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.
Taught by: 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 |
- 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
- 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
- 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
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Very interesting and well presented mathematics course. Amazing how many applications and relationships the Fibonacci Sequence has. Some of the formulas could have been explained in a little more detail as they were incredibly difficult to get my head around (I am an A-Level student).
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.
It was very useful to enhance my knowledge of Golden ration. A very good delivery by Professor Jasnov.
BC
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.