Mathematics - Fibonacci Sequence and the Golden Ratio
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- Опубліковано 19 жов 2024
- This mathematics video tutorial provides a basic introduction into the fibonacci sequence and the golden ratio. It explains how to derive the golden ratio and provides a general formula for finding the nth term in the fibonacci sequence. This sequence approaches a geometric sequence when n becomes very large.
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Can I use this sequence to predict the next lotto draw?
The golden ratio which is 1,618 is an endless number which you cant count. And if you read the verse 16:18 of the holy Quran it says: "And if you should count the favors of Allah, you could not enumerate them. Indeed, Allah is Forgiving and Merciful." The signs are very clear.
this is one of the beauties of the Quran.
thank u so much 💖
For those of you confused about at timestamp 16:12 here is the explanation:
As the author of the video mentioned, the Fibonacci sequence, apart for the first few numbers, has the property that Fn/Fn-1 = k , where k is the golden ratio. Turns out then that the Fibonacci sequence is a geometric progression, and a property of these progressions is that k^n is the n-th number of the sequence. Now, k in our case (fibonacci sequence) is the golden ration, so k^n is the n-th number of the fibonacci sequence. What we are doing at 16:12 is imposing that our generic progression has the property of fibonacci (so that Fn = Fn-1 + Fn-2), and we are looking to find k (the golden ratio). We actually find two values, because there are two values that satifies the equation F^n = F^(n-1) + F^(n-2). Now the problem is that neither 1.618 nor -0.618 approximates the fibonacci sequence. In fact, for example, 1.618^10 is 123 and not 55.
Seems like our calculations are wrong, but not really. We didnt take into account that the first few numbers dont satisfie Fn/Fn-1 = k, and this creates us a problem.
How to find the formula for the fibonacci sequence then? Remember that a linear combination of functions that satisfie the fibonacci sequence saties the fibonacci sequence itself too. Also, the possible sequence that can satisfie Fn = Fn-1 + Fn-2 MUST be a combination of the functions 1.618^n and -0.618^n. This because 1.618 and -0.618 are the roots of F^n = F^n-1 + F^n-2.
So what we are looking for is a way to combine these 2 functions so that we can actually find the fibonacci sequence. Our fibonacci sequence wants the first term to be 1 and the second term to be 1. (In fact 0 (zero-th term), 1 (first ),1(second)). That's enough to find how to combine our two functions, we just need to solve the following system of equations:
c1 * (1.618)^1 + c2 * (-0.618)^1 = 1 (
You confused me more.
@@aleeza7073same lol
If you have time for this shit you have entirely NO LIFE to live so you......
lmaooo, same@@aleeza7073
Huh?
BETTER THAN MY ONLINE TEACHER EXPLAINING FOR 2 HOURS WHILE I GOT IT FOR 24 MINS.
Ikr? we almost had an another class just so that he could explain for another 2 bloody hours, but I understood this in the first 10 minutes
Sana all kuha agad
@@juneljumadain3630 ay-
@@juneljumadain3630 Nag e-ml kapa kanina HAHAHAHAHAHA
yes
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Same ❤ .I'm in college and I found this channel in high school
Same I'm a freshman now
YOU SAVED ME I just started college and in my senior high school, I didn't come across much math except statistics which I was bad at too. Now with the pandemic, I'm left on my own to learn by myself because my teacher isn't teaching at all and just gives vague videos to watch. Thank you so much. I hope I can come across statistics in your channel.
I watched for almost 10times now in God's grace I understood it... Thank you for this video....
Sana all
everyone really has their own pace and I feel happy knowing someone doesn't also learn math in minutes only
I just want to thank you for all these videos. Ever since the pandemic started, math hasn't been a fun ride but the way you just explain these things directly just makes it all seem so easy. Wishing you success in you future endeavors, whatever they may be, thanks for helping us get through life in the mathematical aspect!😊
I cannot express how helpful this video was for me! I love how you break everything down to its simplest form. Keep up the great work!!
huge thanks man!!!
Im in a horse race rn and my friend is teaching me about the "golden ratio" And i dont understand him but now i know it now
ゴゴゴゴ
Lesson six
It's odly satisfying, hearing the taps from the calculator ugghhh✨
Try listening to ASMR
MR. Organic Chemistry Tutor, thank you for a fantastic explanation of the Fibonacci Sequence and a powerful derivation of the old Golden Ratio.
i dnt think theres any better tacher than u on youtube i have been tought by you since i was in grade 10 now am doing my second degree using your maths videos and learning from those i just wanna thank u enough
This channel has taught me more math than Chemistry.
Excellent . The beauty of mathematic. Only with very patient teacher
Hello! We have our Fibonacci distribution in our book, and we also have an assignment about it. My teacher did not discuss anything about it (IDK, is this how college supposed to look like?). The explanations I found in the book are obscure. Thank you because you've explained it and broke the two golden ratios into sections to make it more understandable to students like me.
lifesaver, i’ve been advance studying with your videos!!😭😭
Sir this video is so useful I'm from malaysia I'm an dlp student just because I'm in dlp class not all math teacher helps us in English but ur explanation is great I understand things so easily
ENGAGE ALL DEFENCES, AND GET THIS Man 100million subscribers
I wish that you show the complete solution for each. It would be a big help for me to understand the whole thing you discussed.
Said goodbye to higher than average difficulty level of maths almost 5 years ago.. 🤣🤣 a little rusty but understood the calculations. Uncle Fibonacci is lobh ❤️❤️
I loved the way you explained it, being an 11 year old i could actually understand 👍
I have using this sequence in my mlm company for team building and team managing , I think it's happening 1st time in the world mlm ( direct selling) industry.
Thank you so much.
I have to do a research paper for math and it’s due tomorrow and as I was about to start it I see the notification of ur vid and I was like thank the lord.
THANK YOU!! I badly need this for our project. Aaanndd we haven't learned this yet so this is a big helpppp ❤❤❤
But it would be much better if you showed the full calculation like the other comment said, which is exactly what I need for our project.
Ohhh my goodness
This helps so much !!!
Worth 24mins !!
Guessing r is absolute value I r I.
Found It is just one of best presentation for Fibonacci sequence. Thanks for lesson.
when school is a youtube channel
Fibonacci series is one of the most important tool in the Forex markets and stocks markets to determine the support levels and resistance levels.
Hello, do you know what is the pattern of fibonacci sequence?
Fibonacci squence: Any term equals the sum of the two preceding terms. It starts by 1, 1, 2, 3, 5, 8, 13, ...
@@mathpanther who tf asked?
Only video where I was actually thankful for the adverts to take a breather 😆
Thx for the video used it for my math Olympiad
A sequence that is not understood by many and you make this so simple #man of the century
Kinda long video but covers everything THANKS!!
I just straight up love you, best teacher in my life.
To complete this, you should also show the geometry/trigonometry method of getting the golden ratio.
It helped me understand Fibonacci sequence. Thank you😊
Thankyou so much .....helps me a lots to answer my module about Fibonacci sequence 😘
If I start at 5, does that mean I add 3 as it must be of sequence or is prior number to add 4?
Thank you! Thanks to you I solved task of finding first two number of Fibonacci sequence, where 19th (or 18th, idk, task says it is 19th) number equals 45614. Just by dividing 45614 by golden ratio, which you provided the formula for in your video.
By the way, answer is 14, 9, ....
do you know how to put the formula he used in a scientific calculator?
Thank you for this tutorial! God bless and more contents to come!
Thank you sa wakas na ka anwer na jud ko
16:18 I didn't understand how you got this part. From where did this come ? Of course this doesn't work for any number, so If I assume F means fibonacci number then again in the next step you treat it as a normal number raised to a power.
Someone who understood this part, please explain.
Were having a whole unit on deltas, long multiplication, and this, but i just learned it in less than 1 day
It's nice to see an updated video on this I enjoyed watching it. I'm looking forward to seeing more videos.
This person is my first choice to learn maths and l watch this video in 2024🎉🎉🎉
I love so much math but i gon cause of our mathematics teacher who dont really explain step by step
Btw. Im so very thankful i watch your video i have interest in math again
THANK YOUUU VERY MUCHHHH YOU'RE A LIFESAVER!!!!!!
At 16:19, you introduce F^n = F^(n-1) + F^(n-2). This is unexplained. Initially, n represented the nth Fibonacci number in the sequence, to which you wrote Fn = F(n-1) + F(n-2) where the parantheses are subscripts - not superscripts. These two equations are completely different. If I take your 16:19 equation and use an example: F^14 = F^13 + F^12, under what circumstance does this work? I'm missing something obvious. The rest is well explained and understood.
That's for quadratic equations
@@RAYON10 Sorry how is this a quadratic formula? n could be any number, like the n=14 example I listed. That’s not a quadratic formula with power 2. Also, again you aren’t explaining what you’re doing in this section - you just state this function and then begin reducing it. Still lost on what this portion of the lesson is attempting to explain.
@@jameskirkpatrick361 I scrolled for so long finding this comment bro. I'm 100% with u I don't get where he pulled that from or why. EDIT after finishing the video I see where he was going with it, but tbh he didn't need to do that and it really only served to be a source of confusion because the formula he uses, if I understand correctly, is completely inaccurate.
This is usually proven using limits. lim(n-> infinity) of F_n+1/F_n = (sqrt5+1)/2
Thank you naintindihan ko ng mabuti
Thanks for teaching me.
Love this! You deserve more attention and appreciation!
Best UA-cam channel ever! Thank you so much:)
henlo sa mga hindi naintindihan ang kanilang teacher
Self study is hard thanks to your help
"Hi there, I think it would be easier to read if you used typed-out numbers instead of writing it digitally. Just a suggestion ^_^
But still good explanations and easy to understand ⭐⭐⭐
Very simple and clear....
Thank you so much 🏅🏅🏅🏅
That was perfect. Thank you for sharing your knowledge.God Bless.
my ghad your a good teacher I understand it very well
If math was taught to me like this I just might have gottten it. They are teaching kids all wrong. Math is spiritual! Thank you! I’m sharing this video btw
THis is great but did you know using 0,1 as the start is the trivial case and you can actually pick ANY integers you want to start with and get the same result (golden ratio convergence). Can you dig into the deeper meaning of this?
is it possible for the fibonacci sequence to have negative numbers as the given first two terms? Please explain. Thank you!
Interesting. Saw the Fibonacci sequence in The Da Vinci Code. Super weird but cool.
I loved that movie
Wow great video. So easy to learn!
Thanks for this, it really helped me a lot. God bless
Me using this as my advance “reading” material for tomorrow’s lesson in Math ✨
Just remind 5 should be F5 but you mark it F6. Thanks for the tutorial
Great Explanation
Great Video! Well explained thanks! Also, why not divide the no. by 1.618 to get the previous no. instead of multiplying it with 0.618....both are correct tried and tested (fyi)
Just correct me if i am wrong
Thank for this 😊 I understand clearly
Continue to the 17th or 18th ratio get 1.618034, the golden ratio to 6 decimal places
I didnt understand my teacher at all whole hour in a half in class confused I was like wtf are you saying here in 15 min im good now thank you my real professor haha
It's better than my teacher explanation on my module I got here minutes only..
what's the video that came before? or is this video apart of a larger series/playlist?
How do you get the square root it's hard to understand without showing the solution
Thanks! It makes sense finally.
You are great! Thank you for this! Very clear, got it!
I have a question, just a little curious. During the golden ratio derivation, why did you multiply them to r2 (r squared) before transposing them. Maybe it will sound dumb, still thank you to anyone who will answer.
Where the author wrote F6 above the number 5 in the sequence, he meant F5, since the sequence starts with F0
what about the F10 on the 11th term?
Hello! I'm curious what is the basis of the formula in getting the exact value of Fn? Thank you!
can u explain further where u get 5+1 divided by 2?
the golden ratio
So helpful!im still in 4th grade doing 5th grade stuff😅
School is he same thing as a UA-cam channel😂
*the (he):)
This lesson is for 5th grade????
Uhuh?HAHAHAHHA
Woah! So this lesson is for 5th grade?! When back in the day I fencountered this on my 5th year in college taking a 4 year course!
Determine the pattern in the successive sums from the previous question. What will be the sum of Fib (1)+ Fib (2)+......Fib (10
so what is the answer of this? 55?
Do we need to divide 8/5 ?
Why would I use the golden ratio to get the next number when i could just add the 2 following numbers.
Can we input F sub n to equal to negative number?
I watched ALL UR VIDS SO GOOD😋😋😋😋😋😋😋😋😋
Thankyou for helping me in my activity
I was getting it at first but you said earlier 1:26 that 0 is for F0 and 1 is for F1 and 5 is for F5, but in 8:45 you put the F6 in 5 huhuh Im almost gonna lose it but thanks anyway i still understand
How i wish instructor explained it like you did
9:01 you had a mistake by saying 5 is Fsub6.
Thank youu, my professor ask us to do a advance reading abt this but hahah since im more of a visual learner when it comes to math, i search for it heheh
what type and brand of calculator are you using?
12:36 you lost me here, I dunno whats next, I am trying to get the same number but I can't get it help
Hey I hope this comment gets answered, so I'm trying to find the term F100, and when I put the formula in my calcu and the answer was in a decimal form, is this the final answer or do I literally need to solve it myself without an calculator?
SPIRAL OUT, KEEP GOING!
16:21 why did the coefficient become an exponent? shouldn't it be Fn =Fn-1 + Fn-2 (n, n-1 and n-2 are coefficients not exponents)
If you need a number less than 12 which formula you use?
Thank you for explanation❤️
Excuse me, where did you get 1.618033 from sqroot of 5+1÷2?
13:10. When I use that formula, it keeps on showing 33,825 and not 6,725. Abt possible reasons for this?
How did you get the F12 when getting the 20th Fibonacci?
Thanks for the video. I noticed at timestamp 10:29 you say 6465 instead of 6765. Just thought you would like to know. Thanks Again.