Back to Fibonacci Numbers and the Golden Ratio

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894 ratings

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317 reviews

Learn the mathematics behind the Fibonacci numbers, the golden ratio, and how they are related. These topics are not usually taught in a typical math curriculum, yet contain many fascinating results that are still accessible to an advanced high school student.
The course culminates in an explanation of why the Fibonacci numbers appear unexpectedly in nature, such as the number of spirals in the head of a sunflower.
Download the lecture notes:
https://www.math.ust.hk/~machas/fibonacci.pdf
Watch the promotional video:
https://youtu.be/VWXeDFyB1hc...

BH

Oct 28, 2020

Great course concept for about one of the most intriguing concepts in the mathematical world, however I found it on the difficult side especially for those who find math as a challenging topic.

JR

Jul 12, 2020

Someone has said that God created the integers; all the rest is the work of man. After seeing how the Fibonacci numbers play out in nature, I am not so sure about that. A very enjoyable course.

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By Susannah R

•Aug 8, 2019

This course gives a fascinating insight in the logic behind some of nature's beauty. It requires a lot of maths, far more than I did at school (A Level) many years ago. It is definitely aimed at keen maths students. I found that many of the examples in the videos and the model answers to the questions missed lots of steps that I needed. These logic jumps may be second nature to somebody regularly studying maths , but for the 'casual' MOOCer at home who thinks "Ooh! that looks interesting", it left me struggling.

By Víctor P V

•Aug 12, 2016

The theory explained and the exercises are not at the same level.

By Eleanor H

•Mar 21, 2021

The class is fantastic! The material is fascinating and just challenging enough. The length of the class was good—for keeping motivated for the entire 3 weeks. The instructor’s videos are very clear, precise, thorough and I loved being able to print out the class notes as well as solutions to problems and practice tests. The only thing that I think could be improved would be to include a clear definition of “origin” of the golden spiral. It seems to me that in the problems the origin is sometimes assumed to be the accumulation point, whereas in the proof of problem one for lecture 13 the origin is used as the origin ( of the coordinate system) and assumed to be the lower left hand corner of the largest golden rectangle. This confused me.

By Janet M

•Jun 26, 2021

This is a very exciting course. I was pleased the instructor told us we could continue without worrying about the maths. Although I passed the initial diagnostic maths test and mostly scored high on the quizzes I found the maths well beyond me and could not even follow the solutions to the extra problems at the end of each section let alone attempt the questions. I would nevertheless recommend this course to anyone who finds numbers fascinating. Even if some of the maths goes over your head it is still possible to appreciate the main ideas. The enthusiasm of the instructor encouraged me to persist, thank you

By Thilanka L

•Nov 13, 2020

This course is wonderfully composed to give you a good foundation to the Fibonaccci numbers. A basic knowledge in Algebra is sufficient to follow this course since much of the other required information are delivered during the lecture or as supplementary videos. The best thing about this course is how Professor Casnov step by step explains interesting details which when combines gives a beautiful meaning even towards the nature. Loved every minute of the lecture, and I highly recommend this course to anyone who is curious about this topic.

By CARLOS R A H

•Feb 12, 2021

Great course, as expected from Prof. Chaznov. This course was fun and very interesting. As an Informatics Engineer student, I thought I knew about Fibonacci numbers but wow, I really didn't. There's a whole more to it, and anyone can learn from it. The course is challenging, but fun as well. It takes a while to get used to prove a lot of identities by mathematical induction, with wasn't my favorite thing ever but after this course I think I've learned to like it, it's very satisfying. Looking forward to more math courses like this.

By Mufti M

•Jul 4, 2021

This is a great course which delivered an in-depth of analysis on Fibonacci number to many more related topic like golden ratio to Cassini's / Catalans identity and many more. It was an exceptional course on introduction to advanced mathematical thinking and how Fibonacci number appears in nature like construction of sunflower head with respect to florets arrangement by using golden angle. To complete each assignment need thorough understanding of each derivations.

By Sasha W

•Aug 2, 2020

Very interesting course. By far the most interesting and challenging I have found so far in my preparation to go study maths at uni in a years time. Used some of my previous mathematical knowledge such as matrices and proof by induction, whilst pushing me to use them in different problems and derive new formulas and use new mathematical methods. Will definitely be talking about this on my personal statement!

By Dr. S V C

•Sep 30, 2020

I joined this course out of interest about the existence and visibility of Fibonacci sequence and the Golden Ratio in nature as also its connection with ancient Indian texts. Found this course very interesting. The instructor was very clear with the concepts and presented them very lucidly. Would recommend this course to those who want to understand the basics of Fibonacci Numbers and golden ratio.

By Tenzin W D

•Feb 5, 2021

One of the best course ive taken so far. The assignments were fun to solve due to its challenging nature, cant deny the booklet of being extremely beneficial at such times. Overall, i had an interest on Fibonacci Numbers and after taking this course, it completely changed what i thought and how i thought about Fibonacci. Feeling lucky and grateful to have taken this course.

By Chelam

•Aug 5, 2020

This course is well explained. Interesting. Surprisingly takes less time to complete but consumes a lot of time to dwell deeper into it with proofs and their applications. I would like to repeat all the exercises and want to learn more about the topic, whenever I get a chance. It has opened new world to think. Thanks for the beautiful course.

By Aldrich W

•May 28, 2021

This is my third course with Prof. Chasnov on Coursera. I really love his teaching styles and truly appreciate the greatness of mathematics and its application to our real world. Through this course, I enjoyed seeing the beauty of Fibonacci Numbers, the sequence, the Golden Ratios, the model of sunflowers, etc.

By Nithin T S

•Oct 20, 2020

I had a great time going through this course. I highly recommend students to take up this course as it will change the very imaginative concept of mathematics. I also liked the mentor Mr.Jeffrey. He is so much interested and patient in taking classes. I really liked this course a lot. Thank you.

By Muhammad B A

•Apr 21, 2020

This is really a very wonderful course. This is the first course, I enrolled on Coursera and started it just as a fun course. But at the end, it is much more than my expectations. I learned a lot and revised many concepts. Thank you Professor Chasnov.

By K B

•Oct 24, 2016

In this course so far I have been able to see what different types of patterns are and I have been able to see what kind of counting ways there are. I have also learned that the Fibonacci Sequence is everywhere in nature so I really like this course.

By TAI C C

•Jun 19, 2021

This course is very interesting and I just cant imagine a prof is willing to teach all of us online free in charge! I have been hearing from the famous Fibonacci sequence and the golden ratio and finally , I could learn it and it was amazing !!!!!

By Kevin D

•Jun 10, 2020

Very interesting and entertaining course. I have had many years of advance Math & Engineering courses, and had never covered the subject matter that was provided by this course.

Thanks to everyone that created and provided this course.

By Daniel A

•Mar 23, 2020

Great material; both instructive and fun.

The exercises were just challenging enough to make me think, but achievable with some effort (with one exception so far (Catalan´s identity), but I´ll come back to that).

And a great instructor!!!!

By Patali T

•Dec 14, 2020

I really enjoyed this course! My wholehearted thanks go to Prof.Chasnov. What I really love about the course is you don't have to know a lot of algebra, even if you don't know from watching the lecture videos you can easily understand.

By Soham J

•Apr 27, 2019

This course is absolutely out of the world. It truly showed me how much I didn't know and how fascinating nature is. The best part is that anyone with basic understanding of algebra can take this course. I had a really fun time here.

By Jamal B

•Aug 16, 2020

Excellent professor who made a complex mathematical feat most enjoyable. Your step-by-step walking through, Professor Chasnov, and demonstrating that with examples made me wish I had you for Diff-EQ course in college. Thank you.

By Sergio G C

•Apr 24, 2021

I really enjoyed this course, it was very clear and with the proper mathematical rigor, not too complex but not too simple, very complete course. The teacher was very clear and I really liked the enthusiasm he puts into teaching.

By Shabnam M

•Dec 5, 2020

It was one of the best course that I have taken online. The way the professor explains things are extraordinary and interesting. He made very good presentation and easy to understand with diagrams. Thanks professor.

By Ryan L

•Jun 28, 2020

This class was very interesting and insightful. Being a high school student, some of the math was challenging. However, detailed explanations of each practice problems were provided, making it easier to follow along.

By Christine W

•Sep 12, 2020

Absolutely brilliant course. I was intimidated when I began but learned so much, due to the videos and comprehensive course notes, that I have passed and feel a great sense of achievement.

Thank you very much.

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