返回到 Fibonacci Numbers and the Golden Ratio

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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....

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.

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

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創建者 Sasha W

•Aug 02, 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!

創建者 C R V

•Aug 05, 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.

創建者 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.

創建者 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.

創建者 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.

創建者 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!!!!

創建者 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.

創建者 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.

創建者 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.

創建者 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!

創建者 MAHADEVAPPA H

•Jul 13, 2020

It was a wonderful experience. I have learnt a lot more about Fibonacci numbers and the golden ratio during this course. I urge the professor to create more and more courses like this.

創建者 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.

創建者 Giovanni M

•Mar 16, 2017

Finally I studied the Fibonacci sequence and the golden spiral. I used to say: one day I will.

Very interesting course and made simple by the teacher in spite of the challenging topics

創建者 Hasan J

•Dec 04, 2016

Good course for introduction to Fibonacci Numbers. Should include more introduction lectures such as group theory, category theory, type theory, number theory, and algorithms.

創建者 Dr. A K

•Jun 01, 2020

This was the fourth course of me with Prof Jeffrey. i am really very thankful to our beloved prof and also thanks to The Hong Kong University of Science and Technology

創建者 Burhani T S

•Jun 25, 2020

The course is concise, to the point and very interesting. Though it looks easy at first sight, without practice, you cannot complete it.

Thank you, it was great fun.

創建者 Christopher P

•Jul 19, 2020

Took me awhile to get in the groove — age 76 — but the little gray cells made the grade. Thank you for a well-organized, clearly presented course.

創建者 THANUJA P

•Jul 25, 2020

These kind of courses are always interesting, where the world is full of mathematical calculations and hope to see more videos on nature and maths

創建者 B J R

•Feb 19, 2020

Nice course to explore concepts like Fibonacci NUMBERS, Golden RATIO ,Lucas NUMBERS and many more. Very well taught by professor JEFF CHASNOV.

創建者 Abdullah S A

•Jun 16, 2020

A very educational course taught really well by one of the best professors out there. Thank you professor Chasnov for all your great courses.

創建者 pedro a

•Mar 28, 2020

A very interesting course with great teaching. I recommend it for those who want to go deeper into the topic and test mathematical thinking.

創建者 Wenhsiu H

•Jan 31, 2017

This is a great course. I learn very complete knowledge of fibonacci numbers and the golden ratio. Thanks for professor. Thank you very much!

創建者 Macharla v

•Jun 02, 2020

Macharla Varshitha

Roll no 588

St Martin's engineering college

Sir I have completed 2 courses successfully

But I am not getting certificates

創建者 Thomas S

•Jul 15, 2019

Fantastically explained, and very helpful when difficult in parts. Would recommend to anyone who is interested in maths, not just Fibonacci.

創建者 MAGGIDI V

•Jun 04, 2020

Maggidi vamshi

Roll no 589

St Martin's engineering college

My problem is I completed Coursera successfully

But Iam not getting certificate