À propos de ce cours
4.7
213 ratings
77 reviews
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...
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Beginner Level

Niveau débutant

Clock

Recommandé : 5 hours/week

Approx. 8 heures pour terminer
Comment Dots

English

Sous-titres : English
Globe

Cours en ligne à 100 %

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Calendar

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.
Beginner Level

Niveau débutant

Clock

Recommandé : 5 hours/week

Approx. 8 heures pour terminer
Comment Dots

English

Sous-titres : English

Programme du cours : ce que vous apprendrez dans ce cours

1

Section
Clock
3 heures pour terminer

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. ...
Reading
7 vidéos (Total 55 min), 9 lectures, 4 quiz
Video7 vidéos
The Fibonacci Sequence8 min
The Fibonacci Sequence Redux7 min
The Golden Ratio8 min
Fibonacci Numbers and the Golden Ratio6 min
Binet's Formula10 min
Mathematical Induction7 min
Reading9 lectures
Welcome and Course Information10 min
Get to Know Your Classmates10 min
Fibonacci Numbers with Negative Indices10 min
The Lucas Numbers10 min
Neighbour Swapping10 min
Some Algebra Practice10 min
Linearization of Powers of the Golden Ratio10 min
Another Derivation of Binet's formula10 min
Binet's Formula for the Lucas Numbers10 min
Quiz4 exercices pour s'entraîner
Diagnostic Quiz10 min
The Fibonacci Numbers6 min
The Golden Ratio6 min
Week 120 min

2

Section
Clock
3 heures pour terminer

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. ...
Reading
9 vidéos (Total 65 min), 10 lectures, 3 quiz
Video9 vidéos
Cassini's Identity8 min
The Fibonacci Bamboozlement6 min
Sum of Fibonacci Numbers8 min
Sum of Fibonacci Numbers Squared7 min
The Golden Rectangle5 min
Spiraling Squares3 min
Matrix Algebra: Addition and Multiplication5 min
Matrix Algebra: Determinants7 min
Reading10 lectures
Do You Know Matrices?10 min
The Fibonacci Addition Formula10 min
The Fibonacci Double Index Formula10 min
Do You Know Determinants?10 min
Proof of Cassini's Identity10 min
Catalan's Identity10 min
Sum of Lucas Numbers10 min
Sums of Even and Odd Fibonacci Numbers10 min
Sum of Lucas Numbers Squared10 min
Area of the Spiraling Squares10 min
Quiz3 exercices pour s'entraîner
The Fibonacci Bamboozlement6 min
Fibonacci Sums6 min
Week 220 min

3

Section
Clock
3 heures pour terminer

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. ...
Reading
8 vidéos (Total 61 min), 8 lectures, 3 quiz
Video8 vidéos
An Inner Golden Rectangle5 min
The Fibonacci Spiral6 min
Fibonacci Numbers in Nature4 min
Continued Fractions15 min
The Golden Angle7 min
A Simple Model for the Growth of a Sunflower8 min
Concluding remarks4 min
Reading8 lectures
The Eye of God10 min
Area of the Inner Golden Rectangle10 min
Continued Fractions for Square Roots10 min
Continued Fraction for e10 min
The Golden Ratio and the Ratio of Fibonacci Numbers10 min
The Golden Angle and the Ratio of Fibonacci Numbers10 min
Please Rate this Course10 min
Acknowledgments10 min
Quiz3 exercices pour s'entraîner
Spirals6 min
Fibonacci Numbers in Nature6 min
Week 320 min
4.7

Meilleurs avis

par GMMar 16th 2017

Finally I studied the Fibonacci sequence and the golden spiral. I used to say: one day I will.\n\nVery interesting course and made simple by the teacher in spite of the challenging topics

par BSAug 30th 2017

Very well designed. It was a lot of fun taking this course. It's the kind of course that can get you excited about higher mathematics. Sincere thanks to Prof. Chasnov and HKUST.

Enseignant

Jeffrey R. Chasnov

Professor
Department of Mathematics

À propos de The Hong Kong University of Science and Technology

HKUST - A dynamic, international research university, in relentless pursuit of excellence, leading the advance of science and technology, and educating the new generation of front-runners for Asia and the world....

Foire Aux Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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