Coursera: Fibonacci Numbers and the Golden Ratio

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:


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.

2 Student
Cost Free Online Course (Audit)
Pace Upcoming
Subject Mathematics
Provider Coursera
Language English
Certificates Paid Certificate Available
Calendar 3 weeks long
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Reviews for Coursera's Fibonacci Numbers and the Golden Ratio
5.0 Based on 2 reviews

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5.0 a year ago
Anonymous 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.
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5.0 8 months ago
Anonymous 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
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