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.
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.
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.
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.
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.
Indians have major contributions to maths all around but are underappreciated compared to European mathematicians. Its similar to how Mathematicians are not as well known as physicists.
Yes and Vedic Mathematics is just one inkling of Gelgamek Mathematics. Indian mathematicians rename all those concepts after people who speak their language and share their culture. What a bunch of supremacist a-holes.
@@rohanarshad3728 What has the religion have to do with those scholars ? If you are saying they took their information from The Quran, much of it was already knowledge in existance before the Quran was written.
probably first and probably last time commenting on TH-cam :) : 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.
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.
John Wolsey What on earth? I did not know that. Thanks for sharing that. That is rather weird. Not sure if it's the tip of the iceberg for something larger or just an odd amount of coincidence. I should write this kind of stuff down.
John Wolsey I've often wondered if numbers don't rule reality. We use them to see the universe. We use them to understand concepts and realities. They could be a language. They help use grasp things. I'd like to study the advantages of using diff base counting systems. A base 10 is what I am familiar with. I thought the Maya used a base 20.
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.
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.
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!
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.
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.
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.
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
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)
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.
Yes, it is true that starting with any two numbers converges just as rapidly on phi, but if you thoroughly examine them, the famous Fibonacci Numbers and another Fib sequence called Lucas numbers have amazingly unique and even startling qualities that no other Fib sequence possesses
37rainman I will take a look at Lucas numbers when time and energy permit. A brief glance suggests they are fascinating. My knowledge is limited, but I am in awe regarding various results I've run across. Thanks for the tip.
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. )
What he said was "almost" any Fib number. If one uses Fibs even as low as F22 and F23, by that point you have an accuracy of 10 digits (rounded). How is that for "the same number". (he meant by "same number", that they very quickly become exceedingly accurrately phi) (-: But seriously, there is a way that you can very simply use the Fib numbers and another Fib sequence called "Lucas numbers" to arrive at an EXACT phi. Simply take ANY Fn and the same Ln (where n is anything other than 0): the nth root of [(Fn x sgrt 5) + Ln] / 2 = phi (to infinite digits). I. e. : the average of any (Fib number times the sqrt of 5), and its corresponding Lucas number is always an exact power of phi. (Except where n is 0). Also of interest might be that if you multiply Fn x Ln you get exactly F(n x 2)! The intriquinly beautiful things about Fib/phi are almost endless. And yes, Grammer Communist did have a point -- your post was smug and anal .......... but hey, this IS you tube and you're entitled., as am I. (-;
37rainman Thanks 37rainman. Yes, the Fibonacci sequence is a fascinating creature. My critique was entirely factual. The ratio of successive Fibs, as you say, converges quickly, in fact, exponentially fast, to the Golden Ratio, but NEVER actually gets there. I'm not simply being pedantic. Remember all Fibs are integers, so their ratios are rational numbers. The Golden Ratio on the other hand is an irrational number. It can be approximated by the sequence of ratios as closely as you like, but NEVER exactly. I realize the video is aimed at non-mathematicians, but I think it's dumbing things down too much. My tone and style are irrelevant. But since you raised the issue, I find Hank the presenter's style quite hand wavy, imprecise, flippant and needlessly comedic. Mathematicians take a lot more care when explaining things, even to a general audience. I think this video is likely to leave the non-mathematician mystified, with no clear understanding of the real beauty of the Fibs. Instead, have a look at Prof. Art Benjamin's 6 minute talk here: www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers.html Anyway, ya - I found the talk irritating.
qrubmeeaz You're right on the math thing, but this isn't meant to be entirely precise and entirely correct. Hank isn't going to start talking about limits, which is at best a late-pre-calc topic that most people won't know about, or more accurately an early-calc topic that even fewer people know about. He "dumbed it down" so he could get the beauty of the numbers across to people without having to also teach them the exact stuff behind it. You keep comparing Hank to mathematicians. He's not. He's an educator who teaches by entertainment. There are plenty of these on TH-cam, and they too at times skip over some of the minutia to explain the main idea.
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.
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.
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.
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_
+Timo Meijs I really hope the brainfart of yours was sarcasm or satire. This channel is too intelligent for people who don't "believe" in Evolution and the Big Bang.
+Women's Studies Textbook you refer to scientific theories which are generally based on randomization. The "Fibonacci Sequence" simply demonstrates a pattern throughout nature which can be observed starting from small plants on earth all the way to the form of other galaxies. It is one fact in support of intelligent design as opposed to everything in nature being the result of random events. Not believing in Evolution or the Big Bang does not make one unintelligent. It should be encouraged in the field of science (as in any other professional field) to question the status quo. Where one theory does not explain something or there are gaps one should investigate it further without being afraid to delve into the unknown to learn more.
In response to your last paragraph, I agree that one could easily accept either theory of the origin of life. Nor evolution/big-bang theory nor the existence of God can be proven according to scientific standards for validation. Both require some level of faith to believe one or the other ;)
“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.
"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??
+floralundies The point is that no matter what culture or language you are describing the universe with, the mathematic principles will always be the same. Aliens on the other side of the universe would still understand that 1 + 1 = 2 even if we had no other way of communicating.
+Matthew Kemp No matter what HUMAN culture or Language. How can ANYONE know ANYTHING about "Aliens on the other side of the universe"? They Can't. Human arrogance leads people to believe "Our Math" is consistent everywhere in existence, I guess.
+isolationdisorder It is. The same laws of physics is present everywhere in the universe, therefore so is the math that describes said laws. They might call the number different things, but 1 will always be equal to one.
+floralundies "Math is a human construct, so not sure if that is really correct. " Humanity is part of nature fundamentally first off, second if you'd like to separate them by common lines, math would still be an interpretation of nature regardless. Though humans may find it abstract in their own thoughts if you put thought into any process its fundamentally natural. So i agree with the video's statement and disagree with your launching argument for the the question you pose.
I have used thinking through Fibonacci Series numbers to: calm music performance nerves (running through the numbers I knew a few minutes before going on stage); distract from pain while getting dental crowns put on; and lower my blood pressure numbers, among other things. I know the first 133 numbers (last one is: 2,791,715,456,571,051,233,611,642,553) and usually go through them once a day while walking. I also say or think through the sequence backwards often. It has helped me remember numbers much better, but it does not help me remember why I went to the grocery store.
No, it's more like, he got his hands on a bunch of theoretical books on mathematics, probably from Indian sources which were probably translated in arabic, and then both translated these ideas to the european academia and started doing his own work using the arabic numerals. As for why Indian sources, well, because during the European middle ages Indian kindgdoms went through a golden age in which a lot of new astronomical and mathematical discoveries were made, and that information was later collected into the libraries of large muslim cities, from which copies were brought to Italy by Fibonacci.
You can't STEAL Truth from others or make a claim or trademark on Truth. It's EXISTED SINCE ALL OF CREATION. Long before humans. Your reasoning could be applied to: 2+2 = 4 was stolen from India The color blue was stolen from India
Here in 2023 watching this because I'm taking Concepts of Math and now I'm SUPER invested in the Fibonacci sequence and watching all the videos on it. 😂
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?
Is it not clear that the universe is indeed created by math? If indeed it can be described mathematically because that is its true form? I know creationism is not popular even though its totally obvious. Really the best of the best in science has not even figured out that bees levitate instead of fly. They do this by beating wings that create a standing wave in the cavity of the thorax. This is why college science cannot figure out why the aerodynamics of Bees do not make sense...they carry 90% of weight in pollen with no drop in speed in a straight line...hence the term bee line...But no your people insist that the realm we live in is not created and that Bees actually do fly even though its impossible. No wonder you guys stay in school and do nothing else.
No, it's not clear that the universe was created by math. If the universe can be described by words, does it automatically follow that it was created with words, or that words are the universe's true form? Geez, type a line or two, and suddenly someone thinks they know everything about you. I certainly had no idea you were a creationist from the comment you posted. And by the way, scientists finally have figured out how bees fly, and, BIG SURPRISE, it doesn't violated the laws of physics. Here, for example, is an article from 2006 talking about it. www.livescience.com/528-scientists-finally-figure-bees-fly.html. Don't like that article? Do a Google search; there's plenty of others. Now I'm sorry I gave your comment a thumbs up.
thank you for proving my point...you sent me to a biased reference. Your not getting it...we are not just talking about bees but bees that levitate for miles away from the hive, load up 90% of body weight with pollen, then levitate back miles to the hive in a straight line around 30 mph with no drop in speed regardless of load...they are not flying. Levity is stronger than gravity and it exist in creation everywhere. All you are doing is proving that you stick within fixed circles of thought....this was my original point when I said you stay in school and do nothing else. And in response to your query regarding the universe being created with words.....it was. Again you prove the creationist point..thank you.
how would you deliver this video? he could use some pear juice for sugary pep, and a few drops of oil to smooth out his vocal chords ive done that it works
He brought awareness of the sequence into European academia. Much of what we learn about discoveries is overinflated. For instance, atomic theory has been considered and recorded in India for millennia. The Baghdad battery shows that electricity was likely an existent though rare technology in the ancient world. We credit philosophies that are natural to reason to the men who described them famously in ancient Greek, even though people, even children, discovering those philosophies for themselves always has been and always will be commonplace.
Gordon Freeman He was a white guy. I don't mean that to be flippant or derogatory, but there it is. The scientific establishment is so deeply Eurocentric that a fact could be known in Asia or Africa or Arabia for centuries but would only become "scientific knowledge" when written about in a European journal article or book by a (typically) white European author. It's not uncommon at this point for people to become defensive as though Science Itself is under attack. It isn't, not as such, but the biases of some of its many and varied practitioners are. That is an important distinction. It's also true that there is a distinction between the bias held unknowingly and the bias kept out of foolish pride. Fibonacci got the credit for an old Indian discovery because he was the first person to put it into the formalised scientific literature, and to be able to do that at that time he had to be a white man of financial freedom. That's just part of our history now.
Gordon Freeman A lot of ancient scientific discoveries were done in other parts of the world (particularly Asia) and then were either imported into Europe or the Europeans discovered it later on their own. However, since modern science has its basis in the history of European science, you don't really hear much about the other countries nor is much credit given to them.
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
@@AkhilNArt A Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, suggested that a little circle should be used in calculations if no number appeared in the tens place. The Arabs called this circle "sifr," or "empty." Zero was crucial to al-Khowarizmi, who used it to invent algebra in the ninth century.
that's a huge stretch. a "creator"?, I really don't get how this is supposed to "prove" a creator. creator? creators? , who created the "creator"? , because if something complex and "intelligent" is proof of a creator. then what is a creator proof for?, a higher tier creator of creators?
@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.
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!
On the contrary, I'd argue "found" rather than "lost" because of common core. I'm a CCS Math Teacher, & here I am watching this video to see if it can inspire students. Check out the performance tasks at the Shell Institute's website, or MARS, or NRICH. These are the types of tasks students are being given and they are more rigorous than the curriculum I've been delivering the past 17 years.
It seems with Hank's first statement that he believes that math is inherent in nature and not created by man to translate nature. An interesting position I wasn't expecting from him based on his previous work. Glad the ideas are spreading on this one, either side!
I think that what HanK means when he says that math is in nature is that while humans invented the concepts of number and have abstracted math pretty much as far as we can, the basics of math are still based on how the universe works. The system may be invented, but it still works when applied to the real world.
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:"
My first exposure to this was in No Man's Sky, and God did I have trouble figuring this out because math is definitely not my strong point. I tried looking up how to solve the puzzles on my own but I was constantly given a mathematical formula or equation and no clear instructions on how to solve them. I'm glad to finally see how easy it is, especially within the first few minutes of the video
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.
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, 144, ∞ infinity! We will feel this process as the arrow of time within each reference frame.
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.
You still there, my guy?
@@darellarocho5729 still kicking!
@@BinaryBard011101 Awesome!
What do you use Fibonacci for?
Wooww! 9 years ago. And you are still here.
Haven't you change your mobile or Gmail since 2013?😶
"Math wasn't made up to harass English majors"
-hank green
Ima have to write that quote down, cause it's golden!
Aeroscience
English major loving math here!
Only a scientists would know that due to the very complicated reason of why it exist.
But for non science humans,
IZ BULLSHAIT
Only Middle schoolers
You explained the Fibonnacci sequence in a much more interesting and engaging point of view than my classes ever will
I made a new discovery
th-cam.com/video/B72y9kaM2JI/w-d-xo.html
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
#Fibonacci ..
Hank looks so hammered/ bored in this video:D
Correct 😂
Good for beginners 🙂 grace is always a wonderful 🕊💖🕊
Hes living in the matrix
Just means he's still not getting it?
He's just a mathematician badass, that's why. It would be even more obvious if he wore sunglasses
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.
Are you still here man?
9 years ago, in 2013 😶, I was just 8 years old.
@@amanjyotijatta2085 I was 5
@@amanjyotijatta20851 was 1 was 9😭
@@amanjyotijatta2085I was 8 too
I love the way he is usually so enthusiastic when talking about science but when it comes to maths...
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.
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.
2:24 Now Johnny use the spin!
Yes
That was the best explanation of the the fibonacci number I've seen up to date!
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.
Indians have major contributions to maths all around but are underappreciated compared to European mathematicians. Its similar to how Mathematicians are not as well known as physicists.
@@saminhaque13-52 Same is the issue with muslim scholars
Yes and Vedic Mathematics is just one inkling of Gelgamek Mathematics. Indian mathematicians rename all those concepts after people who speak their language and share their culture. What a bunch of supremacist a-holes.
@@moderncloth682 What is Gelgmek Mathematics ? Google just shows a South Park character Gelgamek lol
@@rohanarshad3728 What has the religion have to do with those scholars ? If you are saying they took their information from The Quran, much of it was already knowledge in existance before the Quran was written.
probably first and probably last time commenting on TH-cam :) :
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.
+Ralitsa Kost. I was once confused by the magical twins as well haha.
+TMSNssto WHAT DOES THAT MEAN???YOU PEOPLE ARE MISSING THE POINT!!!!😕😕😕😕😕😕😕
YVES CAJUSTE What is your point?
It was the unusual lexical phraseology and some exquisitely unusual accent markers that I noticed and wondered upon...
Ralitsa Kost. Fibonacci sequence wasn't created, it was discovered. (:
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.
1.618 Dave Thats actually very interesting.
1.618 Dave ϕ is a symbol for the golden ratio.
ϕ^2 = ϕ + 1
1/ϕ = ϕ - 1
John Wolsey What on earth? I did not know that. Thanks for sharing that. That is rather weird. Not sure if it's the tip of the iceberg for something larger or just an odd amount of coincidence. I should write this kind of stuff down.
+1.618 Dave Oh, it's definitely just the tip.... keep seeking and you'll find SO MUCH MORE!!
John Wolsey I've often wondered if numbers don't rule reality. We use them to see the universe. We use them to understand concepts and realities. They could be a language. They help use grasp things. I'd like to study the advantages of using diff base counting systems. A base 10 is what I am familiar with. I thought the Maya used a base 20.
Uh, Hank? You're not as energetic as usual, you doing okay?
I thought that too. If you aren't feeling great, get well soon Hank!
+Meredith Navin Are you two stupid or something? You really don't understand that this video was uploaded 4 years ago?
discountinn Oh... Then why did it just now show up in my updates?? Wierd...
+discountinn lmao x)
+the Insane Artist even for 2012 hank he seemed kind of out of it
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.
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.
Ohh.. That was actually a very cool way to see this..🤔.. Wow.. Thank You❣️😌.. Or in this case maybe.. Hank You❣️..🥴 (it’s ok.. I see myself out🙄)
aww, no energy-hank, thanks for making me fall in love with fibonacci almost seven years later!
"Over thinking, over analyzing separates the body from the mind"
-Maynard James Keenan
Actually it separates the mind from the body
Tawos Abdalla Actually??????
@@alwayssomewhattiredmind can live without the body but not vice versa
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!
Chris Helms listen to the song ‘Lateralus’ by tool. It uses this sequence.
nerd
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!
I wonder how much the Green brothers make from all their vids
Totally
5th lesson
*THE PERFECT SPIN*
*The infinite spin*
was wondering how far I'd have to scroll to find this comment
"If you are faithfull in little, you will be put in much"
Words of life. Divine Laws of nature that preserve life.
You mean God.
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.
In my opinion we didn't create math we discovered it
The Golden Spin!
Yep
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
Tool's Lateralus brought me here :D
Black
Then
White are
All I see
In my Infancy
Red and yellow then came to be
Stewie from family guy brought me here
Lol 46&2 brought me here
Creepy produce brought me here
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.
It's also the ratio of credit cards length/width - to make them more appealing to use
@No Idols imagine being aggressive for no reason
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
Last 3 characters of the URL is my face right now.
Nice observation! Hahaha
Yoo this was 6 years ago😟
@@mahii7993 yoo your comment was a year ago 🤔
yo 7 years ago?
it's like time travelling
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)
figures of Al Khwarismi, i.e. so-called arabic (actually Indian) numerals
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.
Yes, it is true that starting with any two numbers converges just as rapidly on phi, but if you thoroughly examine them, the famous Fibonacci Numbers and another Fib sequence called Lucas numbers have amazingly unique and even startling qualities that no other Fib sequence possesses
37rainman I will take a look at Lucas numbers when time and energy permit. A brief glance suggests they are fascinating. My knowledge is limited, but I am in awe regarding various results I've run across. Thanks for the tip.
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
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. )
***** Hmm?
What he said was "almost" any Fib number. If one uses Fibs even as low as F22 and F23, by that point you have an accuracy of 10 digits (rounded). How is that for "the same number". (he meant by "same number", that they very quickly become exceedingly accurrately phi) (-:
But seriously, there is a way that you can very simply use the Fib numbers and another Fib sequence called "Lucas numbers" to arrive at an EXACT phi. Simply take ANY Fn and the same Ln (where n is anything other than 0): the nth root of [(Fn x sgrt 5) + Ln] / 2 = phi (to infinite digits). I. e. : the average of any (Fib number times the sqrt of 5), and its corresponding Lucas number is always an exact power of phi. (Except where n is 0).
Also of interest might be that if you multiply Fn x Ln you get exactly F(n x 2)!
The intriquinly beautiful things about Fib/phi are almost endless.
And yes, Grammer Communist did have a point -- your post was smug and anal .......... but hey, this IS you tube and you're entitled., as am I. (-;
37rainman Thanks 37rainman. Yes, the Fibonacci sequence is a fascinating creature.
My critique was entirely factual. The ratio of successive Fibs, as you say, converges quickly, in fact, exponentially fast, to the Golden Ratio, but NEVER actually gets there. I'm not simply being pedantic. Remember all Fibs are integers, so their ratios are rational numbers. The Golden Ratio on the other hand is an irrational number. It can be approximated by the sequence of ratios as closely as you like, but NEVER exactly. I realize the video is aimed at non-mathematicians, but I think it's dumbing things down too much.
My tone and style are irrelevant. But since you raised the issue, I find Hank the presenter's style quite hand wavy, imprecise, flippant and needlessly comedic. Mathematicians take a lot more care when explaining things, even to a general audience. I think this video is likely to leave the non-mathematician mystified, with no clear understanding of the real beauty of the Fibs. Instead, have a look at Prof. Art Benjamin's 6 minute talk here:
www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers.html
Anyway, ya - I found the talk irritating.
qrubmeeaz You're right on the math thing, but this isn't meant to be entirely precise and entirely correct. Hank isn't going to start talking about limits, which is at best a late-pre-calc topic that most people won't know about, or more accurately an early-calc topic that even fewer people know about. He "dumbed it down" so he could get the beauty of the numbers across to people without having to also teach them the exact stuff behind it.
You keep comparing Hank to mathematicians. He's not. He's an educator who teaches by entertainment. There are plenty of these on TH-cam, and they too at times skip over some of the minutia to explain the main idea.
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.
He mentioned that in the beginning
Watch the video
Lol he didn't learned from his neighbours he just derived it by his own
Your matter-of-fact explanation was engaging, entertaining and deeply informative!
Very nicely explained. Thanks Hank. If people appreciated a good video like this instead of criticising they would feel happier.
This sh*t blows my mind for real y'all
honestly same
"Math... it can be beautiful too!" - Truth
Keep Going, Spiral out.
Lateralus
❤
Yes
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.
It’s like having this amazing thing explained from a depressing hipster
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.
"33"
Less than 3.33 percent
Hank seems a little subdued in this one.
Woah... Hank, you are much more animated in your videos now (2015) than here. Lot's of progress has been made 👍🏽😃
There is something perfect yet beautiful about mathematics in nature.
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_
+Timo Meijs I really hope the brainfart of yours was sarcasm or satire. This channel is too intelligent for people who don't "believe" in Evolution and the Big Bang.
+Women's Studies Textbook what are you doing here then? lol
you are right a creater made it all
+Women's Studies Textbook you refer to scientific theories which are generally based on randomization. The "Fibonacci Sequence" simply demonstrates a pattern throughout nature which can be observed starting from small plants on earth all the way to the form of other galaxies. It is one fact in support of intelligent design as opposed to everything in nature being the result of random events. Not believing in Evolution or the Big Bang does not make one unintelligent. It should be encouraged in the field of science (as in any other professional field) to question the status quo. Where one theory does not explain something or there are gaps one should investigate it further without being afraid to delve into the unknown to learn more.
In response to your last paragraph, I agree that one could easily accept either theory of the origin of life. Nor evolution/big-bang theory nor the existence of God can be proven according to scientific standards for validation. Both require some level of faith to believe one or the other ;)
Swing on a spiral too, swing on a spiral ....
SPIRAL OUT
KEEP GOING
As below so above and beyond I imagine
White, black, then red, came to be
NATURE, WHY CANT I BE SO AWZOM???
you are "awzom" because you are nature
So matter of factly describing something so profound.
Very helpful video. Thanks!
Black
And
White are
All I see
In my Infancy
Red and Yellow then came to be
Reaching out to me
Lets me see
“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.
It's Tool, not Tools.
Elizabeth Hogan is correct. You should edit your post so as not to look like a "Tools".
+Mr Pregnant - Atelston Fitzgerald Holder 1st HAHAHAHA "TOOLS"
Mr Pregnant - Atelston Fitzgerald Holder 1st tool*
It's "Tool." Singular.
"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??
+floralundies The point is that no matter what culture or language you are describing the universe with, the mathematic principles will always be the same. Aliens on the other side of the universe would still understand that 1 + 1 = 2 even if we had no other way of communicating.
+Matthew Kemp No matter what HUMAN culture or Language. How can ANYONE know ANYTHING about "Aliens on the other side of the universe"? They Can't. Human arrogance leads people to believe "Our Math" is consistent everywhere in existence, I guess.
isolationdisorder Come on man. A square has four sides. That is a base logic that cannot be altered.
+isolationdisorder It is.
The same laws of physics is present everywhere in the universe, therefore so is the math that describes said laws.
They might call the number different things, but 1 will always be equal to one.
+floralundies "Math is a human construct, so not sure if that is really correct. " Humanity is part of nature fundamentally first off, second if you'd like to separate them by common lines, math would still be an interpretation of nature regardless. Though humans may find it abstract in their own thoughts if you put thought into any process its fundamentally natural. So i agree with the video's statement and disagree with your launching argument for the the question you pose.
Funfact: these Arabic numerals have Indian origin and the numbers we use today are created by Albrecht dürrer.
I have used thinking through Fibonacci Series numbers to: calm music performance nerves (running through the numbers I knew a few minutes before going on stage); distract from pain while getting dental crowns put on; and lower my blood pressure numbers, among other things.
I know the first 133 numbers (last one is: 2,791,715,456,571,051,233,611,642,553) and usually go through them once a day while walking. I also say or think through the sequence backwards often.
It has helped me remember numbers much better, but it does not help me remember why I went to the grocery store.
Sequences created by a random expansion...
Hmm, that doesnt make much sense.
Still trying to figure out Donald Trump's hair...
Lateralus
Wow
That's
Deep, man
Pretty deep
Pretty fucking deep
It's so philosophical, man
Fibonacci song
It's so deep
Thank you, very concise, informative and resourceful
thanks for helping me with my homework
lol, no energy Hank.
He seems high
+computerkopman123 The editing mashed all his words together so it seems like he isn't taking a breath.
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?
No, it's more like, he got his hands on a bunch of theoretical books on mathematics, probably from Indian sources which were probably translated in arabic, and then both translated these ideas to the european academia and started doing his own work using the arabic numerals.
As for why Indian sources, well, because during the European middle ages Indian kindgdoms went through a golden age in which a lot of new astronomical and mathematical discoveries were made, and that information was later collected into the libraries of large muslim cities, from which copies were brought to Italy by Fibonacci.
You can't STEAL Truth from others or make a claim or trademark on Truth. It's EXISTED SINCE ALL OF CREATION. Long before humans.
Your reasoning could be applied to:
2+2 = 4 was stolen from India
The color blue was stolen from India
Love your point of view
Rama Bangera Is Fibonacci, not Fibonachi. It's Italian, dude.
Love how I shared this recently but it came out 11 years ago
Here in 2023 watching this because I'm taking Concepts of Math and now I'm SUPER invested in the Fibonacci sequence and watching all the videos on it. 😂
int a = 1, b = 1;
while (true)
{
println(a);
a = a + b;
b = a;
}
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?
Actually, I'd just say that natural phenomena can be described mathematically, not that it was created with math.
Is it not clear that the universe is indeed created by math? If indeed it can be described mathematically because that is its true form? I know creationism is not popular even though its totally obvious. Really the best of the best in science has not even figured out that bees levitate instead of fly. They do this by beating wings that create a standing wave in the cavity of the thorax. This is why college science cannot figure out why the aerodynamics of Bees do not make sense...they carry 90% of weight in pollen with no drop in speed in a straight line...hence the term bee line...But no your people insist that the realm we live in is not created and that Bees actually do fly even though its impossible. No wonder you guys stay in school and do nothing else.
No, it's not clear that the universe was created by math. If the universe can be described by words, does it automatically follow that it was created with words, or that words are the universe's true form? Geez, type a line or two, and suddenly someone thinks they know everything about you. I certainly had no idea you were a creationist from the comment you posted. And by the way, scientists finally have figured out how bees fly, and, BIG SURPRISE, it doesn't violated the laws of physics. Here, for example, is an article from 2006 talking about it. www.livescience.com/528-scientists-finally-figure-bees-fly.html. Don't like that article? Do a Google search; there's plenty of others. Now I'm sorry I gave your comment a thumbs up.
Or maybe this article will more directly address your bee comments: rationalwiki.org/wiki/Bumblebee_argument.
thank you for proving my point...you sent me to a biased reference. Your not getting it...we are not just talking about bees but bees that levitate for miles away from the hive, load up 90% of body weight with pollen, then levitate back miles to the hive in a straight line around 30 mph with no drop in speed regardless of load...they are not flying. Levity is stronger than gravity and it exist in creation everywhere. All you are doing is proving that you stick within fixed circles of thought....this was my original point when I said you stay in school and do nothing else. And in response to your query regarding the universe being created with words.....it was. Again you prove the creationist point..thank you.
Hank, have you been smoking weed
lol
how would you deliver this video?
he could use some pear juice for sugary pep, and a few drops of oil to smooth out his vocal chords
ive done that
it works
that's.....really specific
Probably the Fibonacci Express, an epicurean delight of the sativa kind. Who needs adderall when you have this stuff?
Thanks for this great video. It's short, sweet, educational, beautiful and simple.
Appreciation to the team!
I made a new discovery
th-cam.com/video/B72y9kaM2JI/w-d-xo.html
pretty interesting series! Really cleared up all my questions.
You learn a lot of this in art class.
hank
you uh..
you alright?
1337
This video gave me 20 points extra credit in my college calculus class. Thanks, I needed it!
I have never understood the fibonacci sequence, or the golden ratio/rectangle till now.. Thanks!!!
0:43 Yeah but Arabic numerals were also invented by indians😏😏😏
Arabs now use Indian numbers and English people are using the original arabic ones .. 123arabic origin .. ١٢٣indian origin
cope
So what did Fibonacci actually do if the Greeks and the Indians new it before him?
He brought awareness of the sequence into European academia. Much of what we learn about discoveries is overinflated. For instance, atomic theory has been considered and recorded in India for millennia. The Baghdad battery shows that electricity was likely an existent though rare technology in the ancient world. We credit philosophies that are natural to reason to the men who described them famously in ancient Greek, even though people, even children, discovering those philosophies for themselves always has been and always will be commonplace.
He gave it a cool name
Triforce Of Gaming David McLauchlan and that, is what matters most in the end
Gordon Freeman He was a white guy. I don't mean that to be flippant or derogatory, but there it is. The scientific establishment is so deeply Eurocentric that a fact could be known in Asia or Africa or Arabia for centuries but would only become "scientific knowledge" when written about in a European journal article or book by a (typically) white European author.
It's not uncommon at this point for people to become defensive as though Science Itself is under attack. It isn't, not as such, but the biases of some of its many and varied practitioners are. That is an important distinction. It's also true that there is a distinction between the bias held unknowingly and the bias kept out of foolish pride.
Fibonacci got the credit for an old Indian discovery because he was the first person to put it into the formalised scientific literature, and to be able to do that at that time he had to be a white man of financial freedom. That's just part of our history now.
Gordon Freeman A lot of ancient scientific discoveries were done in other parts of the world (particularly Asia) and then were either imported into Europe or the Europeans discovered it later on their own. However, since modern science has its basis in the history of European science, you don't really hear much about the other countries nor is much credit given to them.
meek mill brought me here
Also used in stocks (Fib retracement).
ViHart's video IS amazing!!
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
People are so mean, they always give credit to those Europeans, but not the ones who are really worth the honour...
Binary ## haha. Zero was invented by Arabs. Read the history
@Amed Sayed seems like you read the wrong history 🤣
@@AkhilNArt A Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, suggested that a little circle should be used in calculations if no number appeared in the tens place. The Arabs called this circle "sifr," or "empty." Zero was crucial to al-Khowarizmi, who used it to invent algebra in the ninth century.
@@AkhilNArt no idea but history is confusing
Not invented, it was discovered.
If this doesn't Prove intelligent design a creator for everything in existence , I don't know what does .
that's a huge stretch. a "creator"?, I really don't get how this is supposed to "prove" a creator. creator? creators? , who created the "creator"? , because if something complex and "intelligent" is proof of a creator. then what is a creator proof for?, a higher tier creator of creators?
Troll.
And this crushes "God": imgflip.com/i/218q3o imgflip.com/i/2arxzy
You're a good guy. I love your stuff! I kind of wish there had been more on this one in particular.
@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.
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!
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
yes, Obama is the cause for all poor mathematicians...
You spelled 'religion' wrong.
On the contrary, I'd argue "found" rather than "lost" because of common core. I'm a CCS Math Teacher, & here I am watching this video to see if it can inspire students. Check out the performance tasks at the Shell Institute's website, or MARS, or NRICH. These are the types of tasks students are being given and they are more rigorous than the curriculum I've been delivering the past 17 years.
i disagree... this is what common core is made for! this is the perfect problem solving activity to introduce algebraic patterns....
DarkeCrimson *tips fedora*
Interesting information but TERRIBLY annoying presenter! That type of arrogance specific to American pseudo scientists like Myth Busters.
Fibonacci (1175 - 1250), was an Italian Mathematician and considered to be the most talented Mathematician in the middle ages.
It seems with Hank's first statement that he believes that math is inherent in nature and not created by man to translate nature. An interesting position I wasn't expecting from him based on his previous work.
Glad the ideas are spreading on this one, either side!
I think that what HanK means when he says that math is in nature is that while humans invented the concepts of number and have abstracted math pretty much as far as we can, the basics of math are still based on how the universe works.
The system may be invented, but it still works when applied to the real world.
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:"
3069mark I like this
3069mark Beautiful. God is the greatest mathematician.
I dont understand
I was watching this video: th-cam.com/video/EE2_2vuDTao/w-d-xo.html and at the 49 minute mark, it speaks of this code. Pretty cool. :)
My first exposure to this was in No Man's Sky, and God did I have trouble figuring this out because math is definitely not my strong point. I tried looking up how to solve the puzzles on my own but I was constantly given a mathematical formula or equation and no clear instructions on how to solve them. I'm glad to finally see how easy it is, especially within the first few minutes of the video
It shows intelligent design through a mathematical point of view. If I didnt become a doctor, I would have become a mathematician.
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.
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, 144, ∞ infinity!
We will feel this process as the arrow of time within each reference frame.