返回到 Fibonacci Numbers and the Golden Ratio

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213 条评论

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....

Aug 18, 2019

Excellent exposition of a fascinating subject.\n\nVery well organized, including a handout with the course material.\n\nMany thanks to Prof. Chasnov and the HKUST for this worthwhile opportunity!

Jul 13, 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.

筛选依据：

创建者 Fabrizio B

•Dec 22, 2017

Great course

创建者 M .

•Jun 23, 2020

Very useful

创建者 R S S

•Jun 14, 2020

good course

创建者 Serhat G

•Apr 01, 2018

Excellent.

创建者 Marcelo O R d A

•Jan 24, 2017

Excellent!

创建者 Siva k T

•Jun 17, 2020

Excellent

创建者 Ganjikunta A

•May 12, 2020

Excellent

创建者 Darsan E

•Mar 30, 2020

excellent

创建者 李宁

•Sep 01, 2017

非常好，可以下次学

创建者 Alexander A S G

•Dec 04, 2017

superb

创建者 Naveen K

•Aug 04, 2020

Great

创建者 MD A

•Jul 30, 2020

great

创建者 abdul n m

•Jul 17, 2020

Great

创建者 Mrs A C

•Jul 27, 2020

Nice

创建者 Nagireddy s

•Jul 24, 2020

Nice

创建者 Naga M G

•Jun 12, 2020

Good

创建者 Madhapuram m

•Jun 02, 2020

good

创建者 ARAVINDH D

•May 25, 2020

Good

创建者 Rajeshree D

•Jan 28, 2019

best

创建者 Meg- n n

•Jul 02, 2017

in

创建者 Yaprak O

•Nov 08, 2019

Overall, an interesting course that cannot be found ordinarily in a classroom setting. Instructor explains the concepts well, and the personal element adds to the course. Gives new insight into the meaning of numbers and definitely helps improve certain math skills such as proving statements, geometry, algebra etc. Quizzes are easy, a light course in terms of assessments overall.. One downside is that the questions have no solutions posted (at least I could not find it) so we do not have a correct framework for answering these types of questions. Also, some videos had an excessive non-mathematical, historical and oriental side to them which did not exactly appeal to me. However, definitely a unique course that will provide you with a unique perspective.

创建者 Deep P

•Apr 30, 2020

This course did a great job of giving me an amazing understanding of the Fibonacci numbers and the golden ratio. I found it super interesting, and I was delighted whenever a connection was found between the two large subjects was found. One recommendation that I have to improve the course is to provide a little more assistance/hints with solving the HW proofs/problems. I found some of them tricky at times, and giving up made me feel unsatisfied, so help in solving or giving out strategies on how to do difficult proofs would be greatly appreciated.

创建者 Susannah R

•Aug 08, 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.

创建者 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!

创建者 Mike H

•Jul 05, 2020

I enjoyed the course well presented and documented. One suggestion Professor Chasnov mentioned other Maths courses that are available. A problem I have being retired but interested in maths, what other classes are suitable, I often go into high school courses that I did years ago, or head off into really challenging areas that I have no chance of completing. I suggest that there should be a course tree maybe for number theory as a topic that gives guidance.