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Fibonacci Numbers and the Golden Ratio(으)로 돌아가기

홍콩과학기술대학의 Fibonacci Numbers and the Golden Ratio 학습자 리뷰 및 피드백

278개의 평가
97개의 리뷰

강좌 소개

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 Course Overview video:

최상위 리뷰


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!


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

필터링 기준:

Fibonacci Numbers and the Golden Ratio의 92개 리뷰 중 51~75

교육 기관: Sandesh J

Jan 25, 2017

learnt something interesting!

교육 기관: Rahul C

May 11, 2018

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

교육 기관: Slavica P

Mar 10, 2018

Very good course... I was expecting more applications in nature and art after maths being made ... so I suggest adding it.

교육 기관: Matthew F

Aug 04, 2017

This is a really good course. I really enjoyed it.

교육 기관: Alexander A S G

Dec 04, 2017


교육 기관: Serhat G

Apr 01, 2018


교육 기관: Iulian N

Nov 27, 2016

Very interesting course

교육 기관: 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!

교육 기관: 唐海涛

Aug 06, 2017

This is a fantistic topic and I learned a lot from the course!The mode can encourage me to accomplish the homework timely.

교육 기관: 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.

교육 기관: Christophe S

Apr 29, 2019

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

교육 기관: 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.

교육 기관: 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.

교육 기관: 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.

교육 기관: Shafa S K

Jun 28, 2019

This course is indeed perfect for cooling down my brains after burning for so long in classes and my laziness :))

교육 기관: 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.

교육 기관: Vidhya K

Aug 03, 2019

Enjoyed it a lot. Learned a lot. Thank you for making this available.

교육 기관: Nojus J

Aug 04, 2019

I really loved this course. Amazing mathematics that was taught very well and also helped me build my mathematical skills.

교육 기관: 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!

교육 기관: Tarit G

Feb 12, 2019


교육 기관: 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).

교육 기관: AM

Sep 03, 2017

Give practical examples from history and nature!

교육 기관: Sravan G

Dec 08, 2016

great learned a lot .

교육 기관: narendra p

Dec 13, 2017

good course

교육 기관: Brian W

Dec 29, 2016

Great course! A little short.