Fibonacci Numbers and the Golden Ratio

The Hong Kong University of Science and Technology

课程信息

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

100% 在线课程

立即开始，按照自己的计划学习。

初级

完成时间大约为8 小时

建议：5 hours/week

English

字幕：English

100% 在线课程

立即开始，按照自己的计划学习。

初级

完成时间大约为8 小时

建议：5 hours/week

English

字幕：English

Syllabus - What you will learn from this course

1

Section

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. ...

7 videos (Total 55 min), 9 readings, 4 quizzes

7 videos

Course Overview6m

The Fibonacci Sequence8m

The Fibonacci Sequence Redux7m

The Golden Ratio8m

Fibonacci Numbers and the Golden Ratio6m

Binet's Formula10m

Mathematical Induction7m

9 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

4 practice exercises

Diagnostic Quiz10m

The Fibonacci Numbers6m

The Golden Ratio6m

Week 120m

2

Section

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. ...

9 videos (Total 65 min), 10 readings, 3 quizzes

9 videos

The Fibonacci Q-matrix11m

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

10 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

3 practice exercises

The Fibonacci Bamboozlement6m

Fibonacci Sums6m

Week 220m

3

Section

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. ...

8 videos (Total 61 min), 8 readings, 3 quizzes

8 videos

The Golden Spiral8m

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

8 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

3 practice exercises

Spirals6m

Fibonacci Numbers in Nature6m

Week 320m

Instructor

Jeffrey R. Chasnov

Professor

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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What will I get if I pay for this course?
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Fibonacci Numbers and the Golden Ratio