Об этом курсе
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
Globe

Только онлайн-курс

Начните сейчас и учитесь по собственному графику.
Beginner Level

Начальный уровень

Clock

Прибл. 8 ч. на завершение

Предполагаемая нагрузка: 5 hours/week
Comment Dots

English

Субтитры: English
Globe

Только онлайн-курс

Начните сейчас и учитесь по собственному графику.
Beginner Level

Начальный уровень

Clock

Прибл. 8 ч. на завершение

Предполагаемая нагрузка: 5 hours/week
Comment Dots

English

Субтитры: English

Syllabus - What you will learn from this course

1

Section
Clock
3 hours to complete

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 videos (Total 55 min), 9 readings, 4 quizzes
Video7 videos
The Fibonacci Sequence8m
The Fibonacci Sequence Redux7m
The Golden Ratio8m
Fibonacci Numbers and the Golden Ratio6m
Binet's Formula10m
Mathematical Induction7m
Reading9 readings
Welcome and Course Information10m
Get to Know Your Classmates10m
Fibonacci Numbers with Negative Indices10m
The Lucas Numbers10m
Neighbour Swapping10m
Some Algebra Practice10m
Linearization of Powers of the Golden Ratio10m
Another Derivation of Binet's formula10m
Binet's Formula for the Lucas Numbers10m
Quiz4 practice exercises
Diagnostic Quiz10m
The Fibonacci Numbers6m
The Golden Ratio6m
Week 120m

2

Section
Clock
3 hours to complete

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 videos (Total 65 min), 10 readings, 3 quizzes
Video9 videos
Cassini's Identity8m
The Fibonacci Bamboozlement6m
Sum of Fibonacci Numbers8m
Sum of Fibonacci Numbers Squared7m
The Golden Rectangle5m
Spiraling Squares3m
Matrix Algebra: Addition and Multiplication5m
Matrix Algebra: Determinants7m
Reading10 readings
Do You Know Matrices?10m
The Fibonacci Addition Formula10m
The Fibonacci Double Index Formula10m
Do You Know Determinants?10m
Proof of Cassini's Identity10m
Catalan's Identity10m
Sum of Lucas Numbers10m
Sums of Even and Odd Fibonacci Numbers10m
Sum of Lucas Numbers Squared10m
Area of the Spiraling Squares10m
Quiz3 practice exercises
The Fibonacci Bamboozlement6m
Fibonacci Sums6m
Week 220m

3

Section
Clock
3 hours to complete

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 videos (Total 61 min), 8 readings, 3 quizzes
Video8 videos
An Inner Golden Rectangle5m
The Fibonacci Spiral6m
Fibonacci Numbers in Nature4m
Continued Fractions15m
The Golden Angle7m
A Simple Model for the Growth of a Sunflower8m
Concluding remarks4m
Reading8 readings
The Eye of God10m
Area of the Inner Golden Rectangle10m
Continued Fractions for Square Roots10m
Continued Fraction for e10m
The Golden Ratio and the Ratio of Fibonacci Numbers10m
The Golden Angle and the Ratio of Fibonacci Numbers10m
Please Rate this Course10m
Acknowledgments10m
Quiz3 practice exercises
Spirals6m
Fibonacci Numbers in Nature6m
Week 320m
4.8

Top Reviews

By 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

By 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.

Instructor

About 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....

Frequently Asked Questions

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