À propos de ce cours : 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
Les destinataires de ce cours : This course is suitable for anyone who loves mathematics, and should be accessible to those that remember their high school algebra.
Créé par : The Hong Kong University of Science and Technology
Enseigné par : Jeffrey R. Chasnov, Professor
Department of Mathematics
| Niveau | Débutant |
| Langue | English |
| Matériel requis | Pen, paper and the power of your brain. |
| Comment réussir | Réussissez tous les devoirs notés pour terminer le cours. |
| Notes des utilisateurs |
Programme de cours
SEMAINE 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 vidéos, 9 lectures, 3 quiz pour s'exercer
- Reading: Welcome and Course Information
- Practice Quiz: Diagnostic Quiz
- Reading: Get to Know Your Classmates
- Vidéo: The Fibonacci Sequence
- Reading: Fibonacci Numbers with Negative Indices
- Reading: The Lucas Numbers
- Vidéo: The Fibonacci Sequence Redux
- Reading: Neighbour Swapping
- Practice Quiz: The Fibonacci Numbers
- Vidéo: The Golden Ratio
- Reading: Some Algebra Practice
- Vidéo: Fibonacci Numbers and the Golden Ratio
- Reading: Linearization of Powers of the Golden Ratio
- Vidéo: Binet's Formula
- Reading: Another Derivation of Binet's formula
- Reading: Binet's Formula for the Lucas Numbers
- Practice Quiz: The Golden Ratio
- Vidéo: Mathematical Induction
Noté: Week 1
SEMAINE 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 vidéos, 10 lectures, 2 quiz pour s'exercer
- Reading: Do You Know Matrices?
- Reading: The Fibonacci Addition Formula
- Reading: The Fibonacci Double Index Formula
- Reading: Do You Know Determinants?
- Vidéo: Cassini's Identity
- Reading: Proof of Cassini's Identity
- Reading: Catalan's Identity
- Vidéo: The Fibonacci Bamboozlement
- Practice Quiz: The Fibonacci Bamboozlement
- Vidéo: Sum of Fibonacci Numbers
- Reading: Sum of Lucas Numbers
- Reading: Sums of Even and Odd Fibonacci Numbers
- Vidéo: Sum of Fibonacci Numbers Squared
- Reading: Sum of Lucas Numbers Squared
- Practice Quiz: Fibonacci Sums
- Vidéo: The Golden Rectangle
- Vidéo: Spiraling Squares
- Reading: Area of the Spiraling Squares
- Vidéo: Matrix Algebra: Addition and Multiplication
- Vidéo: Matrix Algebra: Determinants
Noté: Week 2
SEMAINE 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 vidéos, 8 lectures, 2 quiz pour s'exercer
- Reading: The Eye of God
- Vidéo: An Inner Golden Rectangle
- Reading: Area of the Inner Golden Rectangle
- Vidéo: The Fibonacci Spiral
- Practice Quiz: Spirals
- Vidéo: Fibonacci Numbers in Nature
- Vidéo: Continued Fractions
- Reading: Continued Fractions for Square Roots
- Reading: Continued Fraction for e
- Reading: The Golden Ratio and the Ratio of Fibonacci Numbers
- Vidéo: The Golden Angle
- Reading: The Golden Angle and the Ratio of Fibonacci Numbers
- Vidéo: A Simple Model for the Growth of a Sunflower
- Practice Quiz: Fibonacci Numbers in Nature
- Vidéo: Concluding remarks
- Reading: Please Rate this Course
- Reading: Acknowledgments
Noté: Week 3
FAQ
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Créateurs
The Hong Kong University of Science and Technology
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Notation et examens
Very clear exposition, interesting and fun. Accessible to anyone interested in maths and patterns.
Good explanation, Good example
This course blends the rational thinking of mathematics and the aesthetics of art in nature. Enjoyed it. Thanks Coursera and Hong Kong University of Science and Technology
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C
It was very useful to enhance my knowledge of Golden ration. A very good delivery by Professor Jasnov.