Retour à Fibonacci Numbers and the Golden Ratio

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143 avis

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....

Mar 23, 2019

Absolutely loved the content discussed in this course! It was challenging but totally worth the effort. Seeing how numbers, patterns and functions pop up in nature was a real eye opener.

Sep 29, 2019

I really enjoyed this class. The video lectures were clear and fascinating, and the math assignments were well-chosen and reinforced learning of the material presented in the lectures.

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par Vishal G

•Dec 03, 2018

I came into this course thinking that it was going to be something relatively basic - being my first MOOC I wanted to do something which is new but not too difficult so I can see what online courses are like.

The first week is mostly easy but was still interesting with its novel application of recursion to seemingly difficult problems like the staircase one but the second week stands out mostly for both its difficulty and use of other areas of math to prove results in far better ways - Cassini's identity with the Q matrix in particular. The second week's content is manageable and the entire course only requires understanding of mathematical induction and the manipulation of matrices, both of which have supplementary material to complement the course for those who don't know it or have forgotten how to do it. The exercises set are some of the most insightful I've seen - Catalan's identities proof in particular. Solving that one is worthy of commendation. A system of hints or solutions may be useful for the more difficult exercises like that one but it's mostly an exception among the others. The second week is mostly isolated to the others, mostly for the introduction of useful algebraic results which tie Fibonacci numbers together rather than for the end goal which is outlined in week 3 with the construction of the Fibonacci and golden spirals. I personally found week 2 the best but week 3 was the main part of the course. It stays mostly easier than week 2 except the difficulty spike in the first exercise about the Eye of God, I recommend watching the video which comes after it before attempting that exercise.

Overall, this is an enjoyable course with some very surprising results and manages to go deeper into seemingly simple concepts like the Fibonacci numbers than expected. Thanks Professor Chasnov for a great first course which is definitely suitable to beginners with the way it eases students into the concepts introduced and the great explanations. Recursion in particular is explained extremely well.

par Peter M

•May 07, 2018

Light, relatively easy and entertaining. Well done Prof. Chasnov

par Bethany B

•Jan 03, 2020

I thoroughly enjoyed this course! I was looking for something fun to study over my 3-week winter break (I'm a student at IU), and thought this looked intriguing. Indeed, I learned so many fascinating things that heightened my love for and appreciation of the complex (literally complex, as well) world of mathematics. I was so continually interested that I just had to keep going with the course until the end! I have a fairly strong background in math (I've taken Calc I, II, and III, and Linear Algebra) so I was able to do the quizzes and most of the hw problems (though I never completely understood proofs by induction). I had no idea that there were this many relationships between the Fibonacci Numbers and the Golden Ratio, and that these intertwined ideas show up elsewhere in real-world situations. As an aspiring professional musician, I'd be very interested to see if and how these show up in music - I myself may have to write something that utilizes and highlights the golden ratio! I've encouraged many of my friends to take this course - it's highly rewarding and one of my favorite courses I've ever taken. The professor was wonderful, and clearly very enthusiastic about these mathematical phenomena. Thank you to all who put this together!

par Lam C K R

•Feb 16, 2020

A fun and engaging introductory mathematics course! Professor Chasnov did a really good job on introducing this topic! The exercises focused on the Fibonacci number and its counterpart, the Lucas Number, and it is aesthetically pleasing to see the connection behind mathematics and nature!

One thing I love about this course is that you don't have to know a lot of mathematics beforehand, just simple algebra will do. There is also a preliminary quiz to see if you are familiar with the basic algebra or not, which is a very good design!

A lot of the exercises in this course is about mathematical induction, which is an extremely important skill in university mathematics. So this course provides an extremely useful insight into it!

All in all, it is a wonderful journey through mathematics! Absolutely recommend to people who love mathematics and want to study it at university!

par Boudokhane M

•Jan 24, 2019

This course has been really fun and informative. I have learned a lot about Fibonacci numbers which i never considered to be that important. At first i thought they were just some quirky numbers and never looked further because they are usually just mentioned in our regular courses but nothing more. This course showed how important they are, their occurrence in nature, their real world application and a multitude of ways to find them and represent them.

The format of this course was also excellent, the videos are rich in content but still entertaining and easy to follow, some of the later ones are worth watching several times because they are quite packed in information. The problems are both challenging and amusing.

overall, i'm really satisfied with this course and i would definitely recommend it to anyone interested in math.

par Lim S M

•Jan 03, 2020

Very interesting course and the topic is covered comprehensively. Though this course is run every week, the instructor replies promptly to any questions asked. Most of the exercises are proofs which was good practice, though I found them rather too challenging for my standard. However, this is inevitable, as these proofs directly relate to formulas which will be used and are not just random exercises and thus I am grateful for the solutions provided by the pdf. Any gaps are also filled in well by the lecture notes pdf provided, though some proofs will be more challenging to understand. Great course for anyone interested in this rather niche area of mathematics.

par Olalla C A

•Apr 30, 2020

It is a very nice course. Although I am a scientist and have a good Mathematics background I have found it sufficiently challenging. I think the lecturer achieves a good balance of explaining basic concepts for those less knowledgeable but also advancing sufficiently fast to the less trivial material. I was a bit disappointed not to have a bit more about applications to the structure of plants, but happy to have understood how before we were even around nature had already worked out the Golden ratio!

par Rishabh J

•Aug 28, 2018

This is a very good course to introduce Fibonacci numbers, their appearances in nature, and their fascinating properties. The instructor explains everything very well, and his overall speed of teaching is also quite flexible and aptly manged. The course can serve as a good one to introduce one to the idea of advanced mathematics, or to assist one to appreciate the intricate ways in which mathematics appears in the nature.

par Bill C

•Sep 03, 2018

Really enjoyed the course. The instructor makes the material very interesting and explains the Fibonacci numbers and their different identities and uses very clearly and easy to understand. The course gave me a better understanding of the Fibonacci numbers and their applications than I previously had. The course also made me think the mathematics through thoroughly and carefully. Highly recommended.

par aBa

•Apr 08, 2020

Dr. Chasnov does an incredible job at explaining many insightful aspects of the Fibonacci sequence and the golden ratio. I came to this class already knowing quite a bit (so I thought) about these topics, but I came away learning a great deal more. And now I am excited to explore further topics that this course led me to think about regarding the Fibonacci numbers.

par Alok K

•Feb 11, 2017

I have learnt so much about Fibonacci numbers and the Golden Ratio in this class. This is so much more information that what I'd learnt way back in school or when solving Fibonacci based problems in Computer Science courses in college. I loved the content and Chasnov's teaching as well. Would love to do another course by Jeffrey R. Chasnov and this university :)

par Ursula B

•Apr 10, 2020

This is a really interesting course. The homework tasks to require a knowledge of proof which is not taught in schools in the UK, generally. However, you do not need this to access the course and to learn some amazing features that link the Fibonacci, Lucas numbers, the Golden Ratio and the Golden Angle.

It is a great course! I strongly recommend it.

par Luis F B G

•Oct 12, 2019

Nice and interesting course to know topics as Fibonacci and Golden Ratio and their relations

very well expalined and with no overwhelming Maths, very comprehensive and self contained

This course help me to solve some doubts and clarify concepts regarding mainly relation Fibonacci and Golden Ratio.

I strongly recommend this course

par Christos G

•Nov 17, 2017

The course is outstanding! Although I suspect it does not offer much in career pursuit, it definitely offers pure knowledge! Fibonacci sequence exists all around in nature. Is it like this or we, as humans, tend to look for patterns? Did we invent or did we discover mathematics?

par I R

•Apr 11, 2020

This course was very clear, and teaches you everything you could possibly want to know about the Fibonacci sequence and the Golden Ratio. It was structured in a way that I could fit it in whenever I could throughout a couple of weeks, too, making it easier to do.

par Dhandhukiya R R

•Apr 26, 2020

I would like to appreciate this course. Prof. Jeffrey R. Chasnov made it more interesting for me. I always want to find this type of interesting courses. As an Assistant Prof. it's a very interesting things to do it. Prof. has done excellent job. Thanks a lot!!

par Andreas Z

•Mar 23, 2019

This is a wonderful course that provides you with insights into a topic much neglected by the university mathematics curriculum but which is of great importance to art and nature. I recommend everyone with an interest in mathematics to follow this eye-opener.

par 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.

par 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.

par daniel a m

•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!!!!

par 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.

par SAUL E M R

•Apr 24, 2020

Phi is one of the most interesting numbers (1/7, Euler-Mascheroni, Euler number, pi). It is the number of recursions (geometrically, algebraically). The course deepens into interesting properties of phi.

par Nilson R R

•Aug 18, 2019

Excellent exposition of a fascinating subject.

Very well organized, including a handout with the course material.

Many thanks to Prof. Chasnov and the HKUST for this worthwhile opportunity!

par Anudha C K

•Mar 23, 2019

Absolutely loved the content discussed in this course! It was challenging but totally worth the effort. Seeing how numbers, patterns and functions pop up in nature was a real eye opener.

par David P L

•Sep 29, 2019

I really enjoyed this class. The video lectures were clear and fascinating, and the math assignments were well-chosen and reinforced learning of the material presented in the lectures.

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