What about the platinum ratio, from the zero-nacci sequence? Hence, P_n = 0*P_(n-1) + P_(n-2) As a result, the sequence is 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 ….. The ratio doesn't approach anything but by the formula, it is (0+sqrt(0^2+4))/2, or 1. And sure enough, if you take 0 squares out of the platinum rectangle, you get a platinum rectangle ;)P

Couldn't we use the silver ratio to create infinitely big prime numbers? Like start at 3, the 3rd index is 5, the 5th index is 29, the 29th index is… Etc.?

I love peregrine falcons too, Those and Snowy owls. Anyway, I think this doesn't get taught at schools is the lies to children. Its easier to just focus on one ratio so that we don't overload them. Really enjoyed this video. I guess there must be Fibonacci sequences which use the negative multiples I wonder if these ever occur in nature?I did a quick excel experiment and I think the spiral becomes a wavy path which tends to y=x as the arcs get shorter and shorter. This is the same for all metallic ratios just they basically get there faster as the ratio cuts down the bounding squares for the arcs quicker. Its just like a damped oscillation along the 45.Anyway very thought provoking, thanks.

6:39 It always confuses me when a variable is used twice with a different meaning in the same formula, could you please start using a/b instead of n/N? I think subtle weird usage patterns like this really throw a lot of people off when trying to follow maths problems, or copyingsomething over and not noticing the different uses of ‘n’ and ater really getting stuck trying to understand it all. I had a maths teacher who would write complex problems on the blackboard using ‘a’ for 2 different nested indexez and it was really really confusing :p

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.

Something I noticed: the formula for the Nth metallic ratio [N+root(N^2+4)]/2 is actually the solution to the general quadratic equation x^2 – Nx – 1 = 0 if you solve it according to the quadratic formula. Not sure if that's relevant to any larger mathematical problem but I thought it was interesting to note!

I ended up doing this by accident (after step 1, when you have the 45 degree angle) when I was trying to figure out how much wood I would remove if I used successive cuts with the table saw to round off the corners of my kalimba. I didn't even know what I was doing. Neat!

Interestingly…after playing with the Pell Sequence in a spreadsheet, i only see six (6) prime Pell numbers with indexes that are also prime. After that, the Pell sequence expands into large numbers with many zeros.

"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.)

101;2,002;30,003;400,004;5,000,005;60,000,006;700,000,007;8,000,000,008;90,000,000,009; and now for the magical Omni-presence of zero: considering that zero is nothing but an integer stuck between positive and negative it sure does make numbers larger… back to the sequence10,000,000,000,001;110,000,000,000,011;1,200,000,000,000,021;13,000,000,000,000,031;140,000,000,000,000,041;1,500,000,000,000,000,051;16,000,000,000,000,000,061;170,000,000,000,000,000,071;1,800,000,000,000,000,000,081;19,000,000,000,000,000,000,091;200,000,000,000,000,000,000,002;

To name theese ratios, grab a periodic table, eliminate all non-metalls (and hydrogen), and go N steps forward to the higher atomic number to name the N ratio. Golden->lithium Silver->beryllium Bronze->natrium Copper->magnesium Nickel->aluminium

Wow! It's amazing… … that this absolute BS made it into numberphile. If a person cuts a nail, then leaves it alone until a later date, then cuts it again in the same manner, the resulting nail clipping is 2 identical curves separated by a distance.

Nail clippings being that silly larger curve with a smaller curve within it is formed out of ignorance + imagination + stupidity.

So the Pell Sequence is a pseudo prime number generator. I wonder why this isn't used to find those larger primes. Just look at the prime indices and you're done.

13:38 – Peregrine Falcons hunt by swooping on prey (mostly birds) at high speed. The swept-back wings are the most striking feature whilst flying. They hit birds from out of the sun, making it easier to see and consequently making it nearly impossible for the prey to see them coming. When striking at great speed, they hit the prey with their talons folded into a "fist", stunning it, then circle back to take the falling bird.

So I was curious about something. I had no idea that the Golden Ratio was a result of a known equation: (N + sqrt(N*2 +4))/2, so I wanted to know what the ratio of ((N + sqrt(N*2 +4))/2)/N looked like. Turns out, it approaches y=x, it approaches N as N increases. And as N decreases or goes negative, it approaches 0. Don't know what that means, but it's fascinating.

What about the platinum ratio, from the zero-nacci sequence?

Hence, P_n = 0*P_(n-1) + P_(n-2)

As a result, the sequence is 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 …..

The ratio doesn't approach anything but by the formula, it is (0+sqrt(0^2+4))/2, or 1.

And sure enough, if you take 0 squares out of the platinum rectangle, you get a platinum rectangle ;)P

can we use this to find larger primes ie if u find the largest prime set position to it and look at the number in the sequence. and repeat

Couldn't we use the silver ratio to create infinitely big prime numbers? Like start at 3, the 3rd index is 5, the 5th index is 29, the 29th index is… Etc.?

Its like metals in the Olympics: 1st is Gold, 2nd is Silver, 3rd is Bronze

'A' paper sizes are a German invention Your Anglo-centricism compelled me to look it up.

How about fibonacci sequences that are recursively defined fron various metallic ratios?

I love peregrine falcons too, Those and Snowy owls. Anyway, I think this doesn't get taught at schools is the lies to children. Its easier to just focus on one ratio so that we don't overload them. Really enjoyed this video. I guess there must be Fibonacci sequences which use the negative multiples I wonder if these ever occur in nature?I did a quick excel experiment and I think the spiral becomes a wavy path which tends to y=x as the arcs get shorter and shorter. This is the same for all metallic ratios just they basically get there faster as the ratio cuts down the bounding squares for the arcs quicker. Its just like a damped oscillation along the 45.Anyway very thought provoking, thanks.

What is the proof about that it will be an arc of a circle, and not, for example, the arc of parabola?

This leaves me with so many more questions than answers

0 , 1 , 3, 6, 10, 15, 21, 28

“N-bonacci” is so fun to say

I tried to solve the ratio between A4 paper long and short side when I was 7

…i thought i could escape japan through numberphile

Fantastic! I love Numberphile!

Is that a baristochrome?

Americans don't use A4 paper??

Also they don't use metric.

Is there any time when America isn't wrong?

6:39 It always confuses me when a variable is used twice with a different meaning in the same formula, could you please start using a/b instead of n/N? I think subtle weird usage patterns like this really throw a lot of people off when trying to follow maths problems, or copyingsomething over and not noticing the different uses of ‘n’ and ater really getting stuck trying to understand it all.

I had a maths teacher who would write complex problems on the blackboard using ‘a’ for 2 different nested indexez and it was really really confusing :p

idk.. I personally trace a curve with the scissors when I cut my nails

0×infinity=1 0×infinity+0×infinity=2

1+777777777777777777777777777777777777777777777777777777777777777777777777777777!!!!!!!!!!!=infinity

Haitch befooa, haitch afteh

It's The Parker Ratio!!

Wow

What about non logarithmic spirals

1, 3, 9, 27 guess the next one

platinum ratio is ? P(n) = P(n-2) + 0 * P(n-1) 🙂

okay maybe not

and imaginary ratios ? P(n) = P(n-2) + i * P(n-1)

but what if you dont want your fingernails to be 2 micrometers short?

I can't seem to find it on the internet, so i hope someone here can answer: is there a limit to the pitch angles as you increase N?

0,1,1,2,5,27… start at 0 & 1, multiply the number by its self, add the previous number, repeat

Who just bites their nails

What happens if 'P’ pitch is irrational??

-"Haich"

gross

Terrible editing. You keep cutting off scenes. You guys are usually much better.

I was so confused when they opened up the video by talking about cutting fingernails.

Also I laughed at "…aluminium?"

I am completely freaked out

16:08 repetition rap

why we had to called "Melalic Rarios" ?

7:20

That's the solution to x² – Nx – 1

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.

Can't wait for Flat Earters to stumble upon this

Something I noticed: the formula for the Nth metallic ratio [N+root(N^2+4)]/2 is actually the solution to the general quadratic equation x^2 – Nx – 1 = 0 if you solve it according to the quadratic formula. Not sure if that's relevant to any larger mathematical problem but I thought it was interesting to note!

Show me the adamantium and vibranium ratios.

3.3027 4.23606 5.19528 … is the sum of the fractional part (also the sum of the reciprocal) for this infinite series, infinite or is it bound

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

Not true! When we arrive to the 7th pell number, we get 169 and it's not a prime number because he has 1, 13, 169 as dividers.

I ended up doing this by accident (after step 1, when you have the 45 degree angle) when I was trying to figure out how much wood I would remove if I used successive cuts with the table saw to round off the corners of my kalimba. I didn't even know what I was doing. Neat!

Those are some big scissors for finger nails.

Fu i have stiletto nails 😘

I tried to find the sequence 17,29,37,42,46,49 at OEIS and it wasn't there! That surprised me, for some reason.

13:40

1:13 except when fashion…

I’m guessing anyone who’s a werewolf will try to avoid this ratio…

Interestingly…after playing with the Pell Sequence in a spreadsheet, i only see six (6) prime Pell numbers with indexes that are also prime. After that, the Pell sequence expands into large numbers with many zeros.

Big in Japan. You have JoJo to thank for that…

I’m not sure I can forgive him for being a Liverpool fan

Everyone on numberphile looks like a serial murderer, I think it's something to do with the passion they show for maths

Is there a rational metalic ratio

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

What about platinum, ruthenium, rhodium, palladium, osmium, iridium, rhenium and mercury? They are always left out.

Americans don't use A4? What ratio paper do they use then?

Yeetbonnaci

1 yeet yeet+1 2yeet+1 3yeet+2 etc

That scissor bit made me surprisingly uncomfortable.

I can't remember where, but I have encountered this stubborn number a few times.

I can cut my nails with my thumbnails

"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.

We can call the √2 ratio the platinum ratio, but in fact it's not a metallic ratio, so maybe the diamond ratio would be better.

6:40 P=NP solved

Aburrido

ITS 1 1 NOT 0 1

I was expecting the Parker Square guy to do this one.

Mind = blown

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

Awesome! 😀 😀 Thank you very much!

Whatever happened to blackboards?

So, there is bronze ratio out there? hmm

"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.)

This is precisely what I used to do when I was younger and used scissors to cut my fingernails. They used to call me Wolverine.

101;2,002;30,003;400,004;5,000,005;60,000,006;700,000,007;8,000,000,008;90,000,000,009; and now for the magical Omni-presence of zero: considering that zero is nothing but an integer stuck between positive and negative it sure does make numbers larger… back to the sequence10,000,000,000,001;110,000,000,000,011;1,200,000,000,000,021;13,000,000,000,000,031;140,000,000,000,000,041;1,500,000,000,000,000,051;16,000,000,000,000,000,061;170,000,000,000,000,000,071;1,800,000,000,000,000,000,081;19,000,000,000,000,000,000,091;200,000,000,000,000,000,000,002;

To name theese ratios, grab a periodic table, eliminate all non-metalls (and hydrogen), and go N steps forward to the higher atomic number to name the N ratio.

Golden->lithium

Silver->beryllium

Bronze->natrium

Copper->magnesium

Nickel->aluminium

Attention!

metalloids are not used!

Did he just say that 169 is a prime number?!

And nobody saw it??

Hold on is this the dude all grown up from the meme where the guy is straining his forehead and the vein is popping out!? Serious inquiryWow! It's amazing…

… that this absolute BS made it into numberphile.

If a person cuts a nail, then leaves it alone until a later date, then cuts it again in the same manner, the resulting nail clipping is 2 identical curves separated by a distance.

Nail clippings being that silly larger curve with a smaller curve within it is formed out of ignorance + imagination + stupidity.

So the Pell Sequence is a pseudo prime number generator. I wonder why this isn't used to find those larger primes. Just look at the prime indices and you're done.

This is

😔😘😘🤨😖😘

So basically Golden Ratio is overrated!

What would a 1/2-bonacci spiral look like?

One day we’re gonna run out of metals and have to start naming relevant spirals after fictional metals

Did he say "haytch", when reading the letter H? (not eigtch) Where is mr. Tony's accent from?

Excellent extension of the Golden Ratio. I love it!

repeatition, repeatition,repeatition………😛

Somehow he manages to avoid talking about fractals

Since the pell number approximately doubles at each step, can it be used to quickly generate extremely large primes?

He constructs a spiral starring at 10:26. I assume it is an approximation, since it is made up of circular segments. Or did I miss something?

So much knowledge

the fibonacci sequence doesn't seem to have any powers of numbers except 0 and 1.

13:38 – Peregrine Falcons hunt by swooping on prey (mostly birds) at high speed. The swept-back wings are the most striking feature whilst flying. They hit birds from out of the sun, making it easier to see and consequently making it nearly impossible for the prey to see them coming. When striking at great speed, they hit the prey with their talons folded into a "fist", stunning it, then circle back to take the falling bird.

So I was curious about something. I had no idea that the Golden Ratio was a result of a known equation: (N + sqrt(N*2 +4))/2, so I wanted to know what the ratio of ((N + sqrt(N*2 +4))/2)/N looked like. Turns out, it approaches y=x, it approaches N as N increases. And as N decreases or goes negative, it approaches 0. Don't know what that means, but it's fascinating.

I shall find the……

Bronze, iron etc

Ratios

shout out mark e smith