The Fibonacci Sequence: Nature's Code 

The Fibonacci sequence is actually the calmest thing I can think of to calculate in stressful situations. It's easy, it's simple, and it's everywhere--and as the numbers get higher, it's JUUUUST difficult enough to make one forget about all the crazy junk going on around one. Works for me.

"Math wasn't made up to harass English majors" -hank green

You explained the Fibonnacci sequence in a much more interesting and engaging point of view than my classes ever will

The Fibonacci Sequence is so important and Hank is such an awesome presenter and this was just not his best day. I would love, LOVE it if this were re-done. For a random video it would not be worth it but this is something really accessible that unlocks SO MUCH else about nature

There was this one time when I was trying to write efficient code for dynamic shadows for a game. I worked it all out in my head and came to the conclusion that there was a very specific numeric sequence that I needed to hardcode to make my technique work properly. Turns out it was the fibonacci sequence. Oh Universe, how I love thee.

0:33 - "The sequence was first described by Indian Mathematicians and Mr Fibonacci introduced it to Europe". Fibonacci is just one small concept of Vedic Mathematics. But you will find all such re-packaged stuff named after either European, American or Greek mathematicians.

Fibonacci's Sequence is all around us in nature. The sequence of numbers can be seen in plants, fruits, and animals. Also the golden ratio and golden rectangle all revert back to the Fibonacci Sequence of numbers. Dividing a number by the one before will give you the same ratio. This is known as the golden ratio (Phi). The golden rectangle can be divided into a serious of squares that have dimensions of the Fibonacci Sequence.

Hank looks so hammered/ bored in this video:D

1,1,2,3,5,8,13,21,34,55,89,144... (...233.377.610...) - I was noticing a while back that 144 is the 12th # in the sequence... - 12 is also its root - &if you take144's mirror-441, it's root is 21, the mirror of 12 who's square is 144 - same thing with 13 (13x13=169 31x31=961) ( I haven't bothered to check how many more numbers might do that but I notice that not all do, so that' is kind of interesting but I don't know if its profound or significant) or if I should see it as pointing toward something else. Also, this could be meaningless or just coincidence... but I was also recalling how I read that the Mayan's use 144,000 (144,000 days in a Baktun) and also 144,000 is used in the Christian Bible too. Maybe someone has some thoughts on this too. Also, the divine number is neat in the way in which if you square 1.618 it will be roughly the same as if you added 1.0 to it. Kind of weird.

I love the way he is usually so enthusiastic when talking about science but when it comes to maths...

Tool even sync lateralus perfect to the sequence. To answer simple questions DNA has limitation called the human body. The fibinanci as an equation has no sky & just goes on. The numbers hit in sync it's harmony

In my opinion we didn't create math we discovered it

2:24 Now Johnny use the spin!

I learned more math from this and the arabic numerals videos you did then all the info my teachers tried to ram into my head without explaining it properly.Great job from the entire team working on this. I kind of suck at exact sciences but I learned a lot from all your crash course series and I will keep studying until i can make a living of either anatomy or math.Hope you do a crash course series on math after you are done with anatomy and big history.

probably first and probably last time commenting on RU-vid :) : After years of watching CrashCourse i decided to watch this math video and i see this guy and think "lol is this john green? looks like him but i feel its not" so i check out the comments to find out the name of this guy cause i've seen him in CrashCourse but i just blanked and couldn't come to terms with it. found out its hank green. searched him. found out his brother is john green. my world is complete. Life makes sense. (no wonder he looks the same but different in crash course videos.) what i learned the most from this video : hank and john are brothers and more than 1 green exists and hank lives in montana and the Fibonacci sequence was made 1300 years ago in India. I hope that one day you too can solve life and feel wholeheartedly complete with a simple math video - 3 min 19 sec of your life.

Uh, Hank? You're not as energetic as usual, you doing okay?

That was the best explanation of the the fibonacci number I've seen up to date!

Incidentally I've always found English (and other languages) to be a lot like math. A structured sentence is like an equation and each are governed by rules that must be followed for clarity. Art is very mathematical too, with variations on the golden rectangle, and triangular compositions popping up everywhere. English, Math, and Art were my fave subjects in high school.

"Over thinking, over analyzing separates the body from the mind" -Maynard James Keenan

I love your show, dude. Very well done. As an artist, I use this sequence in every piece of art I make. I learned very quickly that incorrect use the sequence always results in a botched piece. You should consider tying this episode into Mandelbrot's set, which are a direct correlation to this sequence in surprising ways.

Fibonacci is my favorite number sequence. I remember learning about it first on PBS's Square One TV during the Mathnet portion of the show. They made it fun and interesting, and I was a Fibonacci Fan for life!

aww, no energy-hank, thanks for making me fall in love with fibonacci almost seven years later!

5th lesson *THE PERFECT SPIN*

LOL Hank used to sound miserable before the channel was making a buttload of money, now he sounds so joyful...ah the power of cash!

It's also the ratio of credit cards length/width - to make them more appealing to use

"If you are faithfull in little, you will be put in much" Words of life. Divine Laws of nature that preserve life.

I figured out about this 3 years ago in a simple math class when we looked at patterns with the Fibonacci sequence and rectangles. Man, that was a long time ago.

Finally a video that treats me like a 4 year old and tells me everything and not the hard stuff

The Golden Spin!

Tool's Lateralus brought me here :D

thank you so much for explaining this! I have often had teachers sort of go over the golden ratio, but often their half-hearted attempts left me more mystified than anything.

Last 3 characters of the URL is my face right now.

1:48 "If you divide almost any Fibonacci number by the one before ... especially the larger ones, you get the same number" Dude!! Noooo! Mathematicians don't talk like that!! It's not true anyway! The sequence of ratios of successive Fibonacci numbers has a limit. It is either the golden ratio, or its reciprocal (depending on whether you you used f(n)/f(n-1) or f(n)/f(n+1) as your ratio. )

FYI: Fibonacci learned about this number series from Indians living in his neighborhood. This number series existed in ancient Indian texts thousands of years before Fibonacci was born.

“Tools” is an American metal band pervasively known for incorporating the Fibonacci Sequence in their musical time signatures and lyric patterns, 9/8 to 8/8 etc…I’d like to explore their ironic use of the sequence in their song called “Lateralus,” in the opening lyrics to the song the Fibonacci Sequences were embedded in the numbering of syllables, making the inherent nature of the Fibonacci Sequence applicable beyond the parameters of music, but into writing, poetry and other sorts of linguistic usage. Fibonacci Coriolis Effect: There’s a strong correlation between biological structures and the physics of motion, would “electromagnetism” be an inappropriate metaphor? Because although electricity and magnetism are intertwined, the former is an electric charge and the latter is a force and repel, and it became “electromagnetism” after Maxwell’s juxtaposition of their inner mechanisms in his unified equation. Fibonacci Sequence are in the Coriolis Effects, the sequences are in the non-transparent symmetry of the wind, synonymous to the propagating patterns in pineapple pine-cones outer layers. There’s pairs of spirals widening to the left and right where the numerical systems are found, seems prevalent in the symmetry of Botany. Equivalent to objects in motion on the earths surface that curve in relation to the revolution, Northern Hemisphere deflecting to the right and the Southern Hemisphere deflecting to the left.

hank, the way you totally avoid any emotions is really enioyable to see. it also kinda sounds like you're being really cynic and it's amazing

Thanks for this very informative and just what I needed. Been drawing this for a long while. Along with the rest of my rhythmic art nature influenced art work

"Math... it can be beautiful too!" - Truth

It’s like having this amazing thing explained from a depressing hipster

Keep Going, Spiral out.

Definitely receiving a mysterious cosmic mandate telling them to organize in the most efficient way possible....

Interesting to see that everything is arranged. Everything has its own sequence and fits. From flower petals to the shape of our milkkyway to the shape of things in the rest of the universe, its ALL in the sequence. Yet they still claim it was an explosion of nothing because nothing happened to it. _suure_

This sh*t blows my mind for real y'all

Hank seems a little subdued in this one.

int a = 1, b = 1; while (true) { println(a); a = a + b; b = a; }

We're born twice, once awake we keep it to ourselves and go about living in The Matrix. About 40% of humanity is awake and you can see it in every successful business logo.

Swing on a spiral too, swing on a spiral ....

Black And White are All I see In my Infancy Red and Yellow then came to be

Still trying to figure out Donald Trump's hair...

NATURE, WHY CANT I BE SO AWZOM???

"Math was invented by Nature" - Math is a human construct, so not sure if that is really correct. Which leads to the question: did humans discover or invent math??

lol, no energy Hank.

So, this fibonacchi also stole numbers from india and called his own, and this is how many did. So find out why india was so special then?

Lateralus

Sequences created by a random expansion... Hmm, that doesnt make much sense.

You learn a lot of this in art class.

meek mill brought me here

Did you really just say math was invented by nature? Do you understand the depth and breadth of that statement? I think its more obvious to say the Universe was created with math....don't you?

Hank, have you been smoking weed

hank you uh.. you alright?

He seems high

The Picatrix discusses the figures of Al Khwarismi (namely 0) and it was translated into medieval spanish and latin roughly around the same time as Fibonacci - they were sort of bursting at the seems and into Europe around this time (13th century)

If you look outside, you can see how magnificent it is. If you look at your hand, you can tell it what to do in your mind and it does it. we make sounds and understand each other, we have compassion and feelings for one another. You can't try and convince me that that is a random combination of particles. That is like taking abart an intricate watch, putting it in a shoebox, shaking it up, and thinking it will put itself back together.

1337

Not invented, it was discovered.

Funfact: these Arabic numerals have Indian origin and the numbers we use today are created by Albrecht dürrer.

Could the Fibonacci sequence be formed by the spontaneous absorption and emission of light? All the info I can find says that this process is formed by the quantum wave particle function Ψ of quantum mechanics. When this is reformulated as a linear vector ǀΨ (t) > the two previous vectors are added together to form a new vector this forms the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ∞ add infinity! We will feel this process as the arrow of time within each reference frame.

So what did Fibonacci actually do if the Greeks and the Indians new it before him?

0:43 Yeah but Arabic numerals were also invented by indians😏😏😏

Your matter-of-fact explanation was engaging, entertaining and deeply informative!

It's interesting that tangerines more often then not are divided into 10 pieces, not 8 or 13. I know because, at least where I grew up, they say that you get a wish if you get 10 pieces in a tangerine. I've been counting since I was old enough to do it and about half of the times you get 10. If it's not 10 there is often one really small or really large piece in there.

It was discovered by an Indian mathematician name Pingala...but he never got the credit... anything done by an Indian shouldn't be given credit... This Pingala dude also discovered binary system... anyways

If this doesn't Prove intelligent design a creator for everything in existence , I don't know what does .

Very nicely explained. Thanks Hank. If people appreciated a good video like this instead of criticising they would feel happier.

Fibonacci numbers also appear in reproduction, and I'm not talking about rabbits couples. I'm talking about parthenogenesis. Any creature who reproduces by parthenogenesis will have a number os ancestors who are in the fibonacci sequence. I'm talking about bees. Since female fees do have both a mother and a father (no matter whether they are workers or queen), but male drones only have a mother (and no father), any bee will always have a number of ancestors in the fibonacci sequence. It may be 8, 13, 21, whatever.

It's a damn shame that the art of mathematics such as this will be lost because of Common Core Curriculum (the dumbing down of school kids) and Obama

Whatever like plants have the knowledge to govern the most effective way to create life. HINT: who gave them a brain. I know there's a creator and his name is JESUS!

Actually, not all pine cones use Fibonacci numbers. Vi Hart mentions this. Some use a different but similar sequence starting 1, 3, 4, 7, 11, 18...

There is something perfect yet beautiful about mathematics in nature.

One Word, ie: GOD -- Romans 1:20 "For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse:"

Interesting information but TERRIBLY annoying presenter! That type of arrogance specific to American pseudo scientists like Myth Busters.

Also used in stocks (Fib retracement).

Nice quick overview. A more general fascinating fact is that if you take ANY two positive integers and run a Fibonacci pattern on them (keep summing the largest two you have generated), the quotient of the last two will converge on the Golden Ratio. So you don't have to start with 1,1. You could start with 2,17, for example. This more general result is impressive, fun (WOW!) and provable.

Woah... Hank, you are much more animated in your videos now (2015) than here. Lot's of progress has been made 👍🏽😃

@rebel, you have to realize that even though we don't really know how the big bang happened, you have to realize that the big question is how did the first pieces of matter come into existence. how did your "magic being" get here? that's the question.

Four sequential numbers will add up to the next number after the last forth number. If you add the inner ones and outer ones. 1+2+3+4. 1+4 =5 2+3=5. Works for every number. Realized this in elementary school. Though not sure if it's the same.

Plants don't have 8, 13, or 21 petals. Chances are you are including the sepals as part of the petals or you might be counting leaves. Like what most people think are sunflower "petals" are actually modified leaves. The sunflower is a compound flower. The center circle region is filled with all of the flowers. Each sunflower flower has 5 petals and when pollinated, yields a seed.

So matter of factly describing something so profound.

Hm, thats actually pretty cool, I wonder what other flowers and things have the fibonacci sequence, and people havent even realized yet!

Fibonacci (1175 - 1250), was an Italian Mathematician and considered to be the most talented Mathematician in the middle ages.

It's not only the Fibonacci sequence that has the Golden Ratio between successive values. Any sequence that obeys the Fibonacci rule - adding the preceding two values to get the next value - will eventually reach the Golden Ratio for successive values. e.g: 4, 11, 15, 26, 41, 67, ..., 238605, 386071, and 386071 / 238605 = 1.618033989...

Fibonacci sequence starts to seem more divine when you considee that you can find it in weird places in the mendolbrot set...

Could the Fibonacci sequence be formed by the spontaneous absorption and emission of light? This is represented by the quantum wave particle function Ψ of quantum mechanics. When this is reformulated as a linear vector ǀΨ (t) > the two previous vectors are added together to form a new vector this forms the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,∞ We will feel this process as the arrow of time within each reference frame with the future coming into existence photon by photon!

Thanks for this great video. It's short, sweet, educational, beautiful and simple. Appreciation to the team!

CORRECTION: Fib wasn't the only one borrowing Indian concepts. "Arabic numerals" were also taken/borrowed from Indian culture.

You can see the difference between SciShow 8 years ago to now. A lot has changed

thanks for helping me with my homework

The Green Bros. know exactly how to keep me still. Autism, ADHD, and others make it hard for me to do so. Thanks guys. For real. Thanks. I learn constantly and am entertained. Nearly nothing else is as effective.

I couldn't love this more. Well done.

I'm British too. Please don't make people think we're idiots. That's not how language works. If you want to be taken seriously, it's a lot easier when people can understand you.