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

[@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

[@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.

[@Titnos]

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

[@georgesadler7830]

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

[@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?

[@rodrickngonyoku5042]

This channel has taught me more math than Chemistry.

[@anwar4227]

ENGAGE ALL DEFENCES, AND GET THIS Man 100million subscribers

[@lukemarlow2]

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

[@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.

[@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

[@jeykeyyy2]

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

[@taylorgeswint4668]

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

[@mahfoudbenhadj-djilali5525]

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

[@AlcaMathhelp]

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

[@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.

[@mohammadbahrampour3417]

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

[@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

[@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 ❤️❤️

[@wyattbrowningsmith6433]

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

[@divinematibag7439]

Love this! You deserve more attention and appreciation!

[@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.

[@carljohngrino1458]

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

[@marianne3353]

henlo sa mga hindi naintindihan ang kanilang teacher

[@Jackrabbit.2]

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

[@ElshadayBerihun]

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

[@arleecribe5211]

It helped me understand Fibonacci sequence. Thank you😊

[@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.

[@allene597]

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

[@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.

[@silfrido1768]

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

[@ilyashick3178]

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

[@moustafagebal5366]

Kinda long video but covers everything THANKS!!

[@gelibnl3981]

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

[@UnnieCute]

Thank you sa wakas na ka anwer na jud ko

[@Cherang-u5o]

Thx for the video used it for my math Olympiad

[@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:)

[@anj_3237]

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

[@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?

[@JFK37002]

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

[@jhonallenalarcon6695]

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

[@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

[@unidadecredatimoruct243]

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

[@Cary12361]

Thank you naintindihan ko ng mabuti

[@andrewben346]

Thanks for teaching me.

[@allene597]

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

[@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

[@thehousewife3054]

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

[@Manta2006]

I loved that movie

[@leezx8505]

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

[@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

[@tolentinojohnmiguelp.8229]

Wow great video. So easy to learn!

[@mipaato]

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

[@victorialucernas7470]

Thank for this 😊 I understand clearly

[@lattebearforlife]

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

[@jericksonlomugdang2025]

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

[@kgbbbbbbb6392]

Thanks! It makes sense finally.

[@kadenmikael279]

Self study is hard thanks to your help

[@loveisforyoutoeat8911]

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

[@cagangkimberlyl.9908]

my ghad your a good teacher I understand it very well

[@progrocker2112]

SPIRAL OUT, KEEP GOING!

[@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 ⭐⭐⭐

[@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

[@md.abdurrazzak90]

Great Explanation

[@flexidawngetutua5979]

How i wish instructor explained it like you did

[@gloriousspear1924]

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

[@Strawb3rries.are.not.sw33t]

1 minute and 48 seconds in and I already understand !?

[@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!

[@geangeloreyes1786]

Thankyou for helping me in my activity

[@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

[@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.

[@red4629]

Welcome quarantine edition

[@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?

[@kushanmanahara4073]

Thank you for explanation❤️

[@sheniareesepanares5949]

Mathematics in the modern world bring me here.

[@epikbaconb9780]

I'm on my google class and this is our lesson big brain move

[@demondray]

Love you so much... Thanks!

[@chryssjhymmcalica7739]

Thank you and God bless.

[@johndexlagrosa6310]

this help me so much thank you!

[@kentlaurenceavila9677]

Much better than my teacher OmG

[@taetaehyung5078]

OH MY GOD. THANK YOU SO MUCH.

[@rriccess]

i fell asleep soon i clicked this video and woke up almost this video was done lmao

[@radiocars]

Didn't miss much, just adding numbers

[@favoredhappiness4123]

Thank you, now I understand it!

[@Leslieee.14]

I fail this subject because i didn't understand my teacher back then. And now gosh I'm enlightened. Not that easy but i clearly understand. Hahahahahhahaa

[@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?

[@rodrodrigues5402]

Continue to the 17th or 18th ratio get 1.618034, the golden ratio to 6 decimal places

[@Danylofff]

Wow this is amazing.

[@whatsafterlike5688]

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

[@Walt_KunPlays]

Im back here again. (I am college now).

[@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?

[@vishakaupadhaya4964]

thank you that was really helpful 🙂😀

[@leaguelegend538]

I did stopped halfway I'm gonna come back later this is interesting 🤔

[@shuanenaomialipao8657]

You rock it, amazing!! Thank you

[@maximegr3992]

Magic of maths