Get started with custom lists to organize and share courses.

Sign up

Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

# Fibonacci Numbers and the Golden Ratio

28 Reviews 6531 students interested
• Provider Coursera
• Subject Mathematics
• Cost Free Online Course (Audit)
• Session In progress
• Language English
• Certificate Paid Certificate Available
• Start Date
• Duration 3 weeks long
• Learn more about MOOCs

Taken this course? Share your experience with other students. Write review

## Overview

Sign up to Coursera courses for free Learn how

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

## Syllabus

Fibonacci: It's as easy as 1, 1, 2, 3
By the end of this week, you will be able to: 1) describe the origin of the Fibonacci sequence; 2) describe the origin of the golden ratio; 3) find the relationship between the Fibonacci sequence and the golden ratio; 4) derive Binet’s formula.

Identities, sums and rectangles
By the end of this week, you will be able to: 1) identify the Fibonacci Q-matrix and derive Cassini’s identity; 2) explain the Fibonacci bamboozlement; 3) derive and prove the sum of the first n Fibonacci numbers, and the sum of the squares of the first n Fibonacci numbers; 4) construct a golden rectangle and 5) draw a figure with spiralling squares.

The most irrational number
By the end of this week, you will be able to: 1) describe the golden spiral and its relationship to the spiralling squares; 2) construct an inner golden rectangle; 3) explain continued fractions and be able to compute them; 4) explain why the golden ratio is called the most irrational of the irrational numbers; 5) understand why the golden ratio and the Fibonacci numbers may show up unexpectedly in nature.

#### Taught by

Jeffrey R. Chasnov

## Help Center

Most commonly asked questions about Coursera Coursera

## Reviews for Coursera's Fibonacci Numbers and the Golden Ratio 4.9 Based on 28 reviews

• 5 stars 93%
• 4 stars 7%
• 3 star 0%
• 2 star 0%
• 1 star 0%

Did you take this course? Share your experience with other students.

• 1
Evelina C
5.0 a year ago
completed this course.

I really enjoyed this short course and I recommend it if you are interested in the Fibonacci numbers and its link with the golden ratio. The exercises are well done and the lessons short but clear. There are several interesting things exiting in mathematical and in nature. I really enjoyed.
Was this review helpful to you?
Anonymous
5.0 2 years ago
completed this course.
I really liked this short course and recommend it if you are interested in the Fibonacci numbers and related things. The proof questions in the discussion prompts can sometimes be quite challenging but they are very satisfying to prove and worthwhile to attempt.
Was this review helpful to you?
Anonymous
5.0 2 years ago
is taking this course right now.
I took the course for personal enrichment and to fuel my (clueless, crazy and way too unreachable, for the most who claim to know me best) willing to learn more Maths and sciences! I started attending another MOOC about Mathematical thinking
Was this review helpful to you?
Fernando M
5.0 8 months ago
completed this course, spending 3 hours a week on it and found the course difficulty to be medium.
Excellent course. An extremelly rare opportunity for someone interested in the beauty of Mathematics. The course can be taken by anyone with elementary high school algebra skills.
Was this review helpful to you?
Anonymous
5.0 9 months ago
completed this course.
Really good course for beginners, especially interested in sunflowers ) Hope to read more about this in detail.

Thanks a lot Dr Chasnov and Hong Kong University )
Was this review helpful to you?
Anonymous
5.0 8 months ago
completed this course.
Excellent course. I enjoyed every second of it - finished all the course in less than 2 days. The prof. is great - his explanations are very clear. The course is built very systematically. Lot's of exercises which help understanding the material. I learnt new interesting facts about Fibonacci numbers and more and some interesting stuff about the related mathematicians.

In short, great course - highly recommended!
Was this review helpful to you?
Anonymous
5.0 a year ago
completed this course.
This was a short, but well-done course about Fibonacci numbers and the golden ratio that greatly enhanced my understanding of the topic. A big thanks to the professor and team for creating the course material. The course length, 3 weeks, makes for a good "filler" course in between other courses or obligations. More people should discover this one!
Was this review helpful to you?
Duc T
5.0 5 months ago
by completed this course, spending 3 hours a week on it and found the course difficulty to be medium.
It is a great course where you can learn many cool things about Fibonacci numbers and the golden ratio. Fibonacci numbers are not just 1+1=2, 1+2=3, 2+3=5, etc. they have many other cool characteristics. This course also shows amazing connection between Fibonacci numbers and the golden ratio (1+sqrt(5))/2.
Was this review helpful to you?
Chi D
5.0 a year ago
by is taking this course right now, spending 2 hours a week on it and found the course difficulty to be medium.
I think this is the fundamental course for Fibonacci sequence and golden ratio. After going through this course, there are lots of interesting things exiting in mathematical findings and in nature. So cool! This course would be a trigger to keep digging this field.
Was this review helpful to you?
Andreas Z
5.0 2 months ago
completed this course, spending 7 hours a week on it and found the course difficulty to be medium.
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.
Was this review helpful to you?
Anonymous
5.0 3 months ago
completed this course.
I have been interested in sacred geometry be years this course furthered my understanding of the symbols that are seen by everyone. I wish that the course was a specialization to go further into this field of math, and geometry.
Was this review helpful to you?
Mahendra S
5.0 a year ago
by completed this course, spending 2 hours a week on it and found the course difficulty to be medium.
A very well planned and interactive course prepared by the lecturer, surely it helped to gain basic cum intermediate level of knowledge of Fibonacci numbers, Lucas numbers and the golden ratio.

regards.

:)
Was this review helpful to you?
Anonymous
5.0 a year ago
completed this course.
A must for anyone who loves mathematics. Rigorous derivations, and very rewarding results... because you keep working on the mathematics, and then suddenly you understand how this applies to natural models.
Was this review helpful to you?
Anonymous
5.0 11 months ago
completed this course.
Clearly explained material most of which is accessible to everyone. There is some algebra, but it isn't required, as the interesting properties of the Fibonacci numbers are understandable without it.

Recommended
Was this review helpful to you?
Victoria D
5.0 a year ago
completed this course, spending 3 hours a week on it and found the course difficulty to be medium.
It was amazing. The mathematical fun)

The Fibonacci numbers is a very important instrument for understanding of the universe. And now i can complete my design formula for students. Thank you very much.
Was this review helpful to you?
Vipul T
5.0 12 months ago
is taking this course right now.
Very good introduction to Fibonacci series and explained in a simple manner and clearly . Also all the identities and formulas are properly explained

A must do for all mathematics students
Was this review helpful to you?
Tarit G
4.0 a year ago
completed this course, spending 2 hours a week on it and found the course difficulty to be easy.
It was a good introduction to Fibonacci sequence and it's relation with golden ratio. Welly covered topics and excercises are enjoyable. I have enjoyed this course very much. : )
Was this review helpful to you?
Anonymous
5.0 a year ago
completed this course.
Very informing and interesting. Teaches you step-by-step until it gets you to the interesting examples in nature of the Fibonacci sequence and golden ratio. Highly recommended!
Was this review helpful to you?
Marianne V
5.0 12 months ago
completed this course.
The course was great fun and provided some challenges, while not being too difficult overall. The proofs by induction brought back fond memories of my university days many years ago.
Was this review helpful to you?
Usha K
5.0 3 months ago
completed this course.
Great professor, he expained throughly. Overall it is a excellent course. Week 1 was difficult me to grasp it.

I learned more thing about fibonacci swquence.
Was this review helpful to you?
• 1

## Class Central

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free

### Never Stop Learning!

Get personalized course recommendations, track subjects and courses with reminders, and more.