The Silver Ratio - Numberphile

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The silver ratio (and other metals) with Tony Padilla.
More links & stuff in full description below ↓↓↓
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Опубликовано:

20 июн 2024

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Комментарии : 1,2 тыс.

@TNTPablo 6 лет назад

The animator does an incredible job!

@thesuomi8550 6 лет назад

Thanks :)

@Stilllife1999 6 лет назад

Thanks. (it was me)

@eyflfla 6 лет назад

Yeah, numberphile's animations have gotten better over time. I also like how they're low key and in that same brown-paper hand-drawn style.

@nowonmetube 5 лет назад

@@thesuomi8550 no thanks, me it was!

@nowonmetube 5 лет назад

@@Stilllife1999 no, me x)

@SpeakShibboleth 6 лет назад

why use scissors? just use a numberfile.

@graduator14 6 лет назад

This joke is the pinnacle of this channel! We can all go home now. :^p

@poisonpotato1 6 лет назад

Under appreciated pun

@Sunshine11229 5 лет назад

oof.

@asad210 5 лет назад

Nice.

@tylerhecht3360 5 лет назад

Ba Dum Tss (seriously, though, that was a legendary pun)

@kevinmackie4045 5 лет назад

Can't wait for the Bronze ratio and the Honorable Mention ratios :)

@dielaughing73 3 года назад

Participation ratios

@jwcfive7999 2 года назад

Can’t forget the steel ratio

@geraldsnodd 2 года назад

🤣

@myboatforacar 2 года назад

I'm holding out for the tin ratio

@RWBHere 2 года назад

Then there's the CdB ratio. No; not Cadmium Boride: It's the 'Could do Better' ratio.

@distraughtification 6 лет назад

That sounds like a way to count seconds. One-bonacci, two-bonacci, three-bonacci...

@maishamohiuddin297 6 лет назад

tb to the americans cant count video

@otakuribo 6 лет назад

_one-bonacci_ _two-bonacci_ _red-bonacci_ _blue-bonacci_

@MushookieMan 6 лет назад

Count von Count says, One-bonacci, two-bonacci, three-bonacci, AH AH AH AH!

@klaxoncow 6 лет назад

One-bonacci, two-bonacci, three-bonacci, four. Five-bonacci, six-bonacci, seven-bonacci, more.

@assassin01620 6 лет назад

One-bonacci, two-bonacci, three-bonacci, four. Four bonaccis make a metallic ratio and so do many more!

@cuitaro 9 месяцев назад

sqrt(2): _happily exists irrationally_ Tony: now this *ratio*

@jeremyheminger6882 6 лет назад

"Metallic Ratio" is the name of my new Tool tribute band.

@MisterAppleEsq 6 лет назад

Nice.

@fossilfighters101 6 лет назад

Woah Mister Apple what're you doing in this comment section?

@Pfhorrest 6 лет назад

Are you going to produce n-bonacci variants of Lateralus?

@clyde8759 6 лет назад

Jeremy Heminger lol

@MisterAppleEsq 6 лет назад

+fossilfighters101 I mean, right now I'm replying to your comment.

@Artifexian 6 лет назад

Amazing! Had no idea these existed.

@cuzeverynameistaken1283 6 лет назад

Had no idea you watched numberphile. Ive been following you since 4000 subs

@harry_page 6 лет назад

Hey Edgar!

@Artifexian 6 лет назад

Yup! Numberphile is one of my favourite channels.

@natheniel 6 лет назад

It's one of everybody's favourite channels!

@unvergebeneid 6 лет назад

PBS Infinite Series had a video on these. If you like Numberphile, you'll probably also like them!

@matin563 5 лет назад

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 года назад

That's why it is called fi

@EtienneBotek 2 года назад

@@damianzieba5133 phi is for Φειδίας

@PC_Simo Год назад

So do I 😎. Φbonacci.

@alexandermcclure6185 Год назад

@@PC_Simo Shouldn't it be φbonacci instead of φibonacci? φ sounds like fi, not not f.

@PC_Simo Год назад

@@alexandermcclure6185 True. I think my train of thought changed, mid-word. 🤔😅 *EDIT:* I made the correction ✅😌👍🏻.

@AdeptAscent 6 лет назад

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 лет назад

They aren't weird; They are constant.

@flymypg 6 лет назад

I especially love Numberphile videos that provide generalizations, revealing the wider mathematical landscape extending from and encompassing a better known starting point.

@jamezer7revel471 6 лет назад

The ratios are winning some medals here

@Advection357 6 лет назад

Just the gold counts.. the rest are participation trophies

@thelastspartanS117 6 лет назад

Hopefully no one MEDDLES in the award ceremony

@thelastspartanS117 6 лет назад

Im sure the ratios have the Mettle to withstand such buffoonery

@anticorncob6 6 лет назад

It’s Gold = 1 Silver = 2 Bronze = 3 Just like medals in the Olympics.

@debayanbanerjee 6 лет назад

Jamezer7 Revel I think you meant 'metals'. Not medals. ;-)

@matthijshebly 6 лет назад

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.

@TheInselaffen 6 лет назад

Britain; home of the Aluminium Falcon.

@halyoalex8942 3 года назад

Sounds like an odd crossover of Iron Man and Falcon from Marvel...

@WolfWalrus 6 лет назад

Of course, the Golden Ratio has the special property of allowing [Infinite Spin] according to the ancient Zeppeli family technique

@zanly5039 4 года назад

and the silver ratio allows for the almost-infinite spin

@rubenbohorquez5673 4 года назад

@@zanly5039 ah yes, the TREE(3) spin, not infinite, but stupidly big!

@roskataka2574 4 года назад

I see what you did there, fellow JoJo fan :

@ramiroseltzer5278 3 года назад

the Golden Ratio also allows cripples on a horse and a wheelchair to walk... its amazing what math can do

@yazanabdalluh6251 2 года назад

@@zanly5039 no its for polnareffs silver chariot to spin

@akshat9282 6 лет назад

*REPETITION REPETITION REPETITION*

@3ckitani 6 лет назад

REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION

@cavorkehl6777 6 лет назад

@prasanttwo281 6 лет назад

REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION REPETITION

@Ready4Music 6 лет назад

Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition Repetition

@CarelessMiss 6 лет назад

Akshat K Agarwal *REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION REPITITION*

@nakamakai5553 5 лет назад

As a marine biologist, I love these. Forms like this pop up all over the undersea world, especially among invertebrates. Well done!

@WhiteChocolate74 2 года назад

Ocean studies are underrated 💙

@DeathlyTired 6 лет назад

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 лет назад

Wow!

@leoangere5310 5 лет назад

"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.)

@OlbaidFractalium 6 лет назад

Wow! I did not know The Great Wave of Hokusai is geometric designs.

@WildAnimalChannel 6 лет назад

yeah, if you fudge the results enough.

@donaldasayers 6 лет назад

Looks more like a dragon curve to me.

@pleindespoir 6 лет назад

Hokusai >>> Hokuspokus

@BainesMkII 6 лет назад

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 лет назад

Isn't it Kanagawa?

@SteamPunkLV 6 лет назад

omg I hate when my nails looks like goddamn polygons xD

@ziquaftynny9285 6 лет назад

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 лет назад

Ziquafty Nny that’s not human

@ziquaftynny9285 6 лет назад

No u

@EchoHeo 6 лет назад

Ziquafty Nny yes me

@UnderscoreZeroLP 6 лет назад

I bite my nails. So much easier

@angst_ 6 лет назад

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!

@SNNTV3000 6 лет назад

surely then, the 49° one should become the peregrine ratio?

@fossilfighters101 6 лет назад

Ooh yeah!

@TheOzumat 6 лет назад

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 лет назад

Or "Pippin" for short.

@benjaminmiller3620 6 лет назад

Compromise and call it the Aluminium Falcon ratio?

@rewrose2838 3 года назад

@@benjaminmiller3620 Peregrin-inium

@pakfu 6 лет назад

I’ve been on YT for like 12 yrs and this ranks in one of my favourite videos ever. Thank you so much.

@numberphile 6 лет назад

Limited edition "Golden Ratio" T-Shirts at Fibonacci prices: teespring.com/NP-Seeds and teespring.com/NP-Golden-Rectangle

@torin1006 6 лет назад

I love things that use root(2) anywhere in them.

@void9720 5 лет назад

1.41421356237309504880168872420969807856967...

@unknown360ful 6 лет назад

Prof. TONY! The ratio videos are awesome!

@popogast 6 лет назад

I'm always enlightened by the enthusiasm You mathematicians on this channel have. ITs a delight. Thank You.

@jerombastiaansen9495 5 лет назад

7:20 That's the solution to x² - Nx - 1

@ultra6334 2 года назад

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

@manueldelrio7147 6 лет назад

Love Tony's videos!

@brnsndwch 5 лет назад

6:40 P=NP solved

@efulmer8675 3 года назад

Hah. That made me laugh.

@whjk83921 6 лет назад

Fantastic episode! One of my absolute favorites!

@yogitshankar6348 6 лет назад

Great to see Tony Padilla back!! Love the ratio videos

@thatsleepytitan769 6 лет назад

A ratio for every element

@Henrix1998 6 лет назад

Golden ratio should be hydrogen ratio then

@Smittel 6 лет назад

S U L P H U R S P I R A L

@briandiehl9257 6 лет назад

Yes

@kuro13wolf 6 лет назад

Except bronze, which is an alloy. It's quite upsetting when you think about it.

@Smittel 6 лет назад

Rhyme Bito copper turns green tho. You don't want a green medal do ya?

@benjaminolanderrasmussen3049 6 лет назад

What would the ratio for the phi-bonacci sequence be called?

@ericluque6573 6 лет назад

i was thinking the exact same thing

@benjaminolanderrasmussen3049 6 лет назад

Eric Luque. When you remember the numberphile videos that you have recently watched :)

@heyandy889 6 лет назад

the very golden ratio

@primarysecondaryxd 6 лет назад

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 лет назад

Or π-bonacci?

@captainroll 6 лет назад

I love his enthusiasm for everything!

@acerovalderas 4 года назад

Excellent extension of the Golden Ratio. I love it!

@AnthonyYandow 6 лет назад

I really enjoyed watching Brady with the camera in the window reflection! Neat little "behind the scenes included"

@wanderingrandomer 6 лет назад

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 лет назад

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 года назад

your short story was as long as your long story

@Homs86 4 года назад

same here. woodworking school is kinda obsessed with the golden ratio bcs"so pleasing" blabla finally there is light :)

@bruhmoment1835 3 года назад

Well, it IS a JoJo reference

5 лет назад

I love using golden section in music. I learned so much about this studying Bela Bartok scores back in the 70s and 80s.

@zyrota4295 2 года назад

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 лет назад

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 года назад

This is not related to the ratios

@cbbuntz 2 года назад

@@3c3k Actually it is. It's related to pell number generation

@3c3k 2 года назад

@@cbbuntz Have you not learned surds in school?

@properbeatz 6 лет назад

Im 27 years old and I just found out what the metal part of a ruler was for... Thanks Numberphile!

@nowonmetube 5 лет назад

How did you not think about that yourself

@stan-bi3hl 11 дней назад

@nowonmetube how much do you think about rulers in your life

@prathameshsundaram7509 4 года назад

I love your channel! It's absolutely amazing!

@ricardovalentin5056 5 лет назад

Fantastic! I love Numberphile!

@rider2fois 3 года назад

An interesting thing about logarithmic spirals is that you can use them to define the analytic extansion of the zeta function.

@kinshukdua 6 лет назад

OMG I just learned about the Silver ratio in Persona 5 and Numberphile uploaded a video about it, am I on something lol?

@iAmTheSquidThing 6 лет назад

Pete's animations often elevate Numberphile videos into something beautiful as well as informative.

@LMacNeill 6 лет назад

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!

@ThePrimevalVoid 6 лет назад

Man, the animations are getting trippier by the video.

@MasterHigure 6 лет назад

They're not really logarithmic spirals, though, are they? A true logarithmic spiral isn't piecewice circles.

@Tumbolisu 6 лет назад

The formula is correct, but the whole "circles inside squares" thing is just an approximation.

@stevethecatcouch6532 6 лет назад

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 лет назад

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 лет назад

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 лет назад

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?

@amydebuitleir 6 лет назад

The animation on this video is really satisfying!

@Ruxinator 6 лет назад

Great video! I particularly enjoyed this one

@mioszchrzempiec4429 4 года назад

9:10 I never thought that watching a numberphile episode would be useful in persona 5

@garrettkrawczyk9414 6 лет назад

What about a super metallic ratio where the ratio is between the golden ratio & silver ratio, silver ratio & bronze ratio, etc.

@chrisg3030 6 лет назад

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 5 лет назад

@@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 5 лет назад

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 года назад

so an 18-Karat ratio ...

@Difulsif 6 лет назад

The animations are getting better in each new video :D

@WillToWinvlog 6 лет назад

This video is PURE GOLD!!!

@philosofickle 6 лет назад

Damn the ending was hilarious 😂😂

@sebastianzaczek 6 лет назад

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 лет назад

DerSibbe i think they call that a convergence...

@mannyheffley9551 6 лет назад

but a fraction cannot be irrational so I think this assertion is incorrect

@sebastianzaczek 6 лет назад

FReaKIng FReqUEncIEs i was thinking that too, on the other end however this fraction is theoretically infinite....

@mannyheffley9551 6 лет назад

so then it is possibly irrational

@sebastianzaczek 6 лет назад

FReaKIng FReqUEncIEs exactly... and there we start to need a proof... no idea how to proove/disproove it though...

@zanti4132 4 года назад

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.

@vincentvanveen4436 3 года назад

I'm so glad I clicked on this! Always had my doubts on nature sticking to one single ratio, seemed to simple.

@dkamm65 6 лет назад

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 лет назад

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 лет назад

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.

@quantumhorizon 6 лет назад

Interesting video! I'm curious though, have imaginary analogues to the metallic ratios been explored?

@G8tr1522 2 года назад

ooo, interesting. Could you iterate a sequence of imaginary numbers?

@stevefrandsen 6 лет назад

Very informational Tony. Thank you.

@angry4rtichoke646 3 года назад

This person is awesome! I need to find more videos of them!

@saidatulhusna1533 6 лет назад

i haven't watched the video yet but i assume this is about some sort of a parker ratio

@jogiff 6 лет назад

I legit thought it would be about electrum or the gold standard

@CaseyShontz 5 лет назад

Saidatul Husna not really lol but that’s what I thought

@steph_dreams 5 лет назад

I like the Parker ratio but I prefer Parker squares

@deanwinchest3906 6 лет назад

Don't forget to phile those nails when your finnished;;

@briandiehl9257 6 лет назад

Why would he need to do that?

@deanwinchest3906 6 лет назад

Brian Diehl thought it was mildly ironic to title/intro... Maybe a bit over the head✈️🐒

@briandiehl9257 6 лет назад

I was thinking he could just turn the scissors when he is cutting and avoid all of this

@deanwinchest3906 6 лет назад

Brian Diehl I prefer the old throw away dollar store *fingernail clippers* myself😄

@georgecooper7389 6 лет назад

Extremely well edited!

@user-pq7dy9op6y 6 лет назад

Beautiful fractal geometry!!!

@someweeb3650 5 лет назад

"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.

@Funkotronimus 6 лет назад

I’m gonna start a support group for Americans who pronounce “H” as “Haych,” and “Z” as “zed”

@RiamiAurum 6 лет назад

Bob Trenwith that's the point, he's supporting those Americans tbat pronounce it that way

@izicial7469 6 лет назад

I thought these guys were based in the UK. So wouldn't it make sense for them to say hache and zed???

@ratlinggull2223 6 лет назад

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 лет назад

Saying haytch isn't british

@PhilBoswell 6 лет назад

+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

@p23570 4 года назад

i learn so many new words watching these videos. hache, maths, etc...

@hadhave7961 5 лет назад

This leaves me with so many more questions than answers

@joshpollack5936 6 лет назад

math is fun, adventurous, quirky, and clever. too bad it is delivered to us with the wonder completely striped

@jpdemer5 5 лет назад

I like my wonder completely plaid.

@caiheang 6 лет назад

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 лет назад

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)

@badrunnaimal-faraby309 6 лет назад

As you go inwards, the arc length converges just as the integral of θe^θ from negative infinity to zero converges.

@littlebigphil 6 лет назад

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.

@davidcampos1463 6 лет назад

Thank you. I didn't know about these other ratios.

@johnsnow5305 6 лет назад

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 года назад

pretty much every great mathematician pre 1900 would agree with you I think.

@kujmous 6 лет назад

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 лет назад

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 лет назад

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 лет назад

Ben Fowler To me this is syraight out of /r/vxjunkies

@kennethflorek8532 6 лет назад

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 лет назад

A slightly more succinct representation is: _t_ = (1 + cbr(19 - √297) + cbr(19 + √297))/3. (cbr = cube root)

@st0ox 6 лет назад

Big in Japan lol

@nowonmetube 5 лет назад

Savage

@JasmineDreams 6 лет назад

Why am I so excited about this!

@maxonmendel5757 6 лет назад

I love how comprehensive numberphile is

@blue_tetris 6 лет назад

I never made it to the Silver Ratio without biting.

@TofranBohk 5 лет назад

Mr. blue_tetris, how many spirals does it take to get to the SILVER ratio of a SILVER RATIO POP!?

@mojoface 6 лет назад

I love reducing cognitive load. Probably my favorite thing actually.

@AstroHolden 6 лет назад

The Aluminium Falcon! I love it - hidden Star Wars reference!

@markhagerman3072 6 лет назад

The Pell sequence has another interesting property; every other number in the sequence (1, 5, 29, etc.), when squared, is the sum of the squares of two consecutive integers.

@chrisg3030 5 лет назад

Nice. For example 29^2 = 20^2 + 21^2. Just today I found another square feature. Every 4th term in the partial sum (running total) sequence of Pell terms after the first 5 (1+2+5+12+29 = 49) seems to be a perfect square. So 49 +70+169+408+985 = 1681 = 41^2.

@ishaangovil5572 6 лет назад

The next is the bronze ratio...I think

@sebastianzaczek 6 лет назад

MODERN SCIENCE i thought that too

@hunnymonster2k 6 лет назад

Nah, the Parker Ratio ;-)

@naverilllang 4 года назад

Why should bronze, an alloy, come after two precious metals? Just saying. Platinum should have come next, ya know?

@BiggieCheese 6 лет назад

Where my Platinum Ratio bois at?

@ianmoore5502 5 лет назад

Platinum ratio gang rise up

@user-mz7cn9hq8v 4 года назад

Bruh platinum ratio is technically 1

@yee6870 3 года назад

@@user-mz7cn9hq8v iconic

@SirDominic 6 лет назад

:O those t-shirts look amazing!

@IncolasCopperfield 6 лет назад

thanks for a platinum video

@giddam 6 лет назад

You lost me at 2/pi = pi/2

@alphadad1966 6 лет назад

So European paper uses irrational values for its dimensions? A true A4 sheet of paper can never be accurately measured?

@silkwesir1444 6 лет назад

The A4 standard is defined in terms of whole millimeters (210 × 297), and it has a tolerance of ±2 mm.

@MsSlash89 6 лет назад

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 лет назад

A sheet with integer dimensions can never be exactly measured either

@alphadad1966 6 лет назад

I should have said " A true A4 sheet of does not have dimensions that can be expressed in rational numbers"

@blackhatguy6955 5 лет назад

No, the definition includes, "rounded to the nearest millimetre".

@markusjacobi-piepenbrink9795 4 года назад

Just wonderful!

@Xezlec 6 лет назад

That was really interesting, especially the thing about the 2bonacci sequence and squares and prime numbers!

@KnuxMaster368 6 лет назад

10th! hopefully it's not a Parker Square of a meme Edit: *sniff* I smell a Parker Square

@zero56619 6 лет назад

Show me rubidium ratio

@user-ct1ns6zw4z 6 лет назад

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...

@swoondrones 10 месяцев назад

Great video!

@ryuuzaki24 6 лет назад

amazing video!

@skyscraperfan 6 лет назад

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 лет назад

warumbraucheichfüryoutubekommentareeinescheissgooglepluspagefragezeichen That type of portal is called a logarithmic spiral and it’s the type found in flight patterns and shell growth.