0.7071021245... (I had to trick my calculator in a certain way to let me calculate this last equation, so the result might be slightly off) sqrt(2)/2 equals 0.7071067812... so the last result is equal for the first 5 digits after the decimal point. Now my question: If you continue this process infinitely, does the fraction actually converge towards sqrt(2)/2? And is there a way to prove it?
@unclejoeoakland
6 жыл бұрын
DerSibbe i think they call that a convergence...
@mannyheffley9551
6 жыл бұрын
but a fraction cannot be irrational so I think this assertion is incorrect
@sebastianzaczek
6 жыл бұрын
FReaKIng FReqUEncIEs i was thinking that too, on the other end however this fraction is theoretically infinite....
@mannyheffley9551
6 жыл бұрын
so then it is possibly irrational
@sebastianzaczek
6 жыл бұрын
FReaKIng FReqUEncIEs exactly... and there we start to need a proof... no idea how to proove/disproove it though...
@thesuomi8550
6 жыл бұрын
0-bonacci sequence is my favourite
@thatsleepytitan769
6 жыл бұрын
A ratio for every element
@Henrix1998
6 жыл бұрын
Golden ratio should be hydrogen ratio then
@Smittel
6 жыл бұрын
S U L P H U R S P I R A L
@briandiehl9257
6 жыл бұрын
Yes
@kuro13wolf
6 жыл бұрын
Except bronze, which is an alloy. It's quite upsetting when you think about it.
@Smittel
6 жыл бұрын
Rhyme Bito copper turns green tho. You don't want a green medal do ya?
@mathmachine4266
3 жыл бұрын
The x-th term in the n-bonacci sequence is (k1^x-cos(πx)k2^x)/√(n²+4) Where k1=(√(n²+4)+n)/2 and k2=(√(n²+4)-n)/2
@saidatulhusna1533
6 жыл бұрын
i haven't watched the video yet but i assume this is about some sort of a parker ratio
@jogiff
6 жыл бұрын
I legit thought it would be about electrum or the gold standard
@CaseyShontz
6 жыл бұрын
Saidatul Husna not really lol but that’s what I thought
@steph_dreams
5 жыл бұрын
I like the Parker ratio but I prefer Parker squares
@rudychan8792
Жыл бұрын
You Are Right, Sir. A4 Paper is Silver Ratio^ √2 : 1 * 📄 😉 21×√2 = 29,6948 == 29,7 cm!
@someweeb3650
5 жыл бұрын
"We can easily work out how much you've cut off" You didn't have to explain anything for me to know the answer- too much.
6 жыл бұрын
I love using golden section in music. I learned so much about this studying Bela Bartok scores back in the 70s and 80s.
@deanwinchest3906
6 жыл бұрын
Don't forget to phile those nails when your finnished;;
@briandiehl9257
6 жыл бұрын
Why would he need to do that?
@deanwinchest3906
6 жыл бұрын
Brian Diehl thought it was mildly ironic to title/intro... Maybe a bit over the head✈️🐒
@briandiehl9257
6 жыл бұрын
I was thinking he could just turn the scissors when he is cutting and avoid all of this
@deanwinchest3906
6 жыл бұрын
Brian Diehl I prefer the old throw away dollar store *fingernail clippers* myself😄
@acerovalderas
5 жыл бұрын
Excellent extension of the Golden Ratio. I love it!
@kindredtoast3439
4 жыл бұрын
Wow. I came here to learn what the silver ratio was after playing Persona 5 and then learn that it's different in Japan than the rest of the world.
@joshpollack5936
6 жыл бұрын
math is fun, adventurous, quirky, and clever. too bad it is delivered to us with the wonder completely striped
@jpdemer5
6 жыл бұрын
I like my wonder completely plaid.
@pbj4184
4 жыл бұрын
I know this isn't really a big deal compared to what they do in the video but it turns out, the total length of the curve of the ratio d is π/2(d/d-1). It actually converges and leads to this simple-to-derive formula. This is why I love math.
@giddam
6 жыл бұрын
You lost me at 2/pi = pi/2
@MarcoMa210
3 ай бұрын
pi = 2
@Wurfenkopf
3 жыл бұрын
6:39 I get so easily excited at a graphic sight that I felt you had solved a millennium problem
@skyscraperfan
6 жыл бұрын
Wouldn't it make more sense to define spirals somehow more continuosly, so that they are even self similar, if you rotate them any degree? They way you constructed them was just joining quarter circles together. In a real spiral there should not be parts of a circle anywhere. It should get smaller and smaller at any point.
@xenontesla122
6 жыл бұрын
warumbraucheichfüryoutubekommentareeinescheissgooglepluspagefragezeichen That type of portal is called a logarithmic spiral and it’s the type found in flight patterns and shell growth.
@whjk83921
6 жыл бұрын
Fantastic episode! One of my absolute favorites!
@philosofickle
6 жыл бұрын
Damn the ending was hilarious 😂😂
@hadhave7961
6 жыл бұрын
This leaves me with so many more questions than answers
@alphadad1966
6 жыл бұрын
So European paper uses irrational values for its dimensions? A true A4 sheet of paper can never be accurately measured?
@silkwesir1444
6 жыл бұрын
The A4 standard is defined in terms of whole millimeters (210 × 297), and it has a tolerance of ±2 mm.
@MsSlash89
6 жыл бұрын
At least our sheets are, more or less, capable of keeping the same ratio when folded. Yours, once folded, just become another rectangle, not making any sense with all those "letter, legal..." comparing it to A2, A3, A4, A5...
@OrcinusDrake
6 жыл бұрын
A sheet with integer dimensions can never be exactly measured either
@alphadad1966
6 жыл бұрын
I should have said " A true A4 sheet of does not have dimensions that can be expressed in rational numbers"
@blackhatguy6955
5 жыл бұрын
No, the definition includes, "rounded to the nearest millimetre".
@tifforo1
5 жыл бұрын
Counting the fibonacci numbers backward into the negative: 55, 34, 21, 13, 8, 5, 3, 2, 1, 1, 0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55
@quantumhorizon
6 жыл бұрын
Interesting video! I'm curious though, have imaginary analogues to the metallic ratios been explored?
@G8tr1522
2 жыл бұрын
ooo, interesting. Could you iterate a sequence of imaginary numbers?
@venkatbabu186
4 жыл бұрын
A square is a surface and the ratios factors are like golden ratio and silver ratio along circular symmetry. Any Fibonacci type is a ratio along circular symmetry line. Half circle. Even geometrical shape like cylinder has a symmetry ratios. Others are cone sphere parabolic cylinder etc.
@st0ox
6 жыл бұрын
Big in Japan lol
@nowonmetube
5 жыл бұрын
Savage
@Difulsif
6 жыл бұрын
The animations are getting better in each new video :D
@kujmous
6 жыл бұрын
What is the ratio for 1, 1, 1, 3, 5, 9, 17, 31,… always adding the previous three values to get the next?
@user-ct1ns6zw4z
6 жыл бұрын
Kinda ugly ratio: 1/3(1+ cuberoot(19 - 3sqrt(33)) + cuberoot(19 + 3sqrt(33))) Which is about 1.84. Seems to converge pretty fast, 17*1.84 = 31.28 It's the root to this equation: r^3 - r^2 - r - 1 = 0 Because if we write it out in its recursive form: P_n = P_(n-1) + P_(n-2) + P_(n-3) Then divide to get the ratio: r = (P_n)/(P_(n-1)) = 1 + (P_(n-2))/(P_(n-1)) + (P_(n-3))/(P_(n-1)) We notice that as n->infinity, this equation tends to: r = 1 + 1/r + 1/r^2 Then we simply multiply by r^2 and bring everything to the other side.
@IBioPoxI
6 жыл бұрын
wouldn't it be 1, 1, 2, 4, 7, 13, 24 .... as ϵ+1+1 = 2 not 1 as you seem to suggest?
@chrisroller1397
6 жыл бұрын
Ben Fowler To me this is syraight out of /r/vxjunkies
@kennethflorek8532
6 жыл бұрын
Ben Fowler That series is the one that begins as 0, 1, 1, instead of the one that begins 1, 1, 1. If you need a number before 1, 1, 1, it is -1. That is: 1 = 1 + 1 + (-1)
@AnonimityAssured
6 жыл бұрын
A slightly more succinct representation is: _t_ = (1 + cbr(19 - √297) + cbr(19 + √297))/3. (cbr = cube root)
@ToastyEggs
2 жыл бұрын
For anyone interested, the function (x+√(x^2+4))/2 will give you each of the metallic ratios as long as x is an integer.
@zero56619
6 жыл бұрын
Show me rubidium ratio
@user-ct1ns6zw4z
6 жыл бұрын
If gold is the 79th element and that gives you Sn = Sn-1 + Sn-1, and silver is the 47th element and that gives you Sn = Sn-1 + 2Sn-2, then for Rb = 37th element you could define it to be Sn = Sn-1 + 42/32Sn-2. The ratio for that one would be (42/32 + sqrt((42/32)^2 + 4))/2 = 1.8523537.... What am I doing with my life...
@mfzasr5665
6 жыл бұрын
This is a series I'm long passionate about. Just here is another property of this series, 2*(Pn)^2 +/- 1 would be equal to (Pn + P(n-1))^2. Also this series has a close relative series, -1,1,1,3,7,17,41,99,239,577....
@blue_tetris
6 жыл бұрын
I never made it to the Silver Ratio without biting.
@TofranBohk
5 жыл бұрын
Mr. blue_tetris, how many spirals does it take to get to the SILVER ratio of a SILVER RATIO POP!?
@MalcolmCooks
3 жыл бұрын
> uses scissors to cut his nails > uses a ruler to tear paper instead of cutting it with the scissors
@ishaangovil5572
6 жыл бұрын
The next is the bronze ratio...I think
@sebastianzaczek
6 жыл бұрын
MODERN SCIENCE i thought that too
@hunnymonster2k
6 жыл бұрын
Nah, the Parker Ratio ;-)
@naverilllang
4 жыл бұрын
Why should bronze, an alloy, come after two precious metals? Just saying. Platinum should have come next, ya know?
@____spacecadet____
2 жыл бұрын
That play button display method is hard as nails
@KnuxMaster368
6 жыл бұрын
10th! hopefully it's not a Parker Square of a meme Edit: *sniff* I smell a Parker Square
@amydebuitleir
6 жыл бұрын
The animation on this video is really satisfying!
@BiggieCheese
6 жыл бұрын
Where my Platinum Ratio bois at?
@ianmoore5502
5 жыл бұрын
Platinum ratio gang rise up
@todabsolute
4 жыл бұрын
Bruh platinum ratio is technically 1
@yee6870
4 жыл бұрын
@@todabsolute iconic
@antoniozumpano826
3 жыл бұрын
any linear combination of the two previous number will give us a new constant, say, a, b are given and c = ra +sb, Fibonacci r=1=s; silver ratio is just r = 1 and s = 2.
@Marconius6
6 жыл бұрын
The seven metals used in alchemy are Gold, Silver, Mercury (Quicksilver), Iron, Copper, Tin, Lead. If you're looking for metal suggestions!
@caiheang
6 жыл бұрын
Does the Metallic Ratio Spirals have arc-length limits, or are they "infinitely long"? :O Like 1/2 + 1/4 + 1/8 + ... tends to 1 after infinite iterations. Does someone know the answer?
@mxpxorsist
6 жыл бұрын
The arc length of a quarter circle is pi/4*r where r is the radius. Therefore the arclength of a spiral with ratio 1/delta is (starting with r=1) pi/4*(1+1/delta+1/delta^2+...)=pi/4*delta/(delta-1)
@badrunna-im
6 жыл бұрын
As you go inwards, the arc length converges just as the integral of θe^θ from negative infinity to zero converges.
@littlebigphil
6 жыл бұрын
The arc length of a section decreases by a constant factor (1 over the ratio), so the geometric series describes the total length. Geometric series converges when the factor is less than 1, which it is because the sections are getting smaller.
@captainroll
6 жыл бұрын
I love his enthusiasm for everything!
@westsenkovec
6 жыл бұрын
The silver ratio = *1:925*
@RazvanMihaeanu
6 жыл бұрын
Do that in Base 6! :)
@CarbonRollerCaco
3 жыл бұрын
And √2 is the metallic ratio of its own reciprocal; that is, the successive proportions between consecutive 1/√2-bonacci (one root-second? One root-twoth? Root canal?) numbers approach √2. And I propose we call it the platinum ratio.
@ashishshukla8423
6 жыл бұрын
I liked it earlier when animation was used only to show dynamic ideas which were difficult to describe on paper
@NoNameAtAll2
6 жыл бұрын
Ashish Shukla Agree It was a lot more interesting to watch the actual paper
@iabervon
6 жыл бұрын
Agreed, although I kind of like the animation for things that are trivial but not shown on the paper, such as adding two of these to one of those. If you muted the audio and just looked at the paper, he'd just be writing down some numbers, but the animation shows the calculation he's doing.
@RickySTT
6 жыл бұрын
The animations depict the concepts more accurately than the paper drawings do, though. (Mathematicians can’t necessarily draw straight.)
@JimSteinbrecher
6 жыл бұрын
a4 (and a-size paper in general) is used in all metric countries. its a sqrt(2) ratio starting with an area of 1 square meter (a0), and diving by 2 with each index increase (a1 is half a square meter, a2 is 1/4 of a square meter, etc).
@hanspeter9391
6 жыл бұрын
Got me anxiety how he placed those scissors
@yogitshankar6348
6 жыл бұрын
Great to see Tony Padilla back!! Love the ratio videos
@hanniballector3956
6 жыл бұрын
*I'm watching this after cutting my fingernails!* 😅
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