About this course: 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
Who is this class for: This course is suitable for anyone who loves mathematics, and should be accessible to those that remember their high school algebra.
Created by:Â Â The Hong Kong University of Science and Technology
Taught by:Â Â Jeffrey R. Chasnov, Professor
Department of Mathematics
| Level | Beginner |
| Language | English |
| Hardware Req | Pen, paper and the power of your brain. |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
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.
7 videos, 9 readings, 3 practice quizzes
- Reading: Welcome and Course Information
- Practice Quiz: Diagnostic Quiz
- Reading: Get to Know Your Classmates
- Video: The Fibonacci Sequence
- Reading: Fibonacci Numbers with Negative Indices
- Reading: The Lucas Numbers
- Video: The Fibonacci Sequence Redux
- Reading: Neighbour Swapping
- Practice Quiz: The Fibonacci Numbers
- Video: The Golden Ratio
- Reading: Some Algebra Practice
- Video: Fibonacci Numbers and the Golden Ratio
- Reading: Linearization of Powers of the Golden Ratio
- Video: Binet's Formula
- Reading: Another Derivation of Binet's formula
- Reading: Binet's Formula for the Lucas Numbers
- Practice Quiz: The Golden Ratio
- Video: Mathematical Induction
Graded: Week 1
WEEK 2
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.
9 videos, 10 readings, 2 practice quizzes
- Reading: Do You Know Matrices?
- Reading: The Fibonacci Addition Formula
- Reading: The Fibonacci Double Index Formula
- Reading: Do You Know Determinants?
- Video: Cassini's Identity
- Reading: Proof of Cassini's Identity
- Reading: Catalan's Identity
- Video: The Fibonacci Bamboozlement
- Practice Quiz: The Fibonacci Bamboozlement
- Video: Sum of Fibonacci Numbers
- Reading: Sum of Lucas Numbers
- Reading: Sums of Even and Odd Fibonacci Numbers
- Video: Sum of Fibonacci Numbers Squared
- Reading: Sum of Lucas Numbers Squared
- Practice Quiz: Fibonacci Sums
- Video: The Golden Rectangle
- Video: Spiraling Squares
- Reading: Area of the Spiraling Squares
- Video: Matrix Algebra: Addition and Multiplication
- Video: Matrix Algebra: Determinants
Graded: Week 2
WEEK 3
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.
8 videos, 8 readings, 2 practice quizzes
- Reading: The Eye of God
- Video: An Inner Golden Rectangle
- Reading: Area of the Inner Golden Rectangle
- Video: The Fibonacci Spiral
- Practice Quiz: Spirals
- Video: Fibonacci Numbers in Nature
- Video: Continued Fractions
- Reading: Continued Fractions for Square Roots
- Reading: Continued Fraction for e
- Reading: The Golden Ratio and the Ratio of Fibonacci Numbers
- Video: The Golden Angle
- Reading: The Golden Angle and the Ratio of Fibonacci Numbers
- Video: A Simple Model for the Growth of a Sunflower
- Practice Quiz: Fibonacci Numbers in Nature
- Video: Concluding remarks
- Reading: Please Rate this Course
- Reading: Acknowledgments
Graded: Week 3
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Ratings and Reviews
The course is a fun one and do make me reflect on my on academic major.
Awesome course, easy to follow along and for those who are inquisitive in nature.
Light, relatively easy and entertaining. Well done Prof. Chasnov
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LO
The most fun I had in a long time! Thank you very much. Very interesting.