Вернуться к Fibonacci Numbers and the Golden Ratio

4.7

Оценки: 260

•

88 рецензий

This is a course about the Fibonacci numbers, the golden ratio, and their intimate relationship. In this course, we learn the origin of the Fibonacci numbers and the golden ratio, and derive a formula to compute any Fibonacci number from powers of the golden ratio. We learn how to add a series of Fibonacci numbers and their squares, and unveil the mathematics behind a famous paradox called the Fibonacci bamboozlement. We construct a beautiful golden spiral and an even more beautiful Fibonacci spiral, and we learn why the Fibonacci numbers may appear unexpectedly in nature.
The course lecture notes, problems, and professor's suggested solutions can be downloaded for free from
http://bookboon.com/en/fibonacci-numbers-and-the-golden-ratio-ebook
Course Overview video: https://youtu.be/GRthNC0_mrU...

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.

Aug 30, 2017

Very well designed. It was a lot of fun taking this course. It's the kind of course that can get you excited about higher mathematics. Sincere thanks to Prof. Chasnov and HKUST.

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By Ng T E

•May 30, 2019

One of the many marvels of mathematics is that of the Fibonacci Numbers & the Golden Ratio.

Week 2 was somewhat challenging, but doable.

By Christophe S

•Apr 29, 2019

Thanks for this wonderful course, Jeff. Those Fibonacci are amazing. I hope you will give us even more MOOCs.

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 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.

By 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.

By Tarit G

•Feb 12, 2019

Awesome

By Rajeshree D

•Jan 28, 2019

best

By 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.

By Massimo C

•Jan 17, 2019

Fascinating course about a topic that is not usually taught in maths lessons. It is easy to follow and it has good supporting material.

By 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.

By Brice B

•Sep 21, 2018

Disappointing course. The course is not well-structured (parts of the second part show themselves to be useful only in the third part) and somewhat anecdotal (some more maths of nature would have been welcome). The very monotonous tone of the lecturer doesn't help.

By 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.

By Matthew T

•Aug 31, 2018

Very interesting and well presented mathematics course. Amazing how many applications and relationships the Fibonacci Sequence has. Some of the formulas could have been explained in a little more detail as they were incredibly difficult to get my head around (I am an A-Level student).

By 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.

By Chandrakant N P

•Jul 04, 2018

It was very useful to enhance my knowledge of Golden ration. A very good delivery by Professor Jasnov.

By Andrew M

•Jun 23, 2018

Very clear exposition, interesting and fun. Accessible to anyone interested in maths and patterns.

By GOPIKRISHNA

•Jun 21, 2018

Good explanation, Good example

By Utpal B

•Jun 06, 2018

This course blends the rational thinking of mathematics and the aesthetics of art in nature. Enjoyed it. Thanks Coursera and Hong Kong University of Science and Technology

By Bheemarasetty r v s s

•Jun 06, 2018

fun course,great.

By Linda O

•May 13, 2018

The most fun I had in a long time! Thank you very much. Very interesting.

By Chi L L

•May 13, 2018

The course is a fun one and do make me reflect on my on academic major.

By Rahul C

•May 11, 2018

Awesome course, easy to follow along and for those who are inquisitive in nature.

By Peter M

•May 07, 2018

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

By Paul R M

•Apr 27, 2018

I liked this course, and I discovered the amazing relationships one can derive for Fibonacci numbers and related entities. The lecturer is very clear, and if one does the exercises then one gets a good grasp of the subject. I gave it only four stars partially because the subject matter seems to be more a way to amaze your friends rather than doing something relevant. I would like to understand if it can be applied to real world problems. Maybe that's because I am not a mathematician!

By Jill M

•Apr 25, 2018

Excellent! Interesting, informative, clearly presented, and beautifully done!

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