課程信息
4.7
215 ratings
78 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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100% 在線課程

立即開始,按照自己的計劃學習。
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Beginner Level

初級

Clock

建議:5 hours/week

完成時間大約為8 小時
Comment Dots

English

字幕:English
Globe

100% 在線課程

立即開始,按照自己的計劃學習。
Calendar

可靈活調整截止日期

根據您的日程表重置截止日期。
Beginner Level

初級

Clock

建議:5 hours/week

完成時間大約為8 小時
Comment Dots

English

字幕:English

教學大綱 - 您將從這門課程中學到什麼

1

章節
Clock
完成時間為 3 小時

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 個視頻(共 55 分鐘), 9 個閱讀材料, 4 個測驗
Video7 個視頻
The Fibonacci Sequence8分鐘
The Fibonacci Sequence Redux7分鐘
The Golden Ratio8分鐘
Fibonacci Numbers and the Golden Ratio6分鐘
Binet's Formula10分鐘
Mathematical Induction7分鐘
Reading9 個閱讀材料
Welcome and Course Information10分鐘
Get to Know Your Classmates10分鐘
Fibonacci Numbers with Negative Indices10分鐘
The Lucas Numbers10分鐘
Neighbour Swapping10分鐘
Some Algebra Practice10分鐘
Linearization of Powers of the Golden Ratio10分鐘
Another Derivation of Binet's formula10分鐘
Binet's Formula for the Lucas Numbers10分鐘
Quiz4 個練習
Diagnostic Quiz10分鐘
The Fibonacci Numbers6分鐘
The Golden Ratio6分鐘
Week 120分鐘

2

章節
Clock
完成時間為 3 小時

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 個視頻(共 65 分鐘), 10 個閱讀材料, 3 個測驗
Video9 個視頻
Cassini's Identity8分鐘
The Fibonacci Bamboozlement6分鐘
Sum of Fibonacci Numbers8分鐘
Sum of Fibonacci Numbers Squared7分鐘
The Golden Rectangle5分鐘
Spiraling Squares3分鐘
Matrix Algebra: Addition and Multiplication5分鐘
Matrix Algebra: Determinants7分鐘
Reading10 個閱讀材料
Do You Know Matrices?10分鐘
The Fibonacci Addition Formula10分鐘
The Fibonacci Double Index Formula10分鐘
Do You Know Determinants?10分鐘
Proof of Cassini's Identity10分鐘
Catalan's Identity10分鐘
Sum of Lucas Numbers10分鐘
Sums of Even and Odd Fibonacci Numbers10分鐘
Sum of Lucas Numbers Squared10分鐘
Area of the Spiraling Squares10分鐘
Quiz3 個練習
The Fibonacci Bamboozlement6分鐘
Fibonacci Sums6分鐘
Week 220分鐘

3

章節
Clock
完成時間為 3 小時

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 個視頻(共 61 分鐘), 8 個閱讀材料, 3 個測驗
Video8 個視頻
An Inner Golden Rectangle5分鐘
The Fibonacci Spiral6分鐘
Fibonacci Numbers in Nature4分鐘
Continued Fractions15分鐘
The Golden Angle7分鐘
A Simple Model for the Growth of a Sunflower8分鐘
Concluding remarks4分鐘
Reading8 個閱讀材料
The Eye of God10分鐘
Area of the Inner Golden Rectangle10分鐘
Continued Fractions for Square Roots10分鐘
Continued Fraction for e10分鐘
The Golden Ratio and the Ratio of Fibonacci Numbers10分鐘
The Golden Angle and the Ratio of Fibonacci Numbers10分鐘
Please Rate this Course10分鐘
Acknowledgments10分鐘
Quiz3 個練習
Spirals6分鐘
Fibonacci Numbers in Nature6分鐘
Week 320分鐘
4.7

熱門審閱

創建者 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

創建者 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.

講師

Jeffrey R. Chasnov

Professor
Department of Mathematics

關於 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....

常見問題

  • 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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