Voltar para Fibonacci Numbers and the Golden Ratio

4.7

284 classificações

•

99 avaliações

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...

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

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por Rahul C

•May 11, 2018

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

por 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.

por Matthew F

•Aug 04, 2017

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

por Alexander A S G

•Dec 04, 2017

superb

por Serhat G

•Apr 01, 2018

Excellent.

por Iulian N

•Nov 27, 2016

Very interesting course

por 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!

por 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.

por Rishabh J

•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.

por Bill C

•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.

por Vishal G

•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.

por 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.

por Christophe S

•Apr 29, 2019

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

por 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 :))

por 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.

por 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.

por 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.

por 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!

por L. M l

•Aug 25, 2019

Students friendly

por Muhammad A S

•Sep 14, 2019

I am very glad to learn about Fibonacci number.

por Vidhya K

•Sep 08, 2019

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

por Tarit G

•Feb 12, 2019

Awesome

por AM

•Sep 03, 2017

Give practical examples from history and nature!

por Sravan G

•Dec 08, 2016

great learned a lot .

por narendra p

•Dec 13, 2017

good course