# Coursera: Fibonacci Numbers and the Golden Ratio

with  Jeffrey R. Chasnov
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.

http://bookboon.com/en/fibonacci-numbers-and-the-golden-ratio-ebook

Course Overview video: https://youtu.be/GRthNC0_mrU

## Syllabus

Dip your toes in the water
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, including derive Binet’s formula. Download the lecture notes, problems, and the professor's suggested solutions from http://bookboon.com/en/fibonacci-numbers-and-the-golden-ratio-ebook

Dive deeper
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 spiraling squares. Download the lecture notes, problems, and the professor's suggested solutions from http://bookboon.com/en/fibonacci-numbers-and-the-golden-ratio-ebook

Swim with the big fish
By the end of this week, you will be able to: 1) describe the golden spiral and its relationship to the spiraling squares; 2) construct an inner golden rectangle; 3) explain the continued fraction 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. Download the lecture notes, problems, and the professor's suggested solutions from http://bookboon.com/en/fibonacci-numbers-and-the-golden-ratio-ebook

2 Student
reviews
Cost Free Online Course (Audit)
Pace Upcoming
Subject Mathematics
Provider Coursera
Language English
Certificates Paid Certificate Available
Calendar 3 weeks long

Disclosure: To support our site, Class Central may be compensated by some course providers.

##### FAQ View All
What are MOOCs?
MOOCs stand for Massive Open Online Courses. These are free online courses from universities around the world (eg. Stanford Harvard MIT) offered to anyone with an internet connection.
How do I register?
To register for a course, click on "Go to Class" button on the course page. This will take you to the providers website where you can register for the course.
How do these MOOCs or free online courses work?
MOOCs are designed for an online audience, teaching primarily through short (5-20 min.) pre recorded video lectures, that you watch on weekly schedule when convenient for you.  They also have student discussion forums, homework/assignments, and online quizzes or exams.

## 2 reviews for Coursera's Fibonacci Numbers and the Golden Ratio

12 months 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.