Fibonacci Mystery - Numberphile 

As someone that has always struggled greatly with mathematics, I find myself entranced with these videos. I never thought I'd see the day when math became interesting. Great work, guys.

Funny to think this sequence started as a medieval joke about rabbit reproduction.

i wish there were enthusiastic math teachers when i was young. all we seemed to have was grumpy, unkept men who smelt like tobacco.

The joy this man gets from Math is just infectious.

didn't realise we had been controversial!!!

Almost a decade later and I still love coming back to these videos. I’m done with college and working full time but seeing these videos make me want to learn again

Tool also wrote a song that incorporates the fibonacci sequence in both the vocals and the rythm. The song is called Lateralus.

MATHEMATICS IS POETRY

I like that he knows about the history of mathematicians.

As a non-mathematician I have to say this channel is teaching me a lot. For working on a spreadsheet I learned Modulus math to solve a problem. I am stoked that I connected that math to this before they showed how the remainders switched back after the divisor when adding them like fib. You guys are making a difference out here. I am certainly a bit stronger math wise than before.

It's also interesting to note that when dividing by: 10; the period is 60, or 6 times the divisible (10) 100; the period is 300, or 3 times the divisible (100) 1000; the period is 1500, or 1.5 times the divisible (1000) The period length halves every time we jump up the base ten system. I assume when dividing by 10 000 the period length will be 7500, or 0.75 of the divisible (10 000) Just an interesting pattern I just noticed right now. Also if numberphile ever read this I love you guys, I'm in school for philosophy but I find your videos so very interesting :)

Theres a great song by Tool using the fibonacci sequence to arrange the vowels called Lateralus

James always have his pupils dilated

One of cool things about Pisano Periods is there are types of them. F.ex n=5,6,7,9,14 can be 'cut' in two halves, and the respective digits add up to the divider. There are amazing orders in this sequence yet to be discovered I'm sure.

James is my favourite, he’s always so excited!!

idk if anyone has said this, but the reason the musician divided by 7 is because that's how many notes are in a key or tonality in western music.

+Numberphile - I love your videos so much

wow I just notice how sun burned he is

friggin brilliant. I love seeing all these patterns together. It's a thing of beauty.

10 years after release, this vid found me. As I watch educational stuff in math, physics and tech to calm me down after a panic attack or when my anxiety goes through the roof. And today you did a great job by doing so. Thank you. You matter, even in ways you might not think.

Tool - Lateralus

And if you divide by infinity , and the remainder pattern will be the fibonnaci sequence

I discovered these back in primary school in a special class they had for students that enjoyed maths where they introduced us to new concepts, and let us experiment with them. Great to find out that it was actually a thing after all these years!

This has become one of my favorite RU-vid channels

I don't know whether it has been requested yet, but I'd really love to see a video on the connection between the Fibonacci sequence and the fraction 1/89.

The comments: 20% "I never thought I would like math, but then I found this channel" 2% "Wow, James is so sunburnt!" 78% "THERE IS ALSO A SONG BY TOOL THAT USES THE FIBONACCI SEQUENCE HAVE U HEARD ABOUT IT?"

I expected some mentioning of the "golden angle"

Best explanation of Pisano sequence I've seen to date!

He said at the end that a formula for the period was unknown, but just in my head I predicted that the 1000'th would have a period of 1500 because 10 had a period of 60 and 100 (10 * 10) had a period of 300 (60/2 * 10) and therefore 1000 (100 * 10) had a period of (300/2 * 10) = 1500. I'm guessing that 10,000, therefore, has a period of 7500.

I noticed that when you were dividing by 10, then 100, then 1000, the length of the period increased by 5x every time, there’s definitely some formula you could use to determine the length of the period based on this

This video gave me more appreciation for my favorite sequence, thanx!

I really liked how he explained it. Thank you, it's not too late for me to understand the Fibonacci series

The Hungarian composer Bela Bartok used the fibonacci series in many of his major works from 1907 onwards, esp. "Sonata for Two Pianos and Percussion," "Music for Strings Percussion and Celeste," etc. You should find a music theorist to do a video about Bartok's musical structural use of the series!

This and many other Videos are proving what's wrong with School! Education can be fun despite what the teachers say!

@ Numberphile: As a fellow mathematical person, I really dig what you're doing with these vids -- they really bring out the FUN of math, and that should go a long way toward infecting others who haven't seen that aspect, hitherto! A few observations to consider including, if a new edition of this is ever done: • The "natural" start to the Fibonacci sequence is F₀=0, then F₁=1. • Also, when doing one of these cyclic deals, as soon as you get "1" followed by "0," you know you've come to the end of the current cycle and the start of the next one, because the "0" is the zero-point of the new cycle, and F₋₁ = 1 ensures you're going to get the F's again, rather than some non-unit multiple of them. Also, as a fellow musical person, I'd just like to insert that while 7 is a musically interesting modulus, because it's the repeating length of a (Western) musical scale; 12 is the next musically interesting modulus, because it's the repeating length of a chromatic scale. Perhaps your musical friend can play around with that, if he hasn't done already. I know you know, but for benefit of others, the period of the F's mod 12 is 24, versus the 16-cycle for mod 7; so the Fibonacci'd chromatic scale could make an interesting musical pattern, as well.

Very cool about the addition of remainders wrapping around based on what you're dividing by.

math is trippy.

It's nice to have a non-controversial numberphile again. Thank you Brady and James.

Additionally, it must repeat from the beginning, because you can work out the sequence backwards in a unique way: if there's a section that goes a, b, c, and you know b and c but not a, you can work out a = (c - b + n) mod n. This means that the sequence can't loop back on itself in the middle (or there would be two different numbers before the b and c which you loop back to. Therefore, it must return to the beginning.

Such an accessible video for demonstrating further exploration into a familiar maths concept.

3:30 or 12 - the number of "semitones" in an octave.

I whish you were my teacher for mathematical theory at my university :P

my favorite video so far

Fabulous illustration to Pisano Period, thanks a lot!

16 numbers? that's insane because in music, time is split up into beats. and to human ears, 16 beats is the ideal length of a hook in a song.

In school Iearned Fibonacci's sequence as 0,1,1,2.... and it confused the f*** out of me. I just kept wondering where the first 1 came from?

You are the only person whom I have ever known to actually make math interesting,

Thanks !Happy new year !

Hey Numberphile! Your video actually inspired me to investigate these patterns further, so I wrote a program that would find the remainder for a set of numbers between 2 and x (I went as high as 100,000) and it would find the pattern and it's length. I found something really cool in the graph. It's a little hard to explain, but I could make a video about it if you guys wanted to see. Granted, I'm sure it's probably already known about amongst you guys.

I've noticed the video said that there's a Pisano period of 5^0*60 for 10^1, Pisano period of 5^1*60 for 10^2, and a Pisano period of 5^2*60 for 10^3... is that exact? Is that a random coincidence or a true pattern?

I never understood math at all and still don't, but this interests me because of the patterns, as I've been interested in art my entire life, and the math seems to be behind design and also music, which I love.Thank you for presenting it in an interesting way.I'm going to continue to learn about this.!

Thanks a lot for the video. It completely helped me on solving an algorithm programming assignment.

The Fibonacci tune kinda sounds like something from an N64 Rareware game.

But it seems there is a formula for the length of a sequence in the 10s 10 has a sequence of 60 numbers 100 has a sequence of 300 (60 x 5) 1000 has a sequence of 1500 (300 x 5) Does it keep going like that?

im so flashed! Love ur Vids! im kind of a Numberphille to i guess, allways had an special love for maths and "games with numbers", but what u are showing us is just mindblowing awesome!!!!!!

The Fibonacci Sequence sure has hidden depths. Fascinating video ! Thank you !!

if you divide by 100, the pattern repeats at 300 if you divide it by 1000, the pattern repeats by 1500 s it a mere coincidence that we are getting round numbers?

Your point about Fn|Fm if n|m has an exception F2 is the same as F1 5 cannot be divided by 2 but 5 but can be divided by 1. Could someone explain this to me

Thanks a lot! This video is even a big help of my programming assignment!

That's so crazy! It looks like the remainders create the same sequence basically in the base of the number you divided by

Tool used the Fibonacci in their 2001 song Lateralus =]

I am 51 years old and this is the first time in my life I have been genuinely enthused by maths. I have found my channel! ( My aim is to understand what on earth Godel was on about but its too complicated for me at this time)

The only best video channel

I didn't expect these sequences to sound so melodious. I'd be curious to try other sequences turned into sounds.

I can't explain it, but I just love this! Symmetry!... Sorta!

Dr. Grime, this is for you.I have posted similar question before, without anybody answering it. I will be extremely glad if you kindly do.The question is:What is so special about the number system of base 10 (modulus 10)? Nature follows this base when it adapts Fibonacci sequence or the golden ratio both of which are defined for base 10. Again, if you think of prime numbers in base 10, then you can easily see the first few prime numbers, but if you think base13(say) you will get a head ache,and will need paper and pencil.Why? I will be glad if your next video is on this theme.

I have absolutely no idea why but I thought of this and then decided to look up this video.

Excellent video. Very educational.

7:00 Period of 60, then period of 300, then period of 1,500...would dividing by 10,000 have a period of 7500? 8:00 It's basically the last digits of the fibonacci sequence in base 7, right?

Is it like subjecting Fibonacci numbers to modulo 7 ??

I've also noticed a weird thing about Fibonacci sequence. The quantity of numbers going in a row that have the number of digits that is a multiple of 4 equals 4. For example: 1597, 2584, 4181, 6765 There are four digits in each consecutive number. And the number of these numbers is 4. Next, let's take numbers with the number of digits is a multiple of 8, which, in turn, is also a multiple of 4 14930352, 24157817, 39088169, 63245986 Also 4 of them. And the pattern repeats for each group where the number of digits is a multiple of 4. For the rest it's 5 numbers in a row 2 digits:13 21 34 55 89 3 digits: 144 233 377 610 987 6 digits: 121393 196418 317811 514229 832040 And so on. I don't know why did I find it out and what are the practical applications of this, but whatever.

Interesting that using 7 (number of notes in a major scale) results in a period of 16, a convenient number of notes in music (exactly 4 measures in 4/4 time).

Why are your pupils so dilated...

cant you start the sequence with 0,1 instead of 1,1 the rest goes the same, right?

the song Lateralus by Tool, has the fibonacci code in it. what a beautiful song.

This channel makes me fall in love with math

"No idea what significance this is or where I would use it in life" Yes, rather a common feature of mathematics, that one. Very occasionally, somebody will discover a piece of maths because they needed it. Much more commonly, someone will discover a piece, like this thing, and then some time later, a bright spark will notice something in the real world which corresponds to the odd number fact, then we have a tool to deal with it. What is odd and striking is how quickly these uses for strange bits of number stuff can turn up, and just how very important and useful they can be.

So would the remainders of the fibonacci sequence when diving by seven be the same as the fibonacci sequence in base 7?

Loved the video. Thanks for explaining,

Back in school, I remember graphing some of these patterns for some reason. The only one that sticks out in my mind is dividing by 4 since the graph looked like a heartbeat on an ekg.

So for the last 1 digit the pattern is 60 numbers long, last 2 digits is 300 and last 3 digits is 1500, does that mean last 4 digits will be 7500, and last 5 digits will be 37500?

Wait, so we DON'T have a formula for the length of the periods based on the dividing number? Interesting :)

Fibonacci numbers have been found within the structure and entrance of themes in Bela Bartok's masterpiece, "Music for String Instruments, Percussion and Celesta."

amazing this series is used by me in programming but i never noticed these things

I don't want to brag but I discovered some of these patterns and the sequence on my own when I was 10 years old

Math blows my mind.

I just discovered this channel, so haven't explored it much yet. I have a Fibonacci question about the Golden Mean. While playing around with Excel one day, I discovered that it doesn't matter what values you seed your "Fibonacci" sequence with - the ratio between two consecutive elements of any such series seems to approach the same Golden Mean. You can start with pi and -e, and still approach 1.618... What gives? I think I'm going to like it here.

The fibonacci sequence done in an Ulam spiral gives some really cool new patterns :)

Correct me if I'm wrong, but did James divide 5 by 5 and not get 1?

Every 5th number is divided by 5 because the 5th number of the fibonacci sequence is 5 Every 6th number is divided by 8 because the 6th number of the fibonacci sequence is 8 Every 7th number is divided by 13 because the 7th number of the fibonacci sequence is 13 Every 8th number is divided by 21 because the 8th number of the fibonacci sequence is 21

You just blew my mind

I have become a die hard fan of this guy. He is simply amazing.... Kudos

Lateralus by Tool uses this too.

Divide them by 1 :p

Fibonacci is by far one of my most favourite number sequences. I'm a BIG fan of the swirl.

If I had videos like this to watch back in school, I would have enjoyed math a lot more.

Now divide by G64.

he reminds me of freddie in charlie and the chocolate factory.

Just re-watching all Numberphile videos.

Fibonacci sequence is also related to the golden ratio 1.61800 , if you divide a big number with the priveous one .