Back to Fibonacci Numbers and the Golden Ratio

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927 ratings

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327 reviews

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.
Download the lecture notes:
https://www.math.ust.hk/~machas/fibonacci.pdf
Watch the promotional video:
https://youtu.be/VWXeDFyB1hc...

JR

Jul 12, 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.

BH

Oct 28, 2020

Great course concept for about one of the most intriguing concepts in the mathematical world, however I found it on the difficult side especially for those who find math as a challenging topic.

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By 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.

By Christine W

•Sep 12, 2020

Absolutely brilliant course. I was intimidated when I began but learned so much, due to the videos and comprehensive course notes, that I have passed and feel a great sense of achievement.

Thank you very much.

By 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.

By Bassel A H

•Oct 29, 2020

Great course concept for about one of the most intriguing concepts in the mathematical world, however I found it on the difficult side especially for those who find math as a challenging topic.

By 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!

By Sahag S B

•Sep 3, 2020

this course made mathematics fun and I gained enlightened concerning how mathematics show up in nature, and how to interpret such scenes. I recommend to attend such courses-- Thank you

By 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.

By 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.

By 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

By Xavier F G A

•Jul 8, 2021

A short and interesting course that gives you exposure to some types of university math. Also a great topic that shows some of the wierd and unexpected ways that math is beautiful.

By Pedro S C

•Jan 20, 2021

Simplesmente sensacional!! É incrível ver e estudar sobre um assunto tão bonito quanto esse. O professor explica de forma clara e objetiva. Parabéns pelo curso proporcionado!!!

By Hasan J

•Dec 4, 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.

By Dr. A K

•Jun 1, 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

By 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.

By Chryseis N

•Feb 14, 2021

Very neat and well organized, all material at hand. I liked the skipped math bits that the others mentioned, so that I could myself engage in figuring out.

By Ramy B C

•Nov 1, 2020

Beautiful course, very well organized and doesn't require very high maths skills to complete. The instructor is great and put in a lot of effort into it.

By 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.

By Ashleigh R

•Jan 14, 2021

Very interesting. Much more math heavy than I was expecting, and would very hard to follow if you don't have at least first year university maths.

By 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

By 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.

By Mônica F d S R

•Oct 24, 2020

Adorei o curso. Vídeos precisos, de conteúdo claro e bem explicado. Muito interessante, recordei muitos conceitos e aprendi demais. RECOMENDO.

By 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.

By Pedro A G

•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.

By 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!

By Macharla v

•Jun 2, 2020

Macharla Varshitha

Roll no 588

St Martin's engineering college

Sir I have completed 2 courses successfully

But I am not getting certificates

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