返回到 Fibonacci Numbers and the Golden Ratio

4.7

244 個評分

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83 個審閱

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...

創建者 GM

•Mar 16, 2017

Finally I studied the Fibonacci sequence and the golden spiral. I used to say: one day I will.\n\nVery interesting course and made simple by the teacher in spite of the challenging topics

創建者 BS

•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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78 個審閱

創建者 Tarit Goswami

•Feb 12, 2019

Awesome

創建者 Rajeshree Deotalu

•Jan 28, 2019

best

創建者 Boudokhane Mohamed

•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.

創建者 Massimo Chericoni

•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.

創建者 Vishal Gupta

•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.

創建者 Brice Bantegnie

•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.

創建者 Bill Cox

•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.

創建者 Matthew Taylor

•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).

創建者 Rishabh Jain

•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.

創建者 Chandrakant Nagnath Phadte

•Jul 04, 2018

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