Mathematics - Fibonacci Sequence and the Golden Ratio

[@TheOrganicChemistryTutor]

Sequences - Free Formula Sheet: bit.ly/4eau2KQ Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/qGeUZXR6ZZdkpJI

[@mirriamjulile9738]

Can I use this sequence to predict the next lotto draw?

[@koko-nx3vy]

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.

[@nashnash4966]

thank u so much 💖

[@sadown4490]

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 (

[@aleeza7073]

You confused me more.

[@jesuschrist2029]

@@aleeza7073same lol

[@Randy-v9x]

If you have time for this shit you have entirely NO LIFE to live so you......

[@haryllegianmicotuan5098]

lmaooo, same@@aleeza7073

[@Messier102]

Huh?

[@byel7985]

This youtube channel has always been my life savior. I discovered this channel when I was in high school and now that I'm college, I'm still going back to watch their videos.

[@ns6428]

Same ❤ .I'm in college and I found this channel in high school

[@pybiosa]

Same I'm a freshman now

[@divinorutherforda.9968]

BETTER THAN MY ONLINE TEACHER EXPLAINING FOR 2 HOURS WHILE I GOT IT FOR 24 MINS.

[@yvesdelacruz7241]

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

[@juneljumadain3630]

Sana all kuha agad

[@xolarxyxtem]

@@juneljumadain3630 ay-

[@BLITZMINDTV]

@@juneljumadain3630 Nag e-ml kapa kanina HAHAHAHAHAHA

[@Jade-ko2hi]

yes

[@KB-uw6ne]

If I start at 5, does that mean I add 3 as it must be of sequence or is prior number to add 4?

[@ivymercana5532]

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.

[@lovelyheart3152]

I watched for almost 10times now in God's grace I understood it... Thank you for this video....

[@rae5522]

Sana all

[@yara7903]

everyone really has their own pace and I feel happy knowing someone doesn't also learn math in minutes only

[@kensaishigen1994]

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!😊

[@idunno7916]

It's odly satisfying, hearing the taps from the calculator ugghhh✨

[@periwinkle1]

Try listening to ASMR

[@mackennahatfield9559]

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!!

[@slashr406]

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

[@wiaamalkindi5753]

when school is a youtube channel

[@mathpanther]

Fibonacci series is one of the most important tool in the Forex markets and stocks markets to determine the support levels and resistance levels.

[@christinesn707]

Hello, do you know what is the pattern of fibonacci sequence?

[@mathpanther]

Fibonacci squence: Any term equals the sum of the two preceding terms. It starts by 1, 1, 2, 3, 5, 8, 13, ...

[@etzjunior_]

@@mathpanther who tf asked?

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for a fantastic explanation of the Fibonacci Sequence and a powerful derivation of the old Golden Ratio.

[@rodrickngonyoku5042]

This channel has taught me more math than Chemistry.

[@aerado_0]

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.

[@taylorgeswint4668]

Ohhh my goodness This helps so much !!! Worth 24mins !!

[@jeykeyyy2]

lifesaver, i’ve been advance studying with your videos!!😭😭

[@hussainfawzer]

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.

[@garethsfiso]

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

[@jameskirkpatrick361]

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.

[@RAYON10]

That's for quadratic equations

[@jameskirkpatrick361]

@@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.

[@lukewells6621]

@@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.

[@beru58]

This is usually proven using limits. lim(n-> infinity) of F_n+1/F_n = (sqrt5+1)/2

[@mahfoudbenhadj-djilali5525]

Excellent . The beauty of mathematic. Only with very patient teacher

[@jivi3184]

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

[@LeeMaya-x4k]

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

[@mb1_chris]

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.

[@lukemarlow2]

Only video where I was actually thankful for the adverts to take a breather 😆

[@anwar4227]

ENGAGE ALL DEFENCES, AND GET THIS Man 100million subscribers

[@AlcaMathhelp]

A sequence that is not understood by many and you make this so simple #man of the century

[@mohammadbahrampour3417]

I just straight up love you, best teacher in my life.

[@carljohngrino1458]

Thank you for this tutorial! God bless and more contents to come!

[@arleecribe5211]

It helped me understand Fibonacci sequence. Thank you😊

[@l0v4bleFae]

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.

[@khooshell123]

Cool video! Thanks for helping me solve this question. My practice paper had a question about F set20. (at 10:24) TQ!

[@wyattbrowningsmith6433]

It's nice to see an updated video on this I enjoyed watching it. I'm looking forward to seeing more videos.

[@Sleepylss]

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.

[@notmynamehaha]

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 ❤️❤️

[@UnnieCute]

Thank you sa wakas na ka anwer na jud ko

[@divinematibag7439]

Love this! You deserve more attention and appreciation!

[@allene597]

Thankyou so much .....helps me a lots to answer my module about Fibonacci sequence 😘

[@Jackrabbit.2]

I loved the way you explained it, being an 11 year old i could actually understand 👍

[@LiwaySaGu]

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)

[@ilyashick3178]

Guessing r is absolute value I r I. Found It is just one of best presentation for Fibonacci sequence. Thanks for lesson.

[@marianne3353]

henlo sa mga hindi naintindihan ang kanilang teacher

[@TrueLoveCanada]

6:15 the problem with using 1.618 is that it doesn't work for all numbers in the sequence. How do you determine at which point to start using it? shouldn't it apply to all numbers in the sequence? You selected only a few to calculate on, but because it isn't precise, the calculations are off the higher you go in the sequence. If you can't use it at the beginning of the sequence, you can't say that every number is multiplied by a ratio of 1.618. It simply is not precise therefore it is not true.

[@R.Zephyr]

Pls provide an example in which it doesnt work, I think it works for all the numbers in the sequence

[@TrueLoveCanada]

@@R.Zephyr 0x1.618 does not equal 1 it equals 0. 1x1.618 does not equal 1, it equals 1.618 1x1.618 does not equal 2, it equals 1.618 - do I need to continue?

[@sadown4490]

@@TrueLoveCanada Of course it doesnt, he said that in the video.

[@TrueLoveCanada]

@@sadown4490 His whole argument is that it does

[@sadown4490]

@@TrueLoveCanada No, he says it doesnt for small numbers.

[@anilnamdeo9190]

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.

[@moustafagebal5366]

Kinda long video but covers everything THANKS!!

[@Cherang-u5o]

Thx for the video used it for my math Olympiad

[@gelibnl3981]

THANK YOUUU VERY MUCHHHH YOU'RE A LIFESAVER!!!!!!

[@Yagid]

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, ....

[@sultananizami6616]

do you know how to put the formula he used in a scientific calculator?

[@vanessawelles4760]

To complete this, you should also show the geometry/trigonometry method of getting the golden ratio.

[@-MikaelaWuisan]

Best KZbin channel ever! Thank you so much:)

[@silfrido1768]

To anyone that has a scattered brain like I do, don’t worry we got this 💪🏻

[@gloriousspear1924]

9:01 you had a mistake by saying 5 is Fsub6.

[@ElshadayBerihun]

This person is my first choice to learn maths and l watch this video in 2024🎉🎉🎉

[@mipaato]

Very simple and clear.... Thank you so much 🏅🏅🏅🏅

[@leezx8505]

Just remind 5 should be F5 but you mark it F6. Thanks for the tutorial

[@Cary12361]

Thank you naintindihan ko ng mabuti

[@JFK37002]

Were having a whole unit on deltas, long multiplication, and this, but i just learned it in less than 1 day

[@victorialucernas7470]

Thank for this 😊 I understand clearly

[@lattebearforlife]

I watched ALL UR VIDS SO GOOD😋😋😋😋😋😋😋😋😋

[@gayanc6193]

Great video huge thanks❤

[@unidadecredatimoruct243]

That was perfect. Thank you for sharing your knowledge.God Bless.

[@gynx-bp8mq]

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

[@MauieFabiosa]

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

[@tolentinojohnmiguelp.8229]

Wow great video. So easy to learn!

[@kadenmikael279]

Self study is hard thanks to your help

[@carl8182]

You have a small error in 8:55 the "5" from fibonachi is not 6

[@anjiluu]

13:10. When I use that formula, it keeps on showing 33,825 and not 6,725. Abt possible reasons for this?

[@sajidabrar1]

Its 6765 use brackets and watch out for the raised powers

[@jasondoe6079]

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?

[@overpoweredpoverty54]

9:32, increasing? Like is the series increasing or is it because 20>12

[@yourmomgae7355]

What was the name of the formula on 9:41 ?

[@jhonallenalarcon6695]

Thanks for this, it really helped me a lot. God bless

[@anj_3237]

Me using this as my advance “reading” material for tomorrow’s lesson in Math ✨

[@joeysenpai]

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

[@andrewben346]

Thanks for teaching me.

[@thehousewife3054]

Interesting. Saw the Fibonacci sequence in The Da Vinci Code. Super weird but cool.

[@Manta2006]

I loved that movie

[@kgbbbbbbb6392]

Thanks! It makes sense finally.

[@mylinusudan9535]

"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 ⭐⭐⭐

[@cagangkimberlyl.9908]

my ghad your a good teacher I understand it very well

[@arahdims1886]

I am confused. In the part of golden ratio when you divided them how some of them got rounded up but some of them aren't and how did 55÷34 only got 6 digits and 34 ÷21 have 7 digits? I'm confused. Please someone help my stupid brain. 4:43

[@jericksonlomugdang2025]

You are great! Thank you for this! Very clear, got it!

[@StevenLyall]

While the Fibonacci sequence begins with 0 and 1, no matter what two random numbers you start with, you will still get the get the golden ration from fn/fn-1 after a few iterations.

[@transferz]

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

[@quest2782]

what's the video that came before? or is this video apart of a larger series/playlist?

[@whatsafterlike5688]

How do you get the square root it's hard to understand without showing the solution

[@JesseCotto]

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.

[@danielacarino7126]

is it possible for the fibonacci sequence to have negative numbers as the given first two terms? Please explain. Thank you!

[@progrocker2112]

SPIRAL OUT, KEEP GOING!

[@allene597]

It's better than my teacher explanation on my module I got here minutes only..

[@jzrl7349]

8:48 shouldn't it be F of 5 not 6?

[@LiwaySaGu]

also, what is the significance of the Fibonacci in organic chemistry?

[@Mkb315]

AS ABOVE, SO BELOW!

[@md.abdurrazzak90]

Great Explanation

[@annfrost3698]

Where the author wrote F6 above the number 5 in the sequence, he meant F5, since the sequence starts with F0

[@alexandramogro9]

what about the F10 on the 11th term?

[@zyke_]

Hello! I'm curious what is the basis of the formula in getting the exact value of Fn? Thank you!

[@loveisforyoutoeat8911]

Math is my fav subject but after 6 months of quarantine I don't know what happened lol

[@emanoelpahati9292]

Why would I use the golden ratio to get the next number when i could just add the 2 following numbers.

[@lattebearforlife]

So helpful!im still in 4th grade doing 5th grade stuff😅

[@lattebearforlife]

School is he same thing as a KZbin channel😂

[@lattebearforlife]

*the (he):)

[@somebodyonce3326]

This lesson is for 5th grade????

[@angeldangan5151]

Uhuh?HAHAHAHHA

[@mikkamayor8355]

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!

[@abikg6121]

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

[@kushanmanahara4073]

Thank you for explanation❤️

[@bangsatatv5814]

Do we need to divide 8/5 ?

[@betasamarkiang.4162]

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.