oferecido por

The Hong Kong University of Science and Technology

Informações sobre o curso

4.8

207 ratings

•

74 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...

Comece imediatamente e aprenda em seu próprio cronograma.

Redefinir os prazos de acordo com sua programação.

Aprox. 8 horas restantes

Legendas: English

Comece imediatamente e aprenda em seu próprio cronograma.

Redefinir os prazos de acordo com sua programação.

Aprox. 8 horas restantes

Legendas: English

Seção

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 vídeos (Total de 55 min), 9 leituras, 4 testes

Course Overview6min

The Fibonacci Sequence8min

The Fibonacci Sequence Redux7min

The Golden Ratio8min

Fibonacci Numbers and the Golden Ratio6min

Binet's Formula10min

Mathematical Induction7min

Welcome and Course Information10min

Get to Know Your Classmates10min

Fibonacci Numbers with Negative Indices10min

The Lucas Numbers10min

Neighbour Swapping10min

Some Algebra Practice10min

Linearization of Powers of the Golden Ratio10min

Another Derivation of Binet's formula10min

Binet's Formula for the Lucas Numbers10min

Diagnostic Quiz10min

The Fibonacci Numbers6min

The Golden Ratio6min

Week 120min

Seção

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 vídeos (Total de 65 min), 10 leituras, 3 testes

Cassini's Identity8min

The Fibonacci Bamboozlement6min

Sum of Fibonacci Numbers8min

Sum of Fibonacci Numbers Squared7min

The Golden Rectangle5min

Spiraling Squares3min

Matrix Algebra: Addition and Multiplication5min

Matrix Algebra: Determinants7min

Do You Know Matrices?10min

The Fibonacci Addition Formula10min

The Fibonacci Double Index Formula10min

Do You Know Determinants?10min

Proof of Cassini's Identity10min

Catalan's Identity10min

Sum of Lucas Numbers10min

Sums of Even and Odd Fibonacci Numbers10min

Sum of Lucas Numbers Squared10min

Area of the Spiraling Squares10min

The Fibonacci Bamboozlement6min

Fibonacci Sums6min

Week 220min

Seção

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 vídeos (Total de 61 min), 8 leituras, 3 testes

An Inner Golden Rectangle5min

The Fibonacci Spiral6min

Fibonacci Numbers in Nature4min

Continued Fractions15min

The Golden Angle7min

A Simple Model for the Growth of a Sunflower8min

Concluding remarks4min

The Eye of God10min

Area of the Inner Golden Rectangle10min

Continued Fractions for Square Roots10min

Continued Fraction for e10min

The Golden Ratio and the Ratio of Fibonacci Numbers10min

The Golden Angle and the Ratio of Fibonacci Numbers10min

Please Rate this Course10min

Acknowledgments10min

Spirals6min

Fibonacci Numbers in Nature6min

Week 320min

4.8

por GM•Mar 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

por BS•Aug 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.

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....

When will I have access to the lectures and assignments?

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.

What will I get if I purchase the Certificate?

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.

What is the refund policy?

Is financial aid available?

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