The Fibonacci Sequence and the Golden Ratio
This video introduces the mysterious and mystical Fibonacci Sequence and explores its relationship to the Golden Ratio. While filmed with a fifth grade audience in mind, it should be accessible to kids as young as fourth grade . Hopefully it's interesting to everyone.
If you're interested in learning more about the golden ratio and other mathematical sorcery, I can't say enough about this book:
amzn.to/1Gccuas
#khanacademytalentsearch, #phi, #goldenratio, #fibonacci, #math, #geometry
Пікірлер: 281
Whoa! I just came back to this after a time away. Never thought so many people would view it. Thanks so much for your support. Maybe I should do another...
@Rachel-rr8mf
5 жыл бұрын
Please do if you're having fun sharing math and making vids too :) . Thank you for sharing this. im 31 but just starting to learn about golden ratios and sacred numbers. This is great and i love your presentation. The kids and the dog are cute at the end of your video 😄. I will show this to my mom too who still loves to learn new things. she's great in math as an accountant and she's 63 now but i don't think she learned this at school. You've got a new subscriber here today. Love from the Philippines 💚🌏
@trailtrs1
4 жыл бұрын
I found as a teacher of the Japanese art of iado (SWORP draw with katana) that all our draws, if done properly draw at a golden ratio, Fibonacci sequence. If done with this in mind and disciplined with training you get maximum speed and striking power which turns into maximum cutting ability and Jules of stored energy released at the 3rd keyogi (last 1/3 of the blade). This gives you maximum cutting ability. I first discovered it doing draws with the blade and then wondering why the ancient samari always drew the nautilus shell or waves in their art. They were hiding their secret of speed and precision in their art, as both are built on the Fibonacci sequence.
@jamesfarrell1116
4 жыл бұрын
I love your energy Great video
@jamesjewkiller1630
4 жыл бұрын
Teslas 3 6 9 would be the perfect follow up!
@rocklemillion8041
4 жыл бұрын
Mr. Kevin couldn’t us finding these patterns in nature and art also be chocked up to humans proclivity to find pattern and meaning in things?
This is a perfect example on how the KZread should be used to teach people. Great channel!
@Mcastill11
3 жыл бұрын
no i disagree
If this teacher could have had taught me math back in school...
@possible1513
4 жыл бұрын
I wish tooo
My favorite example is in a pine branch (pitch pine is best). It grows in two spirals in Fibonacci proportion. They run in opposite directions and everywhere they cross an event happens, a pine needle grows.
The dog was running in a Fibonacci spiral
@Mrkientube
6 жыл бұрын
Great observation
@houaidasabbagh5509
5 жыл бұрын
cool
@ThatsJustPeachy1871
4 жыл бұрын
Yes!!😂🤣😂🤣 That was so funny!
@penelope8557
4 жыл бұрын
HA HA HA!!!
@hizzoflow2795
4 жыл бұрын
Uuuuuuuuuhhhhhhhhhh so cool is that the one that you can have a good day at work
Thanks for explaining The Golden Ratio in a simplistic way. I have known about it for some years now, but you have definitely enabled me to get a better understanding of how the patterns start to form, etc. 🙏🏽💕
I LOVE this. Thank you for the explanation in PLAIN ENGLISH.
@MrKevin-ul1qp
5 жыл бұрын
You are most welcome! Thanks for the feedback.
the best explanation so far. thank you
How Amazing Are You!!! ♥️ Omg!! Saved!! Professors, Tutors, Textbooks, You Tube Vids... Left me clueless!!! Until You Saved the Day.. I can't thank you enough!!!! Thank you..
@MrKevin-ul1qp
5 жыл бұрын
My pleasure, Marsha.
Thank you very much for posting this. I am studying art and have come across this rule. I never learned this in the "advanced" art classes in high school. It was not even introduced in college. I must have been in the lower federally funded school district.
_Now_ my mind is blown. I've watched countless videos on this truth but none of them explained how the Fibonacci numbers were directly related to the golden ratio.
@MrKevin-ul1qp
4 жыл бұрын
Thanks! I appreciate you watching.
Thanks. This is just the video i needed to see. It explains this series in the simplest manner.
Hey that was cool to know where Phi comes from. Can you please do a similar presentation for Pi (circle)? Thank You
Credit to your effort, it is important and fantastic. The kids are forever more intuitive for this one act alone. Great for you!
so cool that you engage your children that way
Also there is a relationship between Fibonacci Sequence and Euler’s Numbers.Please search on internet by this title “Quantum Perspective Model by Tahir Ölmez
The difference equation that defines the Fibonacci sequence is: Delta ^ 2 F + Delta F - F = 0 Its characteristic equation is: r ^ 2 + r - 1 = 0 so the roots of this quadratic equation are - (1 + sqrt (5)) / 2 and - (1 - sqrt (5)) / 2 The initial conditions of this difference equation are: F (0) = 0 and Delta F (0) = 1 which leads to the algebreic expression for the nth term of this sequence: F (k) = (((1 + sqrt (5)) / 2) ^ k - ((1-sqrt (5)) / 2) ^ k) / sqrt (5) On the other hand, given a segment of length 1, divided into two segments of length x and (1-x), these 3 segments satisfy the golden ratio if the proportions are given: x / 1 = (1-x) / x This relationship also leads to the cadratic equation: x ^ 2 + x - 1 = 0 So there is no mystery.
Never seen it explained like that. Awesome vid. Thanks for the help/clarification
@MrKevin-ul1qp
5 жыл бұрын
Cheers, Donny.
Really great video! Thank you so much.
Great video. Explanation of the numbers sequence, how the ratio is 'derived' and showing visually with the graphic sections very clear. Nice activity with the calipers for seeing the ratio in nature outside too. Thanks for making and sharing this.
@MrKevin-ul1qp
5 жыл бұрын
Thanks for the feedback, AJ. I got the idea of building the calipers from the book "The Beginner's Guide to Constructing the Universe" by Michael S. Schneider
Great explanation of both the Fibonacci and the Golden R. My "Golden R" essay is due in a few days and I have looked up the basic who, what, where and when's but didn't understand what it was that got folks so excited.... It appears that many "thinkers" find it so fascinating that they allocate precious personal hours/days/weeks etc., just thinking about that rascal R in terms of Fib as well as Phi. I think I am beginning to understand because I went on to watch the "Log e" and understood the compounding interest formulas. Oh, happy day! May 11, 2018 06:53:10;)
Wow I wonder if the woman who first designed the log cabin quilt block knew that this is the same pattern.
@echomei7070
4 жыл бұрын
I heard someone use FS to learn Spanish . How did it work? Can you explain it ?
Thanks for explaining the number Phi, the golden ratio so nicely and understandable!
The calipers are genius, Mr. Kevin! I may steal that! Very nice presentation.
too good explaination 😍
In fluid physics, there are 24 ones around a two, each power in an x-plane, forming a solid three with one set of fluid forces at 'c' (energy waves 🌊and fields), and the next having the graviton, fermi fermat, vortex, etc.... Just by intuition. Great presentation.
@MrKevin-ul1qp
4 жыл бұрын
Thanks! I have no idea what you just said, but I appreciate you watching.
Big Big help! Thank you for sharing. Simple and plain!!! Really appreciated!
@MrKevin-ul1qp
5 жыл бұрын
You are most welcome.
Nice hat.......and thanks for sharing one of the most profound and important foundations of good design.
The kids finding phi on the dog is SOOO ADORABLE! Dog wasn’t having it! LOL
Exceptional post fella! Positive and thought provoking. I use this as a tool for trading but the eloquence and relatability of it is a bit astounding. Thanks for posting.
@MrKevin-ul1qp
4 жыл бұрын
Thanks, Scottie
almost all videos on KZread extremely complicated I couldn't understand anything but you and the you explained it to me was absolutely simple and great thank you so much for that it's a lovely video I wish you could more subscribed to a channel
Love the t-shirt!!
interesting. Thank you!
Omg I need one 👏👏👏
Iv watched 3 videos trying to understand how this ratio actually works and this is by far the best one. great work!
@MrKevin-ul1qp
5 жыл бұрын
Thanks, Rob. I appreciate it.
I love your energy. Great video 📹
@MrKevin-ul1qp
4 жыл бұрын
Thank you so much!! Hope you subscribe and check out my other videos.
Thank you🙏
the 'share' button of KZread looks and goes like a spiral representing golden ratio
Great work, this kind of educational curiosity is important.
@MrKevin-ul1qp
5 жыл бұрын
Couldn't agree more.
Thank you. I understood the adding of the numbers for the Fibonacci Sequence, but, I never knew the division to get Phi . I had heard of the Golden Ratio but didn't quite get how it tied to the Fibonacci Spiral. I had seen the callipers but had not seen such a fun experiment. Tis is excellent. Again, thank you.
Hi from Australia. Thank you so much for enriching my evening. Im genuinely grateful.
@MrKevin-ul1qp
4 жыл бұрын
Very kind of you, John. And, my pleasure. Thanks for watching.
@Mr. Kevin....very interesting. but I for one need some baby steps between the division (that I understand) to the graphic you drew with the spiral. what makes the spiral a 1.6 ratio? what are the different points in the different color boxes represent? can you flush that out a bit more?
@MrKevin-ul1qp
4 жыл бұрын
The colors mean nothing. Just makes it easier to see. The spiral generated actually only approaches a true "golden" spiral, but the fibonacci numbers approach it more closely and more closely as I illustrated earlier. Unfortunately, the grid box demonstration doesn't yield that true ratio, and some may nitpick about that, but I thought it was an interesting illustration for my students so that they could see of numbers at play in the world. If you're really interested in just how the fibonacci sequence generates the spiral, a quick search on Google will give you all the detail you can handle. Thanks for watching!
THUMBS UP! Thank you for the clear explanation of Fibonacci sequence and golden ration. Barb
@MrKevin-ul1qp
5 жыл бұрын
You are most welcome, Barb.
Ok, that was really cute - the way you wrapped that up.
@MrKevin-ul1qp
4 жыл бұрын
Cheers! Appreciate you watching until the end. Your kind is rare!
Thank you Kevin! Simple genius. Now onto make my Caliper Gauge!
@MrKevin-ul1qp
5 жыл бұрын
Cool! I found directions to make the calipers in the book "The Beginner's Guide to Constructing the Universe" by Michael S. Schneider. If you're looking for a really good use for those calipers, and you don't mind people looking at you funny, you should take them to an art museum! Life changing!
@hizzoflow2795
4 жыл бұрын
mark green tea was the first day of my day hahahahaha lol bruh is my day I got this game and I was wondering how to make it to the gym now or I’ll go get back with my bro
Great video!
Well explained.
What an awesome back yard they get to play in! Great video!
@MrKevin-ul1qp
4 жыл бұрын
Yes, I miss it everyday. We live in Thailand now, so it's beautiful in a different way. Thanks for watching.
Thanks for this! It's a tough concept to explain!
when he says turn it off lol
Lesson 5, Johnny.
Awesome video ... easy to follow 👌 great learning tool .seems very important to know this more than ever . So happy to see you teaching your boys this information! 😀💛💜💚💙 thank you 😊
very nice, thanks for making this video..
Thanks... I understand this much better
Awesome work! 👏🏻👏🏻👏🏻
I understand the golden ratio, but what I don't understand is when we draw the Fibonacci sequence through squares it looks like to me that the square next isn't 1.618 times larger. It just looks like it's 1.75 times larger. A rectangle split into sixths. Help.
Excellent video excellent description and graphics I liked it very much. 👍
@MrKevin-ul1qp
5 жыл бұрын
Thanks! I just came back across this after quite a long time and was shocked to see so many views! Glad it was useful to you.
Gyro himself couldn't have explained it better.
@MrKevin-ul1qp
4 жыл бұрын
Thank you!
My father never told me about this when I was a youngster.
@reallyshiesty2436
4 жыл бұрын
Youngster😂
Just watched it, very good and easy to understand, but someone found a toad that was more interesting.
Thanks for thia video. You deserve more subscribers!
Thank you! A real revelation! Thank you Sir!
@MrKevin-ul1qp
4 жыл бұрын
You are very welcome
Wow amazing
super cool!
this video explains it so eaisly and clearly.. wow
that was a very educational video as well as interesting
@MrKevin-ul1qp
5 жыл бұрын
Thanks, Syeda.
This was amazing, 😮you made me understand better 🙏
and he got it from the 10th Book of Pythagoras, as the Unending Fraction, 300 BC, who got it from Ezekiel, 550 BC
Thank You Mr. Kevin
Thank you for the insight into one of the fundamentals of nature. Btw, you've got 2 nice kids that look as smart as you. Take good care of them and teach them well.
@MrKevin-ul1qp
4 жыл бұрын
Thanks for watching and for the nice compliment on my boys. I'm accutely aware of how fortunate I am.
omg..such a great video..in trying to look for a video I can understand, the others just made me more confuse! 🥴 The big words and out of this world computation.😁 Thank you.
Was the fibonacci sequence basically used to create the first computer virus. Basically quickly overloading the processor
thank you for sharing such informative video, I've seen that spiral on many occasion, but never understood it. many thanks to you
@MrKevin-ul1qp
4 жыл бұрын
You are most welcome. Thanks for watching.
Hi there ... whats the name of the program u used graph papre 2 draw ? thnx
@MrKevin-ul1qp
5 жыл бұрын
Hi Riyadh. The program I used was the software that came with my SmartBoard in the school I worked at. I believe it was called Promethean Activ.
What software app are you using for the graph paper? Thanks!!!
@MrKevin-ul1qp
5 жыл бұрын
I believe it was called Promethean Activ. It was the software that came with my school SmartBoard.
Many thanks for the clearness of your demonstration and video. I’d like to know the name of your app. I’got an ipad, can I find it in appstore ? Thanks for your information. C.L
It seems that anything which is impacted by gravity must follow the golden ratio. Otherwise if I choose to draw perfect circle or build a building that is 1775 feet then the golden ratio does not exist or is needed.
thank you
At 4:48 you describe how the 1.68 number was related to the 2 square being 1.68 larger than the two 1 squares. I don't follow this. Please explain.
@maimon1
4 жыл бұрын
The ratios form a sequence of numbers that "tends" to 1.618. here is the sequence: 2.0000 1.5000 1.6667 1.6000 1.6250 1.6154 1.6190 1.6176 1.6182 1.6180 1.6181 1.6180 1.6180 1.6180 1.6180 1.6180 1.6180 1.6180 . . .
@hizzoflow2795
4 жыл бұрын
Ccccccccccccccccoooooooooooooollllllllllllllllll
Great video and a great channel
I still don't get it. When you show how the calipers fit your son's face the first time, you're excited because the mid-point of the caliper hits just below his eye. But what is the significance of that? What makes it so special? Then you reverse the calipers and show that the middle point hits the center of his forehead. Again, what is the significance of that? Is it that no matter whose head you try that on, the result is the same? If so, you need to say so. People always demo this principle in isolation--using a specific painting or a shell they find on the beach or a flower. So I never understand what the big deal is. Can someone clarify this for me?
Part 7 Readers screaming Nani! P.S. This is a really good video!
@MrKevin-ul1qp
4 жыл бұрын
Thanks for watching!
Nice vid. I tried to find PHI in an ice cream cone. Never found it. LOL :)
Does Fe Fi Fo Fum count ?
i wish i had a dad like you all i can remember is my father kicking my ass
@Mrkientube
6 жыл бұрын
JAJAJAJAJAA
@death2pc
4 жыл бұрын
And darned well he did!
Careful. Don't poke little Tobin's eye out with those "calipers".
Just watched this video. Fascinating. But I do have a question. Just before the 5 minute mark, you say: 04:51 here this two is one point six one eight 04:54 times larger than these ones put 04:56 together that ratio is forming this But, if we assume each 1 is 1 square inch, them 2 is 4 square inches and square 2 is 2 times larger than the 1's combined. What am I missing?
@MrKevin-ul1qp
4 жыл бұрын
You're not missing anything. I think it's just a consequence of trying to demonstrate the golden spiral on grid paper. In nature, the fibonacci sequence doesn't have a court so tidy on which to play. I should also say that the fibonacci number only approach the value of phi, they never quite make a true golden spiral. I guess what I was trying to do with this video is spur interest in mathematics for my students. I apologize if it got off track. Thanks for watching!
Best video by far
@MrKevin-ul1qp
5 жыл бұрын
Cheers!
Hmmm... 4:25 You don't explain why you can draw curves here between the box corners. You only have box corners as data points, nothing to define the shape of a line between them. ??
thx
very cool man
Its called "Making things fit your perspective". Like the way that Phi fits Africa very nicely but has no significance at all with Australia
Kevin, how can I make those calipers?
@MrKevin-ul1qp
5 жыл бұрын
So glad you asked! I just made a video this summer on that very subject. Check it out, and thanks for watching! kzread.info/dash/bejne/q6yMq5eaZqWdadY.html
Even cabinet drawers work best using the Golden ratio in their length vs width.
@MrKevin-ul1qp
4 жыл бұрын
No kidding?! That's interesting. What do you mean by "work best?" Mechanically speaking or are we talking about ideal area?
@raiderfandew
4 жыл бұрын
@@MrKevin-ul1qp , no, not as far as ideal area.... it concerns it's ease of opening and closing and it's resistance to binding when doing so. I am a custom furniture maker by trade, and with all of my pieces, I always consider the Golden Ratio. I might not always use it, but more often than not. Thanks for a very interesting video. It's very well put together.
Came for the maths. Stayed for the wholesomeness.
@JMARTIN1947
4 жыл бұрын
I prefer the math and not so much the mush-headed kids.
Thanks a lot
@MrKevin-ul1qp
5 жыл бұрын
Thanks for reaching out.
Very interesting and informative however I take issue with Phi. Being used to describe the shape of the continent of Africa, that surely is a coincidence and calls into question other examples
Mr. Kevin seems like a cool dude. 👍
@MrKevin-ul1qp
4 жыл бұрын
Awww, shucks. Thanks!
Now I know this rule.
What app do you used to make a graph sir?